K. Matchev

In this paper we compute one-loop corrections to masses and couplings in the minimal supersymmetric standard model. We present explicit formulae for the complete corrections and a set of compact approximations which hold over the unified parameter space associated with radiative electroweak symmetry breaking. We illustrate the importance of the corrections and the accuracy of our approximations by scanning over the parameter space. We calculate the supersymmetric one-loop corrections to the W-boson mass, the effective weak mixing angle, and the quark and lepton masses, and discuss implications for gauge and Yukawa coupling unification. We also compute the one-loop corrections to the entire superpartner and Higgs-boson mass spectrum. We find significant corrections over much of the parameter space, and illustrate that our approximations are good to O(1%) for many of the superparticle masses.

The "Snowmass Points and Slopes" (SPS) are a set of benchmark points and parameter lines in the MSSM parameter space corresponding to different scenarios in the search for Supersymmetry at present and future experiments. This set of benchmarks was agreed upon at the 2001 "Snowmass Workshop on the Future of Particle Physics" as a consensus based on different existing proposals.

We propose that cold dark matter is made of Kaluza-Klein particles and explore avenues for its detection. The lightest Kaluza-Klein state is an excellent dark matter candidate if standard model particles propagate in extra dimensions and Kaluza-Klein parity is conserved. We consider Kaluza-Klein gauge bosons. In sharp contrast to the case of supersymmetric dark matter, these annihilate to hard positrons, neutrinos, and photons with unsuppressed rates. Direct detection signals are also promising. These conclusions are generic to bosonic dark matter candidates.

For a top quark mass fixed to its measured value, we find natural regions of minimal supergravity parameter space where all squarks, sleptons, and heavy Higgs scalars have masses far above 1 TeV and are possibly beyond the reach of the Large Hadron Collider at CERN. This result is simply understood in terms of ``focus point'' renormalization group behavior and holds in any supergravity theory with a universal scalar mass that is large relative to other supersymmetry breaking parameters. We highlight the importance of the choice of fundamental parameters for this conclusion and for naturalness discussions in general.

We analyze focus points in supersymmetric theories, where a parameter's renormalization group trajectories meet for a family of ultraviolet boundary conditions. We show that in a class of models including minimal supergravity, the up-type Higgs mass parameter has a focus point at the weak scale, where its value is highly insensitive to the universal scalar mass. As a result, scalar masses as large as 2 to 3 TeV are consistent with naturalness, and all squarks, sleptons and heavy Higgs scalars may be beyond the discovery reaches of the CERN Large Hadron Collider and proposed linear colliders. Gaugino and Higgsino masses are, however, still constrained to be near the weak scale. The focus point behavior is remarkably robust, holding for both moderate and large $\mathrm{tan}\ensuremath{\beta},$ any weak scale gaugino masses and A parameters, variations in the top quark mass within experimental bounds, and for large variations in the boundary condition scale.

Extra-dimensional theories contain a number of almost degenerate states at each Kaluza-Klein level. If extra dimensional momentum is at least approximately conserved then the phenomenology of such nearly degenerate states depends crucially on the mass splittings between KK modes. We calculate the complete one-loop radiative corrections to KK masses in general 5 and 6 dimensional theories. We apply our formulae to the example of universal extra dimensions and show that the radiative corrections are essential to any meaningful study of the phenomenology. Our calculations demonstrate that Feynman diagrams with loops wrapping the extra dimensions are well-defined and cut-off independent even though higher dimensional theories are not renormalizable.

In recent work, it has been argued that multi-TeV masses for scalar superpartners are not unnatural. Indeed, they appear to have significant phenomenological virtues. Here we explore the implications of such `focus point' supersymmetry for the dark matter problem. We find that constraints on relic densities do not place upper bounds on neutralino or scalar masses. We demonstrate that, in the specific context of minimal supergravity, a cosmologically stable mixed gaugino-Higgsino state emerges as an excellent, robust dark matter candidate. We estimate that, over a wide range of the unknown parameters, the spin-independent proton-neutralino cross sections fall in the range accessible to planned search experiments.

We define a minimal model with universal extra dimensions, and begin to study its phenomenology. The collider signals of the first Kaluza-Klein (KK) level are surprisingly similar to those of a supersymmetric model with a nearly degenerate superpartner spectrum. The lightest KK particle (LKP) is neutral and stable because of KK parity. KK excitations cascade decay to the LKP yielding missing energy signatures with relatively soft jets and leptons. Level 2 KK modes may also be probed via their KK number violating decays to standard model particles. In either case we provide initial estimates for the discovery potential of the Fermilab Tevatron and the CERN Large Hadron Collider.

High-precision analyses of supersymmetry parameters aim at reconstructing the fundamental supersymmetric theory and its breaking mechanism. A well defined theoretical framework is needed when higher-order corrections are included. We propose such a scheme, Supersymmetry Parameter Analysis SPA, based on a consistent set of conventions and input parameters. A repository for computer programs is provided which connect parameters in different schemes and relate the Lagrangian parameters to physical observables at LHC and high energy e + e - linear collider experiments, i.e., masses, mixings, decay widths and production cross sections for supersymmetric particles. In addition, programs for calculating high-precision low energy observables, the density of cold dark matter (CDM) in the universe as well as the cross sections for CDM search experiments are included. The SPA scheme still requires extended efforts on both the theoretical and experimental side before data can be evaluated in the future at the level of the desired precision. We take here an initial step of testing the SPA scheme by applying the techniques involved to a specific supersymmetry reference point.

Dark matter candidates arising in models of particle physics incorporating weak scale supersymmetry may produce detectable signals through their annihilation into neutrinos, photons, or positrons. A large number of relevant experiments are planned or underway. The ``logically possible'' parameter space is unwieldy. By working in the framework of minimal supergravity, we can survey the implications of the experiments for each other, as well as for direct searches, collider searches, low-energy experiments, and naturalness in a transparent fashion. We find that a wide variety of experiments provide interesting probes. Particularly promising signals arise in the mixed gaugino-Higgsino region. This region is favored by low-energy particle physics constraints and arises naturally from minimal supergravity due to the focus point mechanism. Indirect dark matter searches and traditional particle searches are highly complementary. In cosmologically preferred models, if there are charged superpartners with masses below 250 GeV, then some signature of supersymmetry must appear before the CERN LHC begins operation.

We contrast the experimental signatures of low-energy supersymmetry and the model of Universal Extra Dimensions and discuss various methods for their discrimination at hadron colliders. We study the discovery reach of the Tevatron and the LHC for level 2 Kaluza-Klein modes, which would indicate the presence of extra dimensions. We find that with $100\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data the LHC will be able to discover the ${\ensuremath{\gamma}}_{2}$ and ${Z}_{2}$ KK modes as separate resonances if their masses are below 2 TeV. We also investigate the possibility to differentiate the spins of the superpartners and KK modes by means of the asymmetry method of Barr.

We revisit the calculation of the relic density of the lightest Kaluza-Klein particle (LKP) in the model of Universal Extra Dimensions. The Kaluza-Klein (KK) particle spectrum at level one is rather degenerate, and various coannihilation processes may be relevant. We extend the calculation of hep-ph/0206071 to include coannihilation processes with all level one KK particles. In our computation we consider a most general KK particle spectrum, without any simplifying assumptions. In particular, we do not assume a completely degenerate KK spectrum and instead retain the dependence on each individual KK mass. As an application of our results, we calculate the Kaluza-Klein relic density in the Minimal UED model, turning on coannihilations with all level one KK particles. We then go beyond the minimal model and discuss the size of the coannihilation effects separately for each class of level 1 KK particles. Our results provide the basis for consistent relic density computations in arbitrarily general models with Universal Extra Dimenions.

We propose to use the MT2 concept to measure the masses of all particles in SUSY-like events with two unobservable, identical particles. To this end we generalize the usual notion of MT2 and define a new MT2(n,p,c) variable, which can be applied to various subsystem topologies, as well as the full event topology. We derive analytic formulas for its endpoint MT2,max(n,p,c) as a function of the unknown test mass c of the final particle in the subchain and the transverse momentum pT due to radiation from the initial state. We show that the endpoint functions MT2,max(n,p,c)(c,pT) may exhibit three different types of kinks and discuss the origin of each type. We prove that the subsystem MT2(n,p,c) variables by themselves already yield a sufficient number of measurements for a complete determination of the mass spectrum (including the overall mass scale). As an illustration, we consider the simple case of a decay chain with up to three heavy particles, X2 → X1 → X0, which is rather problematic for all other mass measurement methods. We propose three different MT2-based methods, each of which allows a complete determination of the masses of particles X0, X1 and X2. The first method only uses MT2(n,p,c) endpoint measurements at a single fixed value of the test mass c. In the second method the unknown mass spectrum is fitted to one or more endpoint functions MT2,max(n,p,c)(c,pT) exhibiting a kink. The third method is hybrid, combining MT2 endpoints with measurements of kinematic edges in invariant mass distributions. As a practical application of our methods, we show that the dilepton W+W− and t samples at the Tevatron can be used for an independent determination of the masses of the top quark, the W boson and the neutrino, without any prior assumptions.

The recently reported measurement of the muon's anomalous magnetic moment differs from the standard model prediction by 2.6 sigma. We examine the implications of this discrepancy for supersymmetry. Deviations of the reported magnitude are generic in supersymmetric theories. Based on the new result, we derive model-independent upper bounds on the masses of observable supersymmetric particles. We also examine several model frameworks. The sign of the reported deviation is as predicted in many simple models, but disfavors anomaly-mediated supersymmetry breaking.

Assuming that cosmological dark matter consists of weakly interacting massive particles, we use the recent precise measurement of cosmological parameters to predict the guaranteed rates of production of such particles in association with photons at electron-positron colliders. Our approach is based on general physical principles such as detailed balancing and soft/collinear factorization. It leads to predictions that are valid across a broad range of models containing WIMPs, including supersymmetry, universal extra dimensions, and many others. We also discuss the discovery prospects for the predicted experimental signatures.

We analyze the Higgs sector in the Next-to-Minimal Supersymmetric Standard Model, emphasizing the possibility of a light CP-odd scalar (axion) in the spectrum. We compute the coupling of the Standard-Model-like Higgs boson to a pair of axions, and show that it can be large enough to modify the Higgs branching fractions, with a significant impact on the Higgs searches. We delineate the range of parameters relevant for this scenario, and also derive analytic expressions for the scalar masses and couplings in two special cases - a decoupling limit where all scalars other than the axion are heavier than the Standard-Model-like Higgs boson, and the large tan beta limit.

In extended Higgs models, the Higgs boson may decay into a pair of light $\mathrm{CP}$-odd scalars, with distinctive collider signatures. We study the ensuing Higgs signals at the upgraded Fermilab Tevatron, considering the subsequent decays of the scalars into pairs of gluons or photons. For $\mathrm{CP}$-odd scalars lighter than a few GeV, the Higgs boson manifests itself as a diphoton resonance and can be discovered up to masses of a few hundred GeV. For heavier $\mathrm{CP}$-odd scalars the reach extends at most up to ${M}_{h}\ensuremath{\sim}120\mathrm{GeV}.$ We also discuss the capabilities of the CERN LHC and lepton colliders in these channels.

We propose a new set of supersymmetric benchmark scenarios, taking into account the constraints from LEP, b to s gamma, g_mu - 2 and cosmology. We work in the context of the constrained MSSM (CMSSM) with universal soft supersymetry-breaking masses and assume that R parity is conserved. We propose benchmark points that exemplify the different generic possibilities, including focus-point models, points where coannihilation effects on the relic density are important, and points with rapid relic annihilation via direct-channel Higgs poles. We discuss the principal decays and signatures of the different classes of benchmark scenarios, and make initial estimates of the physics reaches of different accelerators, including the Tevatron collider, the LHC, and e+ e- colliders in the sub- and multi-TeV ranges. We stress the complementarity of hadron and lepton colliders, with the latter favoured for non-strongly-interacting particles and precision measurements. We mention features that could usefully be included in future versions of supersymmetric event generators.

We construct extensions of the Standard Model in which the gauge symmetries and supersymmetry prevent the dangerously large effects that may potentially be induced in a supersymmetric standard model by Planck scale physics. These include baryon number violation, flavor-changing neutral currents, the μ-term, and masses for singlet or vector-like fields under the Standard Model gauge group. For this purpose we introduce an extra non-anomalous U(1)μ gauge group. Dynamical supersymmetry breaking in a secluded sector triggers the breaking of the U(1)μ and generates soft masses for the superpartners via gauge mediation, with the scalars possibly receiving sizable contributions from the U(1)μ D-term. We find several classes of complete and calculable models, in which the messengers do not present cosmological problems and neutrino masses can also be accommodated. We derive the sparticle spectrum in these models and study the phenomenological consequences. We give an exhaustive list of the potential experimental signatures and discuss their observability in the upcoming Tevatron runs. One class of models exhibits interesting new discovery channels, namely WWT, WγT and WZT, which arise when the next-to-lightest supersymmetric particle is a short-lived SU(2)w neutralino.

We compute the full set of weak-scale gauge and Yukawa threshold corrections in the minimal supersymmetric standard model, including all finite (non-logarithmic) corrections, which we show to be important. We use our results to examine the effects of unification-scale threshold corrections in the minimal and missing-doublet SU(5) models. We work in the context of a unified mass spectrum, with scalar mass M_0 and gaugino mass M_1/2, and find that in minimal SU(5) with squark masses less than one TeV, successful gauge and Yukawa coupling unification requires M_1/2 << M_0 and M_0 \simeq 1 TeV. In contrast, we find that the missing-doublet model permits gauge and Yukawa unification for a wide range of supersymmetric masses.

We compute the leading QCD corrections to K-Kbar mixing in the supersymmetric standard model with general soft supersymmetry-breaking parameters. We construct the \Delta S=2 effective Lagrangian for three hierarchies of supersymmetric particle masses, namely, when the gluino mass is comparable to, much greater than, or much less than the masses of the first two generation squarks. We find that the QCD corrections tighten the limits on squark mass splittings by more than a factor of two.

We consider SUSY-like missing energy events at hadron colliders and critically examine the common assumption that the missing energy is the result of two identical missing particles. In order to experimentally test this hypothesis, we generalize the subsystem MT2 variable to the case of asymmetric event topologies, where the two SUSY decay chains terminate in different "children" particles. In this more general approach, the endpoint MT2max of the MT2 distribution now gives the mass Mp(Mc(a),Mc(b)) of the parent particle as a function of two input children masses Mc(a) and Mc(b). We propose two methods for an independent determination of the individual children masses Mc(a) and Mc(b). First, in the presence of upstream transverse momentum P(UTM) the corresponding function Mp(Mc(a),Mc(b),P(UTM)) is independent of P(UTM) at precisely the right values of the children masses. Second, the previously discussed MT2 "kink" is now generalized to a "ridge" on the 2-dimensional surface Mp(Mc(a),Mc(b)). As we show in several examples, quite often there is a special point along that ridge which marks the true values of the children masses. Our results allow collider experiments to probe a multi-component dark matter sector directly and without any theoretical prejudice.

Recent results from Higgs boson and supersymmetry searches at the Large Hadron Collider provide strong new motivations for supersymmetric theories with heavy superpartners. We reconsider focus point supersymmetry (FP SUSY), in which all squarks and sleptons may have multi-TeV masses without introducing fine-tuning in the weak scale with respect to variations in the fundamental SUSY-breaking parameters. We examine both FP SUSY and its familiar special case, the FP region of minimal supergravity, also known as the constrained minimal supersymmetric standard model (mSUGRA/CMSSM), and show that they are beautifully consistent with all particle, astroparticle, and cosmological data, including Higgs boson mass limits, null results from SUSY searches, electric dipole moments, $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$, ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, the thermal relic density of neutralinos, and dark matter searches. The observed deviation of the muon's anomalous magnetic moment from its standard model value may also be explained in FP SUSY, although not in the FP region of mSUGRA/CMSSM. In light of recent data, we advocate refined searches for FP SUSY and related scenarios with heavy squarks and sleptons, and we present a simplified parameter space within mSUGRA/CMSSM to aid such analyses.

We discuss nonstandard interpretations of the 750 GeV diphoton excess recently reported by the ATLAS and CMS Collaborations which do not involve a new, relatively broad resonance with a mass near 750 GeV. Instead, we consider the sequential cascade decay of a much heavier, possibly quite narrow, resonance into two photons along with one or more additional particles. The resulting diphoton invariant mass signal is generically rather broad, as suggested by the data. We examine three specific event topologies-the "antler," the "sandwich," and the two-step cascade decay-and show that they all can provide a good fit to the observed published data. In each case, we delineate the preferred mass parameter space selected by the best fit. In spite of the presence of extra particles in the final state, the measured diphoton p_{T} spectrum is moderate due to its anticorrelation with the diphoton invariant mass. We comment on the future prospects of discriminating with higher statistics between our scenarios, as well as from more conventional interpretations.

Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To improve the accuracy of MC integration, a number of useful variance reduction algorithms have been developed, including importance sampling and control variates. In this work, we demonstrate how these two methods can be applied simultaneously, thus combining their benefits. We provide a python wrapper, named CoVVVR, which implements our approach in the VEGAS program. The improvements are quantified with several benchmark examples from the literature.

Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To improve the accuracy of MC integration, a number of useful variance reduction algorithms have been developed, including importance sampling and control variates. In this work, we demonstrate how these two methods can be applied simultaneously, thus combining their benefits. We provide a python wrapper, named COVVVR, which implements our approach in the VEGAS program. The improvements are quantified with several benchmark examples from the literature.

Universal extra dimensions and supersymmetry have rather similar experimental signatures at hadron colliders. The proper interpretation of an LHC discovery in either case may therefore require further data from a lepton collider. In this paper we identify methods for discriminating between the two scenarios at the linear collider. We study the processes of Kaluza-Klein muon pair production in universal extra dimensions in parallel to smuon pair production in supersymmetry, accounting for the effects of detector resolution, beam-beam interactions and accelerator induced backgrounds. We find that the angular distributions of the final state muons, the energy spectrum of the radiative return photon and the total cross-section measurement are powerful discriminators between the two models. Accurate determination of the particle masses can be obtained both by a study of the momentum spectrum of the final state leptons and by a scan of the particle pair production thresholds. We also calculate the production rates of various Kaluza-Klein particles and discuss the associated signatures.

We identify and study the signatures of the recently proposed Higgsless models at the CERN Large Hadron Collider (LHC). We concentrate on tests of the mechanism of partial unitarity restoration in the longitudinal vector boson scattering, which is crucial to the phenomenological success of any Higgsless model and does not depend on the model-building details. We investigate the discovery reach for charged massive vector boson resonances and show that all of the preferred parameter space will be probed with 100 fb(-1) of LHC data. Unitarity restoration requires that the masses and couplings of the resonances obey certain sum rules. We discuss the prospects for their experimental verification at the LHC.

We propose a new model-independent technique for mass measurements in missing energy events at hadron colliders. We illustrate our method with the most challenging case of a single-step decay chain. We consider inclusive same-sign chargino pair production in supersymmetry, followed by leptonic decays to sneutrinos ${\ensuremath{\chi}}^{+}{\ensuremath{\chi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{'}+}{\stackrel{\texttildelow{}}{\ensuremath{\nu}}}_{\ensuremath{\ell}}{\stackrel{\texttildelow{}}{\ensuremath{\nu}}}_{{\ensuremath{\ell}}^{\ensuremath{'}}}$ and invisible decays ${\stackrel{\texttildelow{}}{\ensuremath{\nu}}}_{\ensuremath{\ell}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\ell}}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}$. We introduce two one-dimensional decompositions of the Cambridge ${M}_{T2}$ variable: ${M}_{T{2}_{\ensuremath{\parallel}}}$ and ${M}_{T{2}_{\ensuremath{\perp}}}$, on the direction of the upstream transverse momentum ${\stackrel{\ensuremath{\rightarrow}}{P}}_{T}$ and the direction orthogonal to it, respectively. We show that the sneutrino mass ${M}_{c}$ can be measured directly by minimizing the number of events $N({\stackrel{\texttildelow{}}{M}}_{c})$ in which ${M}_{T2}$ exceeds a certain threshold, conveniently measured from the end point ${M}_{T{2}_{\ensuremath{\perp}}}^{\mathrm{max}}({\stackrel{\texttildelow{}}{M}}_{c})$.

We propose a new global and fully inclusive variable 1/2min for determining the mass scale of new particles in events with missing energy at hadron colliders. We define 1/2min as the minimum center-of-mass parton level energy consistent with the measured values of the total calorimeter energy E and the total visible momentum . We prove that for an arbitrary event, 1/2min is simply given by the formula is the total mass of all invisible particles produced in the event. We use t production and several supersymmetry examples to argue that the peak in the 1/2min distribution is correlated with the mass threshold of the parent particles originally produced in the event. This conjecture allows an estimate of the heavy superpartner mass scale (as a function of the LSP mass) in a completely general and model-independent way, and without the need for any exclusive event reconstruction. In our SUSY examples of several multijet plus missing energy signals, the accuracy of the mass measurement based on 1/2min is typically at the percent level, and never worse than 10%. After including the effects of initial state radiation and multiple parton interactions, the precision gets worse, but for heavy SUSY mass spectra remains ∼ 10%.

We present a general solution to the long-standing problem of determining the masses of pair-produced, semi-invisibly decaying particles at hadron colliders. We define two new transverse kinematic variables M(CT)(⊥) and M(CT)(∥), which are suitable one-dimensional projections of the contransverse mass M(CT). We derive analytical formulas for the boundaries of the kinematically allowed regions in the (M(CT)(⊥),M(CT)(∥)) and (M(CT)(⊥),M(CT)) parameter planes and introduce suitable variables D(CT)(∥) and D(CT) to measure the distance to those boundaries on an event per event basis. We show that the masses can be reliably extracted from the end-point measurements of M(CT)(⊥)(max) and D(CT)(min) (or D(CT)(∥)(min)). We illustrate our method with dilepton tt events at the LHC.

This paper seeks to demonstrate that many of the existing mass-measurement variables proposed for hadron colliders (mT, mEff, mT2, missing pT, hT, rootsHatMin, etc.) are far more closely related to each other than is widely appreciated, and indeed can all be viewed as a common mass bound specialized for a variety of purposes. A consequence of this is that one may understand better the strengths and weaknesses of each variable, and the circumstances in which each can be used to best effect. In order to achieve this, we find it necessary first to revisit the seemingly empty and infertile wilderness populated by the subscript "T" (as in pT) in order to remind ourselves what this process of transversification actually means. We note that, far from being simple, transversification can mean quite different things to different people. Those readers who manage to battle through the barrage of transverse notation distinguishing mass-preserving projections from velocity preserving projections, and `early projection' from `late projection', will find their efforts rewarded towards the end of the paper with (i) a better understanding of how collider mass variables fit together, (ii) an appreciation of how these variables could be generalized to search for things more complicated than supersymmetry, (iii) will depart with an aversion to thoughtless or naive use of the so-called `transverse' methods of any of the popular computer Lorentz-vector libraries, and (iv) will take care in their subsequent papers to be explicit about which of the 61 identified variants of the `transverse mass' they are employing.

We extend the study of Higgs boson couplings in the ``golden'' $gg\ensuremath{\rightarrow}H\ensuremath{\rightarrow}Z{Z}^{*}\ensuremath{\rightarrow}4\ensuremath{\ell}$ channel in two important respects. First, we demonstrate the importance of off-shell Higgs boson production ($gg\ensuremath{\rightarrow}{H}^{*}\ensuremath{\rightarrow}ZZ\ensuremath{\rightarrow}4\ensuremath{\ell}$) in determining which operators contribute to the $HZZ$ vertex. Second, we include the five operators of lowest nontrivial dimension, including the ${Z}_{\ensuremath{\mu}}{Z}^{\ensuremath{\mu}}\ensuremath{\square}H$ and $H{Z}_{\ensuremath{\mu}}\ensuremath{\square}{Z}^{\ensuremath{\mu}}$ operators that are often neglected. We point out that the former operator can be severely constrained by the measurement of the off-shell ${H}^{*}\ensuremath{\rightarrow}ZZ$ rate and/or unitarity considerations. We provide analytic expressions for the off-peak cross sections in the presence of these five operators. On shell, the ${Z}_{\ensuremath{\mu}}{Z}^{\ensuremath{\mu}}\ensuremath{\square}H$ operator is indistinguishable from its Standard Model counterpart $H{Z}_{\ensuremath{\mu}}{Z}^{\ensuremath{\mu}}$, while the $H{Z}_{\ensuremath{\mu}}\ensuremath{\square}{Z}^{\ensuremath{\mu}}$ operator can be probed, in particular, by the ${Z}^{*}$ invariant mass distribution.

Recently, Generative Adversarial Networks (GANs) trained on samples of traditionally simulated collider events have been proposed as a way of generating larger simulated datasets at a reduced computational cost. In this paper we point out that data generated by a GAN cannot statistically be better than the data it was trained on, and critically examine the applicability of GANs in various situations, including a) for replacing the entire Monte Carlo pipeline or parts of it, and b) to produce datasets for usage in highly sensitive analyses or sub-optimal ones. We present our arguments using information theoretic demonstrations, a toy example, as well as in the form of a formal statement, and identify some potential valid uses of GANs in collider simulations.

We study in some detail the spectral phenomenology of models in which supersymmetry is dynamically broken and transmitted to the supersymmetric partners of the quarks, leptons and gauge bosons, and the Higgs bosons themselves, via the usual gauge interactions. We elucidate the parameter space of what we consider to be the minimal model, and explore the regions which give rise to consistent radiative electroweak symmetry breaking. We include the weak-scale threshold corrections, and show how they considerably reduce the scale dependence of the results. We examine the sensitivity of our results to unknown higher-order messenger-sector corrections. We compute the superpartner spectrum across the entire parameter space, and compare it to that of the minimal supergravity-inspired model. We delineate the regions where the lightest neutralino or tau slepton is the next-to-lightest supersymmetric particle, and compute the lifetime and branching ratios of the NLSP. In contrast to the minimal supergravity-inspired model, we find that the lightest neutralino can have a large Higgsino component, of order 50%. Nevertheless, the neutralino branching fraction to the gravitino and the light Higgs boson remains small, < 10^{-4}, so the observation of such a decay would point to a non-minimal Higgs sector.

A new set of supersymmetric benchmark scenarios has recently been proposed in the context of the constrained MSSM (CMSSM) with universal soft supersymmetry-breaking masses, taking into account the constraints from LEP, $b \rightarrow s \gamma$ and $g_\mu - 2$ . These points have previously been used to discuss the physics reaches of different accelerators. In this paper, we discuss the prospects for discovering supersymmetric dark matter in these scenarios. We consider direct detection through spin-independent and spin-dependent nuclear scattering, as well as indirect detection through relic annihilations to neutrinos, photons, and positrons. We find that several of the benchmark scenarios offer good prospects for direct detection via spin-independent nuclear scattering and indirect detection via muons produced by neutrinos from relic annihilations inside the Sun, and some models offer good prospects for detecting photons from relic annihilations in the galactic centre.

The left-handed sneutrino in the minimal supersymmetric standard model (MSSM) has been ruled out as a viable thermal dark matter candidate, due to conflicting constraints from direct detection experiments and from the measurement of the dark matter relic density. The intrinsic fine-tuning problem of the MSSM, however, motivates an extension with a new $U(1{)}^{\ensuremath{'}}$ gauge symmetry. We show that in the $U(1{)}^{\ensuremath{'}}$-extended MSSM the right-handed sneutrino ${\stackrel{\texttildelow{}}{\ensuremath{\nu}}}_{R}$ becomes a good thermal dark matter candidate. We identify two generic parameter space regions where the combined constraints from relic density determinations, direct detection, and collider searches are all satisfied.

We revisit the method of kinematical endpoints for particle mass determination, applied to the popular SUSY decay chain → 02 → → 01. We analyze the uniqueness of the solutions for the mass spectrum in terms of the measured endpoints in the observable invariant mass distributions. We provide simple analytical inversion formulas for the masses in terms of the measured endpoints. We show that in a sizable portion of the SUSY mass parameter space the solutions always suffer from a two-fold ambiguity, due to the fact that the original relations between the masses and the endpoints are piecewise-defined functions. The ambiguity persists even in the ideal case of a perfect detector and infinite statistics. We delineate the corresponding dangerous regions of parameter space and identify the sets of ``twin'' mass spectra. In order to resolve the ambiguity, we propose a generalization of the endpoint method, from single-variable distributions to two-variable distributions. In particular, we study analytically the boundaries of the {mjℓ(lo),mjℓ(hi)} and {mℓℓ,mjℓℓ} distributions and prove that their shapes are in principle sufficient to resolve the ambiguity in the mass determination. We identify several additional independent measurements which can be obtained from the boundary lines of these bivariate distributions. The purely kinematical nature of our method makes it generally applicable to any model that exhibits a SUSY-like cascade decay.

We consider a class of on-shell constrained mass variables that are 3+1 dimensional generalizations of the Cambridge M T2 variable and that automatically incorporate various assumptions about the underlying event topology. The presence of additional on-shell constraints causes their kinematic distributions to exhibit sharper endpoints than the usual M T2 distribution. We study the mathematical properties of these new variables, e.g., the uniqueness of the solution selected by the minimization over the invisible particle 4-momenta. We then use this solution to reconstruct the masses of various particles along the decay chain. We propose several tests for validating the assumed event topology in missing energy events from new physics. The tests are able to determine: 1) whether the decays in the event are two-body or three-body, 2) if the decay is two-body, whether the intermediate resonances in the two decay chains are the same, and 3) the exact sequence in which the visible particles are emitted from each decay chain.

The importance of the $H\ensuremath{\rightarrow}ZZ\ensuremath{\rightarrow}4\ensuremath{\ell}$ ``golden'' channel was shown by its major role in the discovery, by the ATLAS and CMS collaborations, of a Higgs-like boson with mass near 125 GeV. We analyze the discrimination power of the matrix element method both for separating the signal from the irreducible $ZZ$ background and for distinguishing various spin and parity hypotheses describing a signal in this channel. We show that the proper treatment of interference effects associated with permutations of identical leptons in the $4e$ and $4\ensuremath{\mu}$ final states plays an important role in achieving the best sensitivity in measuring the properties of the newly discovered boson. We provide a code, mekd, that calculates kinematic discriminants based on the full leading-order matrix elements and which will aid experimentalists and phenomenologists in their continuing studies of the $H\ensuremath{\rightarrow}ZZ\ensuremath{\rightarrow}4\ensuremath{\ell}$ channel.

The latest results from the ATLAS and CMS experiments at the CERN Large Hadron Collider unequivocally confirm the existence of a resonance X with mass near 125 GeV which could be the Higgs boson of the standard model. Measuring the properties (quantum numbers and couplings) of this resonance is of paramount importance. Initial analyses by the LHC Collaborations disfavor specific alternative benchmark hypotheses, e.g., pure pseudoscalars or gravitons. However, this is just the first step in a long-term program of detailed measurements. We consider the most general set of operators in the decay channels X→ZZ, WW, Zγ, γγ, and derive the constraint implied by the measured rate. This allows us to provide a useful parametrization of the orthogonal independent Higgs coupling degrees of freedom as coordinates on a suitably defined sphere.

We examine the discovery potential for double Higgs production at the high luminosity LHC in the final state with two $b$-tagged jets, two leptons and missing transverse momentum. Although this dilepton final state has been considered a difficult channel due to the large backgrounds, we argue that it is possible to obtain sizable signal significance, by adopting a deep learning framework making full use of the relevant kinematics along with the jet images from the Higgs decay. For the relevant number of signal events we obtain a substantial increase in signal sensitivity over existing analyses. We discuss relative improvements at each stage and the correlations among the different input variables for the neutral network. The proposed method can be easily generalized to the semi-leptonic channel of double Higgs production, as well as to other processes with similar final states.

Abstract The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra, which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep-learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot-Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parameterize the most general family of degeneracies among the input atmospheric parameters that affect the characterization of an exoplanet atmosphere through transit spectroscopy.

We propose a novel quantum technique to search for unmodelled anomalies in multi-dimensional binned collider data.We propose associating an Ising lattice spin site with each bin, with the Ising Hamiltonian suitably constructed from the observed data and a corresponding theoretical expectation.In order to capture spatially correlated anomalies in the data, we introduce spin-spin interactions between neighboring sites, as well as self-interactions.The ground state energy of the resulting Ising Hamiltonian can be used as a new test statistic, which can be computed either classically or via adiabatic quantum optimization.We demonstrate that our test statistic outperforms some of the most commonly used goodness-of-fit tests.The new approach greatly reduces the look-elsewhere effect by exploiting the typical differences between statistical noise and genuine new physics signals.

The choice of optimal event variables is crucial for achieving the maximal sensitivity of experimental analyses. Over time, physicists have derived suitable kinematic variables for many typical event topologies in collider physics. Here, we introduce a deep-learning technique to design good event variables, which are sensitive over a wide range of values for the unknown model parameters. We demonstrate that the neural networks trained with our technique on some simple event topologies are able to reproduce standard event variables like invariant mass, transverse mass, and stransverse mass. The method is automatable and completely general and can be used to derive sensitive, previously unknown, event variables for other, more complex event topologies.

A fundamental task in data science is the discovery, description, and identification of any symmetries present in the data. We developed a deep learning methodology for the simultaneous discovery of multiple non-trivial continuous symmetries across an entire labeled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function, ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to invariant transformations with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset, where the oracle is provided by the 10-dimensional vector of logits of a trained classifier. We find classes of symmetries that transform each image from the dataset into new synthetic images while conserving the values of the logits. We illustrate these transformations as lines of equal probability (“flows”) in the reduced latent space. These results show that symmetries in the data can be successfully searched for and identified as interpretable non-trivial transformations in the equivalent latent space.

Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the $U(n)$ and $SU(n)$ families of Lie groups. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.

Kinematic variables are important tools for analyzing collider experiments. This article reviews a variety of such tools, which were designed primarily for the experiments at the Large Hadron Collider, but which have potential uses in other experiments. The article also discusses the interconnection and mutual complementarity of kinematic variables and modern machine-learning techniques.

We contrast the experimental signatures of low energy supersymmetry and the model of Universal Extra Dimensions and discuss various methods for their discrimination at hadron colliders. We study the discovery reach of the Tevatron and the LHC for level 2 Kaluza-Klein modes, which would indicate the presence of extra dimensions. We find that with 100 ${\rm fb}^{-1}$ of data the LHC will be able to discover the $\gamma_2$ and $Z_2$ KK modes as separate resonances if their masses are below 2 TeV. We also investigate the possibility to differentiate the spins of the superpartners and KK modes by means of the asymmetry method of Barr.

We examine the muon's electric dipole moment dμ from a variety of theoretical perspectives. We point out that the reported deviation in the muon's g−2 can be due partially or even entirely to a new physics contribution to the muon's electric dipole moment. In fact, the recent g−2 measurement provides the most stringent bound on dμ to date. This ambiguity could be definitively resolved by the dedicated search for dμ recently proposed. We then consider both model-independent and supersymmetric frameworks. Under the assumptions of scalar degeneracy, proportionality, and flavor conservation, the theoretical expectations for dμ in supersymmetry fall just below the proposed sensitivity. However, nondegeneracy can give an order of magnitude enhancement, and lepton flavor violation can lead to dμ∼10−22ecm, two orders of magnitude above the sensitivity of the dμ experiment. We present compact expressions for leptonic dipole moments and lepton flavor violating amplitudes. We also derive new limits on the amount of flavor violation allowed and demonstrate that approximations previously used to obtain such limits are highly inaccurate in much of parameter space.

We critically reexamine the standard applications of the method of kinematical endpoints for sparticle mass determination. We consider the typical decay chain in supersymmetry (SUSY) → 02 → → 01, which yields a jet j, and two leptons ℓn± and ℓf∓. The conventional approaches use the upper kinematical endpoints of the individual distributions mjℓℓ, mjℓ(lo) = min {mjℓn,mjℓf} and mjℓ(hi) = max {mjℓn,mjℓf}, all three of which suffer from parameter space region ambiguities and may lead to multiple solutions for the SUSY mass spectrum. In contrast, we do not use mjℓℓ, mjℓ(lo) and mjℓ(hi), and instead propose a new set of (infinitely many) variables whose upper kinematic endpoints exhibit reduced sensitivity to the parameter space region. We then outline an alternative, much simplified procedure for obtaining the SUSY mass spectrum. In particular, we show that the four endpoints observed in the three distributions m2ℓℓ, m2jℓn∪m2jℓf and m2jℓn+m2jℓf are sufficient to completely pin down the squark mass m and the two neutralino masses m02 and m01, leaving only a discrete 2-fold ambiguity for the slepton mass m. This remaining ambiguity can be easily resolved in a number of different ways: for example, by a single additional measurement of the kinematic endpoint of any one out of the many remaining 1-dimensional distributions at our disposal, or by exploring the correlations in the 2-dimensional distribution of m2jℓn∪m2jℓf versus m2ℓℓ. We illustrate our method with two examples: the LM1 and LM6 CMS study points. An additional advantage of our method is the expected improvement in the accuracy of the SUSY mass determination, due to the multitude and variety of available measurements.

We explore the phenomenology of Kaluza-Klein (KK) dark matter in very general models with universal extra dimensions (UEDs), emphasizing the complementarity between high-energy colliders and dark matter direct detection experiments. In models with relatively small mass splittings between the dark matter candidate and the rest of the (colored) spectrum, the collider sensitivity is diminished, but direct detection rates are enhanced. UEDs provide a natural framework for such mass degeneracies. We consider both five-dimensional and six-dimensional nonminimal UED models, and discuss the detection prospects for various KK dark matter candidates: the KK photon ${\ensuremath{\gamma}}_{1}$, the KK $Z$ boson ${Z}_{1}$, the KK Higgs boson ${H}_{1}$, and the spinless KK photon ${\ensuremath{\gamma}}_{H}$. We combine collider limits, such as electroweak precision data and expected LHC reach, with cosmological constraints from WMAP, and the sensitivity of current or planned direct detection experiments. Allowing for general mass splittings, we show that neither colliders nor direct detection experiments by themselves can explore all of the relevant KK dark matter parameter space. Nevertheless, they probe different parameter space regions, and the combination of the two types of constraints can be quite powerful. For example, in the case of ${\ensuremath{\gamma}}_{1}$ in 5D UEDs the relevant parameter space will be almost completely covered by the combined CERN LHC and direct detection sensitivities expected in the near future.

We present an implementation of the model of minimal universal extra dimensions (MUED) in CalcHEP/CompHEP. We include all level-1 and level-2 Kaluza-Klein (KK) particles outside the Higgs sector. The mass spectrum is automatically calculated at one loop in terms of the two input parameters in MUED: the radius of the extra dimension and the cut-off scale of the model. We implement both the KK number conserving and the KK number violating interactions of the KK particles. We also account for the proper running of the gauge coupling constants above the electroweak scale. The implementation has been extensively cross-checked against known analytical results in the literature and numerical results from other programs. Our files are publicly available and can be used to perform various automated calculations within the MUED model.

The variable $ {\sqrt {s}_{\min }} $ was originally proposed in [1] as a model-independent, global and fully inclusive measure of the new physics mass scale in missing energy events at hadron colliders. In the original incarnation of $ {\sqrt {s}_{\min }} $ , however, the connection to the new physics mass scale was blurred by the effects of the underlying event, most notably initial state radiation and multiple parton interactions. In this paper we advertize two improved variants of the $ {\sqrt {s}_{\min }} $ variable, which overcome this problem. First we show that by evaluating the $ {\sqrt {s}_{\min }} $ variable at the RECO level, in terms of the reconstructed objects in the event, the effects from the underlying event are significantly diminished and the nice correlation between the peak in the $ \sqrt {s}_{_{\min }}^{\left( {{reco}} \right)} $ distribution and the new physics mass scale is restored. Secondly, the underlying event problem can be avoided altogether when the $ {\sqrt {s}_{\min }} $ concept is applied to a subsystem of the event which does not involve any QCD jets. We supply an analytic formula for the resulting subsystem $ \sqrt {s}_{_{\min }}^{\left( {{sub}} \right)} $ variable and show that its peak exhibits the usual correlation with the mass scale of the particles produced in the subsystem. Finally, we contrast $ {\sqrt {s}_{\min }} $ to other popular inclusive variables such as H T , M Tgen and M TTgen . We illustrate our discussion with several examples from supersymmetry, and with dilepton events from top quark pair production.

This is a written account of the computer tutorial offered at the Sixth MC4BSM workshop at Cornell University, March 22-24, 2012. The tools covered during the tutorial include: FeynRules, LanHEP, MadGraph, CalcHEP, Pythia 8, Herwig++, and Sherpa. In the tutorial, we specify a simple extension of the Standard Model, at the level of a Lagrangian. The software tools are then used to automatically generate a set of Feynman rules, compute the invariant matrix element for a sample process, and generate both parton-level and fully hadronized/showered Monte Carlo event samples. The tutorial is designed to be self-paced, and detailed instructions for all steps are included in this write-up. Installation instructions for each tool on a variety of popular platforms are also provided.

We consider the decay of a generic resonance to two visible particles and any number of invisible particles. We show that the shape of the invariant mass distribution of the two visible particles is sensitive to both the mass spectrum of the new particles, as well as the decay topology. We provide the analytical formulas describing the invariant mass shapes for the nine simplest topologies (with up to two invisible particles in the final state). Any such distribution can be simply categorized by its end point, peak location, and curvature, which are typically sufficient to discriminate among the competing topologies. In each case, we list the effective mass parameters which can be measured by experiment. In certain cases, the invariant mass shape is sufficient to completely determine the new particle mass spectrum, including the overall mass scale.

In this report we summarize the many dark matter searches currently being pursued through four complementary approaches: direct detection, indirect detection, collider experiments, and astrophysical probes. The essential features of broad classes of experiments are described, each with their own strengths and weaknesses. The complementarity of the different dark matter searches is discussed qualitatively and illustrated quantitatively in two simple theoretical frameworks. Our primary conclusion is that the diversity of possible dark matter candidates requires a balanced program drawing from all four approaches.

We present a general procedure for measuring the tensor structure of the coupling of the scalar Higgs-like boson recently discovered at the LHC to two Z bosons, including the effects of interference among different operators. To motivate our concern with this interference, we explore the parameter space of the couplings in the effective theory describing these interactions and illustrate the effects of interference on the differential dilepton mass distributions. Kinematic discriminants for performing coupling measurements that utilize the effects of interference are developed and described. We present projections for the sensitivity of coupling measurements that use these discriminants in future LHC operation in a variety of physics scenarios.

We propose a technique called Optimal Analysis-Specific Importance Sampling (OASIS) to reduce the number of simulated events required for a high-energy experimental analysis to reach a target sensitivity. We provide recipes to obtain the optimal sampling distributions which preferentially focus the event generation on the regions of phase space with high utility to the experimental analyses. OASIS leads to a conservation of resources at all stages of the Monte Carlo pipeline, including full-detector simulation, and is complementary to approaches which seek to speed-up the simulation pipeline.

We determine the Tevatron's reach in supersymmetric parameter space in trilepton, like-sign dilepton, and dilepton plus tau-jet channels, taking all relevant backgrounds into account. We show results for the minimal supergravity model. With a standard set of cuts we find that the previously unaccounted for Wγ∗ background is larger than all other backgrounds combined. We include cuts on the dilepton invariant mass and the W-boson transverse mass to reduce the Wγ∗ background to a reasonable level. We optimize cuts at each point in supersymmetry parameter space in order to maximize signal-to-noise.

We determine the Fermilab Tevatron's reach in supersymmetric parameter space in trilepton, like-sign dilepton, and dilepton plus tau-jet channels. We critically study the standard model background processes. We find larger backgrounds and, hence, significantly smaller reach regions than recent analyses. We identify the major cause of the background discrepancy. We improve signal-to-noise by introducing an invariant mass cut which takes advantage of a sharp edge in the signal dilepton invariant mass distribution. Also, we independently vary the cuts at each point in SUSY parameter space to determine the set which yields the maximal reach. We find that this cut optimization can significantly enhance the Tevatron reach.

Kination dominated quintessence models of dark energy have the intriguing feature that the relic abundance of thermal cold dark matter can be significantly enhanced compared to the predictions from standard cosmology. Previous treatments of such models do not include a realistic embedding of inflationary initial conditions. We remedy this situation by constructing a viable inflationary model in which the inflaton and quintessence field are the same scalar degree of freedom. Kination domination is achieved after inflation through a strong push or ``kick'' of the inflaton, and sufficient reheating can be achieved depending on model parameters. This allows us to explore both model-dependent and model-independent cosmological predictions of this scenario. We find that measurements of the B-mode cosmic microwave background polarization can rule out this class of scenarios almost model independently. We also discuss other experimentally accessible signatures for this class of models.

The minimal supersymmetric standard model (MSSM) is plagued by two major fine-tuning problems: the $\ensuremath{\mu}$-problem and the proton decay problem. We present a simultaneous solution to both problems within the framework of a $U(1{)}^{\ensuremath{'}}$-extended MSSM (UMSSM), without requiring $R$-parity conservation. We identify several classes of phenomenologically viable models and provide specific examples of $U(1{)}^{\ensuremath{'}}$ charge assignments. Our models generically contain either lepton number violating or baryon number violating renormalizable interactions, whose coexistence is nevertheless automatically forbidden by the new $U(1{)}^{\ensuremath{'}}$ gauge symmetry. The $U(1{)}^{\ensuremath{'}}$ symmetry also prohibits the potentially dangerous and often ignored higher-dimensional proton decay operators such as $QQQL$ and ${U}^{c}{U}^{c}{D}^{c}{E}^{c}$ which are still allowed by $R$-parity. Thus, under minimal assumptions, we show that once the $\ensuremath{\mu}$-problem is solved, the proton is sufficiently stable, even in the presence of a minimum set of exotics fields, as required for anomaly cancellation. Our models provide impetus for pursuing the collider phenomenology of $R$-parity violation within the UMSSM framework.

A weakly interacting massive particle (WIMP) provides an attractive dark matter candidate, and should be within reach of the next generation of high-energy colliders. We consider the process of direct WIMP pair-production, accompanied by an initial-state radiation photon, in electron–positron collisions at the proposed International Linear Collider (ILC). We present a parametrization of the differential cross section for this process which conveniently separates the model-independent information provided by cosmology from the model-dependent inputs from particle physics. As an application, we consider two simple models, one supersymmetric and another of the 'universal extra dimensions' (UED) type. The discovery reach of the ILC and the expected precision of parameter measurements are studied in each model. In addition, for each of the two examples, we also investigate the ability of the ILC to distinguish between the two models through a shape-discrimination analysis of the photon energy spectrum. We show that with sufficient beam polarization the alternative model interpretation can be ruled out in a large part of the relevant parameter space.

A bstract We extend the range of possible applications of M T 2 type analyses to decay chains with multiple invisible particles, as well as to asymmetric event topologies with different parent and/or different children particles. We advocate two possible approaches. In the first, we introduce suitably defined 3 + 1-dimensional analogues of the M T 2 variable, which take into account all relevant on-shell kinematic constraints in a given event topology. The second approach utilizes the conventional M T 2 variable, but its kinematic endpoint is suitably reinterpreted on a case by case basis, depending on the specific event topology at hand. We provide the general prescription for this reinterpretation, including the formulas relating the measured M T 2 endpoint (as a function of the test masses of all the invisible particles) to the underlying physical mass spectrum. We also provide analytical formulas for the shape of the differential distribution of the doubly projected $ {M_{{T{2_{\bot }}}}} $ variable for the ten possible event topologies with one visible particle and up to two invisible particles per decay chain. We illustrate our results with the example of leptonic chargino decays $ {{\widetilde{\chi}}^{+}}\to {\ell^{+}}\nu {{\widetilde{\chi}}^0} $ in supersymmetry.

Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental attempts to constrain the parameter space of motivated new physics models with a high degree of generality quite challenging. We describe how the reweighting of events may allow this challenge to be met, as fully simulated Monte Carlo samples generated for arbitrary benchmark models can be effectively re-used. In particular, we suggest procedures that allow more efficient collaboration between theorists and experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.

We discuss the collider phenomenology of the model of Minimal Universal Extra Dimensions (MUED) at the Large hadron Collider (LHC). We derive analytical results for all relevant strong pair-production processes of two level 1 Kaluza-Klein partners and use them to validate and correct the existing MUED implementation in the fortran version of the PYTHIA event generator. We also develop a new implementation of the model in the C++ version of PYTHIA. We use our implementations in conjunction with the CHECKMATE package to derive the LHC bounds on MUED from a large number of published experimental analyses from Run 1 at the LHC.

We demonstrate the use of symbolic regression in deriving analytical formulas, which are needed at various stages of a typical experimental analysis in collider phenomenology. As a first application, we consider kinematic variables like the stransverse mass, $M_{T2}$, which are defined algorithmically through an optimization procedure and not in terms of an analytical formula. We then train a symbolic regression and obtain the correct analytical expressions for all known special cases of $M_{T2}$ in the literature. As a second application, we reproduce the correct analytical expression for a next-to-leading order (NLO) kinematic distribution from data, which is simulated with a NLO event generator. Finally, we derive analytical approximations for the NLO kinematic distributions after detector simulation, for which no known analytical formulas currently exist.

We estimate the Fermilab Tevatron run II potential for top and bottom squark searches. We find an impressive reach in several of the possible discovery channels. We also study some new channels which may arise in nonconventional supersymmetry models. In each case we rely on a detailed Monte Carlo simulation of the collider events and the CDF detector performance in run I.

In focus point supersymmetry, all squarks and sleptons, including those of the third generation, have multi-TeV masses without sacrificing naturalness. We examine the implications of this framework for low energy constraints and the light Higgs boson mass. Undesirable contributions to proton decay and electric dipole moments, generic in many supersymmetric models, are strongly suppressed. As a result, the prediction for ${\ensuremath{\alpha}}_{s}$ in simple grand unified theories is $3\ensuremath{\sigma}$--$5\ensuremath{\sigma}$ closer to the experimental value, and the allowed $\mathrm{CP}$-violating phases are larger by one to two orders of magnitude. In addition, the very heavy top and bottom squarks of focus point supersymmetry naturally produce a Higgs boson mass at or above 115 GeV without requiring heavy gauginos. We conclude with an extended discussion of issues related to the definition of naturalness and comment on several other prescriptions given in the literature.

In supersymmetric theories of nature the Higgsino fermionic superpartner of the Higgs boson can arise as the lightest standard model superpartner depending on the couplings between the Higgs and supersymmetry breaking sectors. In this Brief Report the production and decay of Higgsino pairs to the Goldstone fermion of supersymmetry breaking and the Higgs boson h, or gauge bosons Z or $\ensuremath{\gamma}$ are considered. Relatively clean diboson final states $hh,$ $h\ensuremath{\gamma},$ $hZ,$ $Z\ensuremath{\gamma},$ or $\mathrm{ZZ}$ with a large amount of missing energy result. The latter channels provide novel discovery modes for supersymmetry at high energy colliders since events with Z bosons are generally rejected in supersymmetry searches. In addition, final states with real Higgs bosons can potentially provide efficient channels to discover and study a Higgs signal at the Fermilab Tevatron run II.

This report summarizes a study of the physics potential of the CLIC e+e- linear collider operating at centre-of-mass energies from 1 TeV to 5 TeV with luminosity of the order of 10^35 cm^-2 s^-1. First, the CLIC collider complex is surveyed, with emphasis on aspects related to its physics capabilities, particularly the luminosity and energy, and also possible polarization, \gamma\gamma and e-e- collisions. The next CLIC Test facility, CTF3, and its R&D programme are also reviewed. We then discuss aspects of experimentation at CLIC, including backgrounds and experimental conditions, and present a conceptual detector design used in the physics analyses, most of which use the nominal CLIC centre-of-mass energy of 3 TeV. CLIC contributions to Higgs physics could include completing the profile of a light Higgs boson by measuring rare decays and reconstructing the Higgs potential, or discovering one or more heavy Higgs bosons, or probing CP violation in the Higgs sector. Turning to physics beyond the Standard Model, CLIC might be able to complete the supersymmetric spectrum and make more precise measurements of sparticles detected previously at the LHC or a lower-energy linear e+e- collider: \gamma\gamma collisions and polarization would be particularly useful for these tasks. CLIC would also have unique capabilities for probing other possible extensions of the Standard Model, such as theories with extra dimensions or new vector resonances, new contact interactions and models with strong WW scattering at high energies. In all the scenarios we have studied, CLIC would provide significant fundamental physics information beyond that available from the LHC and a lower-energy linear e+e- collider, as a result of its unique combination of high energy and experimental precision.

The search for light stops is of paramount importance, both in general as a promising path to the discovery of beyond the standard model physics and more specifically as a way of evaluating the success of the naturalness paradigm. While the LHC experiments have ruled out much of the relevant parameter space, there are "stop gaps", i.e., values of sparticle masses for which existing LHC analyses have relatively little sensitivity to light stops. We point out that techniques involving on-shell constrained M_2 variables can do much to enhance sensitivity in this region and hence help close the stop gaps. We demonstrate the use of these variables for several benchmark points and describe the effect of realistic complications, such as detector effects and combinatorial backgrounds, in order to provide a useful toolkit for light stop searches in particular, and new physics searches at the LHC in general.

We propose a novel kinematic method to expedite the discovery of the double Higgs ($hh$) production in the $\ell^+\ell^- b \bar{b} + E_T \hspace{-0.52cm} \big / ~$ final state. We make full use of recently developed kinematic variables, as well as the variables $\it Topness$ for the dominant background (top quark pair production) and $\it Higgsness$ for the signal. We obtain a significant increase in sensitivity compared to the previous analyses which used sophisticated algorithms like boosted decision trees or neutral networks. The method can be easily generalized to resonant $hh$ production as well as other non-resonant channels.

Theoretical physicists describe nature by i) building a theory model and ii) determining the model parameters. The latter step involves the dual aspect of both fitting to the existing experimental data and satisfying abstract criteria like beauty, naturalness, etc. We use the Yukawa quark sector as a toy example to demonstrate how both of those tasks can be accomplished with machine learning techniques. We propose loss functions whose minimization results in true models that are also beautiful as measured by three different criteria - uniformity, sparsity, or symmetry.

The stransverse mass variable $M_{T2}$ was originally proposed for the study of hadron collider events in which $N=2$ parent particles are produced and then decay semi-invisibly. Here we consider the generalization to the case of $N\ge 3$ semi-invisibly decaying parent particles. We introduce the corresponding class of kinematic variables $M_{TN}$ and illustrate their mathematical properties. Many of the celebrated features of the $M_{T2}$ kinematic endpoint are retained in this more general case, including the ability to measure the mass of the invisible daughter particle from the stransverse mass kink. We describe and validate a numerical procedure for computing $M_{TN}$ in practice. We also identify the configurations of visible momenta which result in nontrivial ($M_{TN}\ne 0$) values, and derive a pure phase-space estimate for the fraction of such events for any $N$.

We propose a supersymmetric extension of the Standard Model with an extra U(1) gauge symmetry, so that all supersymmetric mass terms, including the μ-term, are forbidden by the gauge symmetries. Supersymmetry is broken dynamically which results in U(1) breaking and generation of realistic μ term and soft breaking masses. The additional fields required to cancel the U(1) anomalies are identified with the messengers of supersymmetry breaking. The gaugino masses arise as in the usual gauge mediated scenario, while squarks and sleptons receive their masses from both the U(1) D-term and the two-loop gauge mediation contributions. The scale of supersymmetry breaking in this model can be below 106 GeV, yielding collider signatures with decays to goldstinos inside the detector.

If the cold dark matter consists of weakly interacting massive particles (WIMPs), anticipated measurements of the WIMP properties at the Large Hadron Collider (LHC) and the International Linear Collider (ILC) will provide an unprecedented experimental probe of cosmology at temperatures of order 1 GeV. It is worth emphasizing that the expected outcome of these tests may or may not be consistent with the picture of standard cosmology. For example, in kination-dominated quintessence models of dark energy, the dark matter relic abundance can be significantly enhanced compared to that obtained from freeze out in a radiation-dominated universe. Collider measurements then will simultaneously probe both dark matter and dark energy. In this article, we investigate the precision to which the LHC and ILC can determine the dark matter and dark energy parameters under those circumstances. We use an illustrative set of four benchmark points in minimal supergravity in analogy with the four LCC benchmark points. The precision achievable together at the LHC and ILC is sufficient to discover kination-dominated quintessence, under the assumption that the WIMPs are the only dark matter component. The LHC and ILC can thus play important roles as alternative probes of both dark matter and dark energy.

Reconstructed mass variables, such as M 2, M 2C , M * , and M 2 , play an essential role in searches for new physics at hadron colliders. The calculation of these variables generally involves constrained minimization in a large parameter space, which is numerically challenging. We provide a C++ code, Optimass, which interfaces with the Minuit library to perform this constrained minimization using the Augmented Lagrangian Method. The code can be applied to arbitrarily general event topologies, thus allowing the user to significantly extend the existing set of kinematic variables. We describe this code, explain its physics motivation, and demonstrate its use in the analysis of the fully leptonic decay of pair-produced top quarks using M 2 variables.

Edge detection is an important tool in the search for and exploration of physics beyond the standard model. Ideally one would be able to perform edge detection in a relatively model-independent way, however most analyses rely on more detailed properties (i.e. shapes or likelihood distributions) of the variable(s) of interest. We therefore present a sketch of how edge detection can be accomplished using Voronoi tessellations, focusing on the case of two-dimensional distributions for simplicity. After deriving some useful properties of the Voronoi tessellations of simplified distributions containing edges, we propose several algorithms for tagging the Voronoi cells in the vicinity of kinematic edges in real data and show that the efficiency of our methods is improved by the addition of a few Voronoi relaxation steps via Lloyd's method. Our results suggest specifically that Voronoi-based methods should be useful for relatively model-independent edge detection, and, more generally, that the wider adaptation of Voronoi tessellations may be useful in collider physics.

We discuss singularity variables which are properly suited for analyzing the kinematics of events with missing transverse energy at the LHC. We consider six of the simplest event topologies encountered in studies of leptonic W-bosons and top quarks, as well as in SUSY-like searches for new physics with dark matter particles. In each case, we illustrate the general prescription for finding the relevant singularity variable, which in turn helps delineate the visible parameter subspace on which the singularities are located. Our results can be used in two different ways - first, as a guide for targeting the signal-rich regions of parameter space during the stage of discovery, and second, as a sensitive focus point method for measuring the particle mass spectrum after the initial discovery.

Abstract We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the applied transformations are symmetries and the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups SO (2), SO (3), and SO (4), and of the Lorentz group <?CDATA $SO(1,3)$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> . Other examples include squeeze mapping, piecewise discontinuous labels, and SO (10), demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.

Models based on vision transformer architectures are considered state-of-the-art when it comes to image classification tasks. However, they require extensive computational resources both for training and deployment. The problem is exacerbated as the amount and complexity of the data increases. Quantum-based vision transformer models could potentially alleviate this issue by reducing the training and operating time while maintaining the same predictive power. Although current quantum computers are not yet able to perform high-dimensional tasks yet, they do offer one of the most efficient solutions for the future. In this work, we construct several variations of a quantum hybrid vision transformer for a classification problem in high energy physics (distinguishing photons and electrons in the electromagnetic calorimeter). We test them against classical vision transformer architectures. Our findings indicate that the hybrid models can achieve comparable performance to their classical analogues with a similar number of parameters.

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been leveraged for various data analysis tasks in high-energy physics. One typical task is jet tagging, where jets are viewed as point clouds with distinct features and edge connections between their constituent particles. The increasing size and complexity of the LHC particle datasets, as well as the computational models used for their analysis, have greatly motivated the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, we can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we provide a fair and comprehensive comparison of classical graph neural networks (GNNs) and equivariant graph neural networks (EGNNs) and their quantum counterparts: quantum graph neural networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The four architectures were benchmarked on a binary classification task to classify the parton-level particle initiating the jet. Based on their area under the curve (AUC) scores, the quantum networks were found to outperform the classical networks. However, seeing the computational advantage of quantum networks in practice may have to wait for the further development of quantum technology and its associated application programming interfaces (APIs).

Models based on vision transformer architectures are considered state-of-the-art when it comes to image classification tasks. However, they require extensive computational resources both for training and deployment. The problem is exacerbated as the amount and complexity of the data increases. Quantum-based vision transformer models could potentially alleviate this issue by reducing the training and operating time while maintaining the same predictive power. Although current quantum computers are not yet able to perform high-dimensional tasks, they do offer one of the most efficient solutions for the future. In this work, we construct several variations of a quantum hybrid vision transformer for a classification problem in high-energy physics (distinguishing photons and electrons in the electromagnetic calorimeter). We test them against classical vision transformer architectures. Our findings indicate that the hybrid models can achieve comparable performance to their classical analogs with a similar number of parameters.

This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the Z2×Z2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.

We construct a supersymmetric grand unified model in the framework of a latticized extra dimension. The SU(5) symmetries on the lattice are broken by the vacuum expectation values of the link fields connecting adjacent SU(5) sites, leaving just the MSSM at low energies. Below the SU(5) breaking scale, the theory gives rise to a similar spectrum as in orbifold breaking of SU(5) symmetry in 5 dimensions, and shares many features with the latter scenario. We discuss gauge coupling unification and proton decay emphasizing the differences with respect to the usual grand unified theories. Our model may be viewed as an effective four dimensional description of the orbifold symmetry breaking in higher dimensions.

We develop the helicity formalism for spin-2 particles and apply it to the case of gravity in flat extra dimensions. We then implement the large extra dimensions scenario of Arkani-Hamed, Dimopoulos and Dvali in the program AMEGIC++, allowing for an easy calculation of arbitrary processes involving the emission or exchange of gravitons. We complete the set of Feynman rules derived by Han, Lykken and Zhang, and perform several consistency checks of our implementation.

We apply a model-independent, agnostic approach to the collider phenomenology of supersymmetry (SUSY), in which all mass parameters are taken as free inputs at the weak scale. We consider the gauginos, higgsinos, and the first two generations of sleptons and squarks, and analyze all possible mass hierarchies among them ($4\times 8!=161,280$ in total) in which the lightest superpartner is neutral, leading to missing energy. In each case, we identify the full set of the dominant (i.e. least suppressed by phase space, small mixing angles or Yukawa couplings) decay chains originating from the lightest colored superpartner. Our exhaustive search reveals several quite dramatic yet unexplored multilepton signatures with up to 8 isolated leptons (plus possibly up to 2 massive gauge or Higgs bosons) in the final state. Such events are spectacular, background-free for all practical purposes, and may lead to a discovery of SUSY in the very early stage ($\sim 10\ {\rm pb}^{-1}$) of LHC operations at 7 TeV.

We advocate the use of on-shell constrained ${M}_{2}$ variables in order to mitigate the combinatorial problem in supersymmetry-like events with two invisible particles at the LHC. We show that in comparison to other approaches in the literature, the constrained ${M}_{2}$ variables provide superior ans\"atze for the unmeasured invisible momenta and therefore can be usefully applied to discriminate combinatorial ambiguities. We illustrate our procedure with the example of dilepton $t\overline{t}$ events. We critically review the existing methods based on the Cambridge ${M}_{T2}$ variable and MAOS reconstruction of invisible momenta, and show that their algorithm can be simplified without loss of sensitivity, due to a perfect correlation between events with complex solutions for the invisible momenta and events exhibiting a kinematic endpoint violation. Then we demonstrate that the efficiency for selecting the correct partition is further improved by utilizing the ${M}_{2}$ variables instead. Finally, we also consider the general case when the underlying mass spectrum is unknown, and no kinematic endpoint information is available.

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.

Abstract Transit spectroscopy is a powerful tool for decoding the chemical compositions of the atmospheres of extrasolar planets. In this paper, we focus on unsupervised techniques for analyzing spectral data from transiting exoplanets. After cleaning and validating the data, we demonstrate methods for: (i) initial exploratory data analysis, based on summary statistics (estimates of location and variability); (ii) exploring and quantifying the existing correlations in the data; (iii) preprocessing and linearly transforming the data to its principal components; (iv) dimensionality reduction and manifold learning; (v) clustering and anomaly detection; and (vi) visualization and interpretation of the data. To illustrate the proposed unsupervised methodology, we use a well-known public benchmark data set of synthetic transit spectra. We show that there is a high degree of correlation in the spectral data, which calls for appropriate low-dimensional representations. We explore a number of different techniques for such dimensionality reduction and identify several suitable options in terms of summary statistics, principal components, etc. We uncover interesting structures in the principal component basis, namely well-defined branches corresponding to different chemical regimes of the underlying atmospheres. We demonstrate that those branches can be successfully recovered with a K-means clustering algorithm in a fully unsupervised fashion. We advocate for lower-dimensional representations of the spectroscopic data in terms of the main principal components, in order to reveal the existing structure in the data and quickly characterize the chemical class of a planet.

This Resource Book reviews the physics opportunities of a next-generation e+e- linear collider and discusses options for the experimental program. Part 1 contains the table of contents and introduction and gives a summary of the case for a 500 GeV linear collider.

A bstract We investigate spin correlation effects in the “antler” event topology pp → A ( A* ) → B 1 B 2 → ( ℓ − C 1 )( ℓ + C 2 ) at the LHC. We study the shapes of several kinematic variables, including the relative pseudorapidity, relative azimuthal angle and the energies of the two leptons, as well as several mass variables M ℓℓ , M eff , $ \sqrt {{{{s}_{{\min }}}}} $ , M T 2 , M CT and M CT x . We focus on the two kinematic extremes of $\sqrt{S}$ — threshold and infinity — and derive analytical expressions for the differential distributions of several variables, most notably the cos $\theta_{{\ell -\ell +}}^{*}$ variable proposed by Barr in hep-ph/0511115. For all possible spin assignments of particles A, B and C, we derive the cos $\theta_{{\ell -\ell +}}^{*}$ differential distribution at threshold, including the effects of spin correlations. Our analytical results help identify the problematic cases for spin discrimination.

The increasing use of multivariate methods, and in particular the Matrix Element Method (MEM), represents a revolution in experimental particle physics. With continued exponential growth in computing capabilities, the use of sophisticated multivariate methods-- already common-- will soon become ubiquitous and ultimately almost compulsory. While the existence of sophisticated algorithms for disentangling signal and background might naively suggest a diminished role for theorists, the use of the MEM, with its inherent connection to the calculation of differential cross sections will benefit from collaboration between theorists and experimentalists. In this white paper, we will briefly describe the MEM and some of its recent uses, note some current issues and potential resolutions, and speculate about exciting future opportunities.

We consider SUSY-like events with two decay chains, each terminating in an invisible particle, whose true energy and momentum are not measured in the detector. Nevertheless, a useful educated guess about the invisible momenta can still be obtained by optimizing a suitable invariant mass function. We review and contrast several proposals in the literature for such ansatze: four versions of the M T 2-assisted on-shell reconstruction (MAOS), as well as several variants of the on-shell constrained M 2 variables. We compare the performance of these methods with regards to the mass determination of a new particle resonance along the decay chain from the peak of the reconstructed invariant mass distribution. For concreteness, we consider the event topology of dilepton $$ t\overline{t} $$ events and study each of the three possible subsystems, in both a $$ t\overline{t} $$ and a SUSY example. We find that the M 2 variables generally provide sharper peaks and therefore better ansatze for the invisible momenta. We show that the performance can be further improved by preselecting events near the kinematic endpoint of the corresponding variable from which the momentum ansatz originates.

The classic method for mass determination in a SUSY-like cascade decay chain relies on measurements of the kinematic endpoints in the invariant mass distributions of suitable collections of visible decay products. However, the procedure is complicated by combinatorial ambiguities: e.g., the visible final state particles may be indistinguishable (as in the case of QCD jets), or one may not know the exact order in which they are emitted along the decay chain. In order to avoid such combinatorial ambiguities, we propose to treat the final state particles fully democratically and consider the sorted set of the invariant masses of all possible partitions of the visible particles in the decay chain. In particular, for a decay to N visible particles, one considers the sorted sets of all possible n-body invariant mass combinations (2 ≤ n ≤ N) and determines the kinematic endpoint m (,) max of the distribution of the r-th largest n-body invariant mass m (n,r) for each possible value of n and r. For the classic example of a squark decay in supersymmetry, we provide analytical formulas for the interpretation of these endpoints in terms of the underlying physical masses. We point out that these measurements can be used to determine the structure of the decay topology, e.g., the number and position of intermediate on-shell resonances.

We examine gauge and Yukawa coupling unification in models with gauge-mediated supersymmetry breaking. We work consistently to two-loop order, and include all weak, messenger, and unification-scale threshold corrections. We find that successful unification requires unification-scale threshold corrections that are in conflict with the minimal SU(5) model, but are consistent with the modified missing-doublet SU(5) model for small $\mathrm{tan}\ensuremath{\beta}$, and large $\mathrm{tan}\ensuremath{\beta}$ with $\ensuremath{\mu}&gt;0$.

The inclusive same-sign dilepton channel is already recognized as a promising discovery signature for supersymmetry in the early days of the LHC. We point out that it can also be used for precision measurements of sparticle masses after the initial discovery. As an illustration, we consider the LM6 CMS study point in minimal supergravity, where the same-sign leptons most often result from chargino decays to sneutrinos. We discuss three different techniques for determining the chargino and sneutrino masses in an inclusive manner, i.e., using only the two well measured lepton momenta, while treating all other upstream objects in the event as a single entity of total transverse momentum ${\stackrel{\ensuremath{\rightarrow}}{P}}_{T}$. This approach takes full advantage of the large production rates of colored superpartners, but does not rely on the poorly measured hadronic jets, and avoids any jet combinatorics problems.