A. Morelos Pineda

Within an effective field theory framework we study heavy-quark–antiquark systems with a typical distance between the heavy quark and the antiquark smaller than 1/ΛQCD. A suitable definition of the potential is given within this framework, while non-potential (retardation) effects are taken into account in a systematic way. We explore different physical systems. Model-independent results on the short distance behaviour of the energies of the gluonic excitations between static quarks are obtained. Finally, we show how infrared renormalons affecting the static potential get cancelled in the effective theory.

We review recent theoretical developments in heavy quarkonium physics from the point of view of Effective Field Theories of QCD. We discuss Non-Relativistic QCD and concentrate on potential Non-Relativistic QCD. Our main goal will be to derive QCD Schrödinger-like equations that govern the heavy quarkonium physics in the weak and strong coupling regime. We also discuss a selected set of applications, which include spectroscopy, inclusive decays and electromagnetic threshold production.

We propose an effective field theory for heavy quark-antiquark bound states once the soft gluons have been integrated out. We also new results for the matching between QCD (QED) and NRQCD (NRQED).

The definition of the quark-antiquark static potential is given within an effective field theory framework. The leading infrared divergences of the static singlet potential in perturbation theory are explicitly calculated.

We approximately compute the normalization constant of the first infrared renormalon of the pole mass (and the singlet static potential). Estimates of higher order terms in the perturbative relation between the pole mass and the MSbar mass (and in the relation between the singlet static potential and αs) are given. We define a matching scheme (the renormalon subtracted scheme) between QCD and any effective field theory with heavy quarks where, besides the usual perturbative matching, the first renormalon in the Borel plane of the pole mass is subtracted. A determination of the bottom MSbar quark mass from the Υ(1S) system is performed with this new scheme and the errors studied. Our result readsmb,MSbar(mb,MSbar) = 4210+90−90(theory)−25+25(αs) MeV. Using the mass difference between theB and D meson, we also obtain a value for the charm quark mass:mc,MSbar(mc,MSbar) = 1210+70−70(theory)+65−65(mb,MSbar)−45+45(λ1) MeV. We finally discuss upon eventual improvements of these determinations.

Within an effective field theory framework, we obtain an expression for the next-to-leading term in the 1/m expansion of the singlet QQ ¯QCD potential in terms of Wilson loops, which holds beyond perturbation theory.The ambiguities in the definition of the QCD potential beyond leading order in 1/m are discussed and a specific expression for the 1/m potential is given.We explicitly evaluate this expression at one loop and compare the outcome with the existing perturbative results.On general grounds we show that for quenched QED and fully Abelian-like models this expression exactly vanishes.

New lattice data for the ${\ensuremath{\Pi}}_{u}$ and ${\ensuremath{\Sigma}}_{u}^{\ensuremath{-}}$ potentials at short distances are presented. We compare perturbation theory to the lower static hybrid potentials and find good agreement at short distances, once the renormalon ambiguities are accounted for. We use the nonperturbatively determined continuum-limit static hybrid and ground state potentials at short distances to determine the gluelump energies. The result is consistent with an estimate obtained from the gluelump data at finite lattice spacings. For the lightest gluelump, we obtain ${\ensuremath{\Lambda}}_{B}^{\mathrm{RS}}({\ensuremath{\nu}}_{f}{=2.5r}_{0}^{\ensuremath{-}1})=[2.25\ifmmode\pm\else\textpm\fi{}0.10(\mathrm{latt}.)\ifmmode\pm\else\textpm\fi{}0.21(\mathrm{th}.)\ifmmode\pm\else\textpm\fi{}0.08({\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}})]{r}_{0}^{\ensuremath{-}1}$ in the quenched approximation with ${r}_{0}^{\ensuremath{-}1}\ensuremath{\approx}400\mathrm{MeV}.$ We show that, to quote sensible numbers for the absolute values of the gluelump energies, it is necessary to handle the singularities of the singlet and octet potentials in the Borel plane. We propose to subtract the renormalons of the short-distance matching coefficients, the potentials in this case. For the singlet potential the leading renormalon is already known and related to that of the pole mass; for the octet potential a new renormalon appears, which we approximately evaluate. We also apply our methods to heavy-light mesons in the static limit and from the lattice simulations available in the literature we obtain the quenched result ${\overline{\ensuremath{\Lambda}}}^{\mathrm{RS}}({\ensuremath{\nu}}_{f}{=2.5r}_{0}^{\ensuremath{-}1})=[1.17\ifmmode\pm\else\textpm\fi{}0.08(\mathrm{latt}.)\ifmmode\pm\else\textpm\fi{}0.13(\mathrm{th}.)\ifmmode\pm\else\textpm\fi{}0.09({\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}})]{r}_{0}^{\ensuremath{-}1}.$ We calculate ${m}_{b,\overline{\mathrm{MS}}}{(m}_{b,\overline{\mathrm{MS}}})$ and apply our methods to gluinonia whose dynamics are governed by the singlet potential between adjoint sources. We can exclude nonstandard linear short-distance contributions to the static potentials, with good accuracy.

We review weakly-bound heavy quarkonium systems using effective field theories of QCD. We concentrate on potential non-relativistic QCD, which provides with a well founded connection between QCD and descriptions of the heavy quarkonium dynamics in terms of Schrödinger-like equations. This connection is obtained using standard quantum field theory techniques such as dimensional regularization, which is used throughout, and renormalization. Renormalization group equations naturally follow. Certain effort is made to illustrate how computations are performed, and the necessary techniques, providing some examples. Finally, we briefly review a selected set of applications, which include spectroscopy, radiative transitions, non-relativistic sum rules, inclusive decays, and electromagnetic threshold production.

We compute the spin-dependent and spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at O(p3) using heavy baryon effective theory including the Delta particle. We compare with previous results when existing. Using these results we obtain the leading hadronic contributions, associated to the pion and Delta particles, to the Wilson coefficients of the lepton–proton four fermion operators in NRQED. The spin-independent coefficient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, ΔETPE(π&Δ)=34(13) μeV. We also compute the charge, 〈rn〉, and Zemach, 〈rn〉(2), moments for n≥3. Finally, we discuss the spin-dependent case, for which we compute the difference between the four-fermion Wilson coefficients relevant for hydrogen and muonic hydrogen.

We obtain an improved determination of the normalization constant of the first infrared renormalon of the pole mass (and the singlet static potential). For N f = 3 it reads N m = 0.563(26). Charm quark effects in the bottom quark mass determination are carefully investigated. Finally, we determine the bottom quark mass using the NNNLO perturbative expression for the $$ \boldsymbol{\Upsilon} (1S) $$ mass. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to pole mass renormalon. Our result for the $$ \overline{\mathrm{MS}} $$ mass reads $$ {\overline{m}}_b\left({m}_b\right)=4201(43) $$ MeV.

Within an effective field theory framework, we obtain an expression, with ${O(1/m}^{2})$ accuracy, for the energies of the gluonic excitations between heavy quarks, which holds beyond perturbation theory. For the singlet heavy-quark--antiquark energy, in particular, we also obtain an expression in terms of Wilson loops. This provides, twenty years after the seminal work of Eichten and Feinberg, the first complete expression for the heavy quarkonium potential up to ${O(1/m}^{2})$ for pure gluodynamics. Several errors present in the previous literature (also in the work of Eichten and Feinberg) have been corrected. We also briefly discuss the power counting of NRQCD in the nonperturbative regime.

We discuss in detail potential NRQED (pNRQED), a previously proposed effective field theory for ultrasoft photons. The pNRQED Lagrangian for the equal mass case is presented, and it is shown that it correctly reproduces the positronium spectrum at order $m{\ensuremath{\alpha}}^{5}.$ The pNRQED Lagrangian for the unequal mass case is also presented at the same order. Dimensional regularization is used throughout.

We compute the complete leading-log terms of the next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a by-product we obtain the leading logs at $O(m\alpha_s^5)$ in the heavy quarkonium spectrum. These leading logs, when $\Lambda_{QCD} \ll m\alpha_s^2$, give the complete $O(m\alpha_s^5 \ln \alpha_s)$ corrections to the heavy quarkonium spectrum.

We include two loop, relativistic one loop and second order relativistic tree level corrections, plus leading nonperturbative contributions, to obtain a calculation of the lower states in the heavy quarkonium spectrum correct up to, and including, $O(\alpha_s^4)$ and leading $\Lambda^4/m^4$ terms. This allows us, in particular, to obtain a model independent determination of the pole masses of the $b, c$ quarks, $$m_b=5 015^{+110}_{-70} mev; m_c=1 884^{+222}_{-133} mev$$ to which correspond the $\bar{\hbox{MS}}$ masses, $$\bar{m}_b(\bar{m}_b^2)=4 453^{+50}_{-32} mev; \bar{m}_c(\bar{m}_c^2)=1 547^{+169}_{-102} mev.$$ The decay $\Gamma(\Upsilon\to e^+e^-)$ is found in agreement with experiment, $$\Gamma(\Upsilon\to e^+e^-)=1.135^{+0.27}_{-0.29} kev (\hbox{exp.}=1.320\pm0.04 kev),$$ and the hyperfine splitting is predicted to be $$M(\Upsilon)-M(\eta)=48.5^{+15.7}_{-12.2} mev.$$

We present a simple derivation of the Lamb shift using effective field theory techniques and dimensional regularisation.

This report is the result of the collaboration and research effort of the Quarkonium Working Group over the last three years. It provides a comprehensive overview of the state of the art in heavy-quarkonium theory and experiment, covering quarkonium spectroscopy, decay, and production, the determination of QCD parameters from quarkonium observables, quarkonia in media, and the effects on quarkonia of physics beyond the Standard Model. An introduction to common theoretical and experimental tools is included. Future opportunities for research in quarkonium physics are also discussed.

We study the effect of the resummation of logarithms for tt¯ production near threshold and inclusive electromagnetic decays of heavy quarkonium. This analysis is complete at next-to-next-to-leading order and includes the full resummation of logarithms at next-to-leading-logarithmic accuracy and some partial contributions at next-to-next-to-leading logarithmic accuracy. Compared with fixed-order computations at next-to-next-to-leading order the scale dependence and convergence of the perturbative series is greatly improved for both the position of the peak and the normalization of the total cross section. Nevertheless, we identify a possible source of large scale dependence in the result. At present we estimate the remaining theoretical uncertainty of the normalization of the total cross section to be of the order of 10% and for the position of the peak of the order of 100 MeV.

We sum up the next-to-leading logarithmic corrections to the heavy-quarkonium hyperfine splitting, using the nonrelativistic renormalization group. On the basis of this result, we predict the mass of the ${\ensuremath{\eta}}_{b}$ meson to be $M({\ensuremath{\eta}}_{b})=9421\ifmmode\pm\else\textpm\fi{}11(\mathrm{th}{)}_{\ensuremath{-}8}^{+9}(\ensuremath{\delta}{\ensuremath{\alpha}}_{s})\text{ }\mathrm{MeV}$. The experimental measurement of $M({\ensuremath{\eta}}_{b})$ with a few MeV error would be sufficient to determine ${\ensuremath{\alpha}}_{s}({M}_{Z})$ with an accuracy of $\ifmmode\pm\else\textpm\fi{}0.003$. For the hyperfine splitting in charmonium, the use of the nonrelativistic renormalization group brings the perturbative prediction significantly closer to the experimental figure.

We determine the nonperturbative gluon condensate of four-dimensional SU(3) gauge theory in a model-independent way. This is achieved by carefully subtracting high-order perturbation theory results from nonperturbative lattice QCD determinations of the average plaquette. No indications of dimension-two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition. We also determine the binding energy of a $B$ meson in the heavy quark mass limit.

We compute the static self-energy of SU(3) gauge theory in four spacetime dimensions to order ${\ensuremath{\alpha}}^{20}$ in the strong coupling constant $\ensuremath{\alpha}$. We employ lattice regularization to enable a numerical simulation within the framework of stochastic perturbation theory. We find perfect agreement with the factorial growth of high order coefficients predicted by the conjectured renormalon picture based on the operator product expansion.

A bstract We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $$ {Z}_3^F $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Z</mml:mi> <mml:mn>3</mml:mn> <mml:mi>F</mml:mi> </mml:msubsup> </mml:math> ( n f = 3) = $$ 2{Z}_3^V $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>2</mml:mn> <mml:msubsup> <mml:mi>Z</mml:mi> <mml:mn>3</mml:mn> <mml:mi>V</mml:mi> </mml:msubsup> </mml:math> ( n f = 3) = 0 . 37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $$ {\Lambda}_{\overline{\mathrm{MS}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:msub> </mml:math> when fitting to short-distance lattice data of the static energy. We obtain $$ {\Lambda}_{\overline{\mathrm{MS}}}^{\left({n}_f=3\right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfenced> </mml:msubsup> </mml:math> = 338(12) MeV and α ( M z ) = 0 . 1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

We resum the leading ultrasoft logs of the singlet and octet static QCD potentials within potential NRQCD. We then obtain the complete three-loop renormalization group improvement of the singlet QCD static potential. The discrepancies between the perturbative evaluation and the lattice results at short distances are slightly reduced.

We derive the imaginary part of the potential nonrelativistic QCD (pNRQCD) Hamiltonian up to order ${1/m}^{4},$ when the typical momentum transfer between the heavy quarks is of the order of ${\ensuremath{\Lambda}}_{\mathrm{QCD}}$ or greater, and the binding energy E much smaller than ${\ensuremath{\Lambda}}_{\mathrm{QCD}}.$ We use this result to calculate the inclusive decay widths into light hadrons, photons and lepton pairs, up to $\mathcal{O}({\mathrm{mv}}^{3}\ifmmode\times\else\texttimes\fi{}({\ensuremath{\Lambda}}_{\mathrm{QCD}}^{2}{/m}^{2},E/m))$ and $\mathcal{O}{(mv}^{5})$ times a short-distance coefficient, for $S\ensuremath{-}$ and P-wave heavy quarkonium states, respectively. We achieve a large reduction in the number of unknown nonperturbative parameters and, therefore, we obtain new model-independent QCD predictions. All the NRQCD matrix elements relevant to that order are expressed in terms of the wave functions at the origin and six universal nonperturbative parameters. The wave-function dependence factorizes and drops out in the ratio of hadronic and electromagnetic decay widths. The universal nonperturbative parameters are expressed in terms of gluonic field-strength correlators, which may be fixed by experimental data or, alternatively, by lattice simulations. Our expressions are expected to hold for most of the charmonium and bottomonium states below threshold. The calculations and methodology are explained in detail so that the evaluation of higher order NRQCD matrix elements in this framework should be straightforward. An example is provided.

We compute the spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon chiral perturbation theory and dispersion relations. We study the relation between both approaches. We use these results to generalize some sum rules to virtual photon transfer momentum and relate them with sum rules in deep inelastic scattering. We then compute the leading chiral term of the polarizability correction to the Lamb shift of hydrogen and muonic hydrogen. We obtain $\ensuremath{-}87.05/{n}^{3}\mathrm{Hz}$ and $\ensuremath{-}0.148/{n}^{3}\mathrm{meV}$ for the correction to the hydrogen and muonic hydrogen Lamb shift, respectively.

We determine the infinite volume coefficients of the perturbative expansions of the self-energies of static sources in the fundamental and adjoint representations in SU(3) gluodynamics to order ${\ensuremath{\alpha}}^{20}$ in the strong coupling parameter $\ensuremath{\alpha}$. We use numerical stochastic perturbation theory, where we employ a new second order integrator and twisted boundary conditions. The expansions are obtained in lattice regularization with the Wilson action and two different discretizations of the covariant time derivative within the Polyakov loop. Overall, we obtain four different perturbative series. For all of them the high order coefficients display the factorial growth predicted by the conjectured renormalon picture, based on the operator product expansion. This enables us to determine the normalization constants of the leading infrared renormalons of heavy quark and heavy gluino pole masses and to translate these into the modified minimal subtraction scheme ($\overline{\mathrm{MS}}$). We also estimate the four-loop $\ensuremath{\beta}$-function coefficient of the lattice scheme.

We compute the magnetic dipole transitions between low-lying heavy quarkonium states in a model-independent way. We use the weak-coupling version of the effective field theory named potential nonrelativistic QCD, with the static potential exactly incorporated in the leading order Hamiltonian. The precision we reach is ${k}_{\ensuremath{\gamma}}^{3}/{m}^{2}\ifmmode\times\else\texttimes\fi{}\mathcal{O}({\ensuremath{\alpha}}_{\mathrm{s}}^{2},{v}^{2})$ and ${k}_{\ensuremath{\gamma}}^{3}/{m}^{2}\ifmmode\times\else\texttimes\fi{}\mathcal{O}({v}^{4})$ for the allowed and forbidden transitions, respectively, where ${k}_{\ensuremath{\gamma}}$ is the photon energy. We also resum the large logarithms associated with the heavy quark mass scale. The specific transitions considered in this paper are the following: $\ensuremath{\Upsilon}(1S)\ensuremath{\rightarrow}{\ensuremath{\eta}}_{b}(1S)\ensuremath{\gamma}$, $J/\ensuremath{\psi}(1S)\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}(1S)\ensuremath{\gamma}$, ${h}_{b}(1P)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{b0,1}(1P)\ensuremath{\gamma}$, ${\ensuremath{\chi}}_{b2}(1P)\ensuremath{\rightarrow}{h}_{b}(1P)\ensuremath{\gamma}$, $\ensuremath{\Upsilon}(2S)\ensuremath{\rightarrow}{\ensuremath{\eta}}_{b}(2S)\ensuremath{\gamma}$, $\ensuremath{\Upsilon}(2S)\ensuremath{\rightarrow}{\ensuremath{\eta}}_{b}(1S)\ensuremath{\gamma}$ and ${\ensuremath{\eta}}_{b}(2S)\ensuremath{\rightarrow}\ensuremath{\Upsilon}(1S)\ensuremath{\gamma}$. The effect of the new power counting is found to be large, and the exact treatment of the soft logarithms of the static potential makes the factorization scale dependence much smaller. The convergence for the $b\overline{b}$ ground state is quite good, and also quite reasonable for the $c\overline{c}$ ground state and the $b\overline{b}$ $1P$ state. For all of them we give solid predictions. For the $2S$ decays the situation is less conclusive, yet our results are perfectly consistent with existing data, as the previous disagreement with experiment for the $\ensuremath{\Upsilon}(2S)\ensuremath{\rightarrow}{\ensuremath{\eta}}_{b}(1S)\ensuremath{\gamma}$ decay fades away. We also compute some expectation values like the electromagnetic radius, $⟨{r}^{2}⟩$, or $⟨{p}^{2}⟩$. We find $⟨{r}^{2}⟩$ to be nicely convergent in all cases, whereas the convergence of $⟨{p}^{2}⟩$ is typically worse.

We determine the root-mean-square proton charge radius, $R_{\rm p}$, from a fit to low-$Q^2$ electron-proton elastic scattering cross section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain $R_{\rm p}=0.857(11)$ fm. This number falls between the value obtained from muonic hydrogen analyses and the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations).

A bstract We determine the charm and bottom quark masses using the N 3 LO perturbative expression of the ground state (pseudoscalar) energy of the bottomonium, charmonium and B c systems: the η b , η c and B c masses. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to the pole mass renormalon. Our result for the $$ \overline{\mathrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mrow><mml:mi>M</mml:mi><mml:mi>S</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math> masses reads $$ {\overline{m}}_c\left({\overline{m}}_c\right)=1223(33) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mover><mml:mi>m</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>c</mml:mi></mml:msub><mml:mfenced><mml:msub><mml:mover><mml:mi>m</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>c</mml:mi></mml:msub></mml:mfenced><mml:mo>=</mml:mo><mml:mn>1223</mml:mn><mml:mfenced><mml:mn>33</mml:mn></mml:mfenced></mml:math> MeV and $$ {\overline{m}}_b\left({\overline{m}}_b\right)=4186(37) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mover><mml:mi>m</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>b</mml:mi></mml:msub><mml:mfenced><mml:msub><mml:mover><mml:mi>m</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>b</mml:mi></mml:msub></mml:mfenced><mml:mo>=</mml:mo><mml:mn>4186</mml:mn><mml:mfenced><mml:mn>37</mml:mn></mml:mfenced></mml:math> MeV. We also extract a value of α s from a renormalon-free combination of the η b , η c and B c masses: α s ( M z ) = 0 . 1195(53). We explore the applicability of the weak coupling approximation to bottomonium n = 2 states. Finally, we consider an alternative computational scheme that treats the static potential exactly and study its convergence properties.

We review determinations of the electric proton charge radius from a diverse set of low-energy observables. We explore under which conditions it can be related to Wilson coefficients of appropriate effective field theories. This discussion is generalized to other low-energy constants. This provides us with a unified framework to deal with a set of low-energy constants of the proton associated with its electromagnetic interactions. Unambiguous definitions of these objects are given, as well as their relation with expectation values of QCD operators. We show that the proton radius obtained from spectroscopy and lepton-proton scattering (when both the lepton and proton move with nonrelativistic velocities) is related to the same object of the underlying field theory with ${\cal O}(\alpha)$ precision. The model dependence of these analyses is discussed. The prospects of constructing effective field theories valid for the kinematic configuration of present, or near-future, lepton-proton scattering experiments are discussed.

We complete the leading-log renormalization group scaling of the NRQCD Lagrangian at $O(1/m^2)$. The next-to-next-to-leading-log renormalization group scaling of the potential NRQCD Lagrangian (as far as the singlet is concerned) is also obtained in the situation $m\alpha_s \gg \Lambda_{QCD}$. As a by-product, we obtain the heavy quarkonium spectrum with the same accuracy in the situation $m\alpha_s^2 \simg \Lambda_{QCD}$. When $\Lambda_{QCD} \ll m\alpha_s^2$, this is equivalent to obtain the whole set of $O(m\alpha_s^{(n+4)} \ln^n \alpha_s)$ terms in the heavy quarkonium spectrum. The implications of our results in the non-perturbative situation $m\alpha_s \sim \Lambda_{QCD}$ are also mentioned.

The matching coefficients for the four-quark operators in NRQCD (NRQED) are calculated at one loop using dimensional regularization for ultraviolet and infrared divergences. The matching for the electromagnetic current follows easily from our results. Both the unequal and equal mass cases are considered. The role played by the Coulomb infrared singularities is explained in detail.

We compare, for the static potential and at short distances, perturbation theory with the results of lattice simulations. We show that a renormalon-dominance picture explains why in the literature sometimes agreement, and at other times disagreement, is found between lattice simulations and perturbation theory depending on the different implementations of the latter. We also show that, within a renormalon-based scheme, perturbation theory agrees with lattice simulations.

The ratio of the photon mediated production or annihilation rates of spin triplet and spin singlet heavy quarkonium states is computed to the next-to-next-to-leading logarithmic accuracy within the nonrelativistic renormalization group approach. The result is presented in analytical form and applied to the phenomenology of tt¯, bb¯ and cc¯ systems. The use of the nonrelativistic renormalization group considerably improves the behaviour of the perturbative expansion and is crucial for accurate theoretical analysis. For bottomonium decays we predict Γ(ηb(1S)→γγ)=0.659±0.089(th.)−0.018+0.019(δαs)±0.015(exp.)keV. Our results question the accuracy of the existing extractions of the strong coupling constant from the bottomonium annihilation. As a by-product we obtain a novel result for the ratio of the ortho- and parapositronium decay rates: the corrections of order α4ln2α and α5ln3α.

Using numerical stochastic perturbation theory, we determine the first 35 infinite volume coefficients of the perturbative expansion in powers of the strong-coupling constant $\ensuremath{\alpha}$ of the plaquette in SU(3) gluodynamics. These coefficients are obtained in lattice regularization with the standard Wilson gauge action. The onset of the dominance of the dimension-four renormalon associated to the gluon condensate is clearly observed. We determine the normalization of the corresponding singularity in the Borel plane and convert this into the $\overline{\mathrm{MS}}$ scheme. We also comment on the impact of the renormalon on nonperturbative determinations of the gluon condensate.

We comprehensively analyse the theoretical prediction for the Lamb shift in muonic hydrogen, and the associated determination of the proton radius. We use effective field theories. This allows us to relate the proton radius with well-defined objects in quantum field theory, eliminating unnecessary model dependence. The use of effective field theories also helps us to organize the computation so that we can clearly state the parametric accuracy of the result. In this paper we review all (and check several of) the contributions to the energy shift of order $α^5$, as well as those that scale like $α^6\times$logarithms in the context of non-relativistic effective field theories of QED.

We obtain a model-independent prediction for the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen. We use the relation of the Wilson coefficients of the spin-dependent dimension-six four-fermion operator of NRQED applied to the electron-proton and to the muon-proton sectors. Their difference can be reliably computed using chiral perturbation theory, whereas the Wilson coefficient of the electron-proton sector can be determined from the hyperfine splitting in hydrogen. This allows us to give a precise model-independent determination of the Wilson coefficient for the muon-proton sector, and consequently of the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen, which reads $\delta \bar E_{p\mu,\rm HF}^{\rm TPE}(nS)=-\frac{1}{n^3}1.161(20)$ meV. Together with the associated QED analysis, we obtain a prediction for the hyperfine splitting in muonic hydrogen that reads $E^{\rm th}_{p\mu,\rm HF}(1S)=182.623(27)$ meV and $E^{\rm th}_{p\mu,\rm HF}(2S)=22.8123(33)$ meV. The error is dominated by the two-photon exchange contribution.

Given an observable and its operator product expansion, we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $\ensuremath{\alpha}$ from the nonperturbative (NP) corrections. This splitting is done with NP power accuracy. Analytic control of the splitting is achieved and the organization of the different terms is done along an super/hyperasymptotic expansion. As a test we apply the methods to the static potential in the large ${\ensuremath{\beta}}_{0}$ approximation. We see the superasymptotic and hyperasymptotic structure of the observable in full glory.

We construct hyperasymptotic expansions for the heavy quark pole mass regulated using the principal value (PV) prescription. We apply such hyperasymptotic expansions to the $B/D$ meson masses, and $\bar \Lambda $ computed in the lattice. The issue of the uncertainty of the (top) pole mass is critically reexamined. The present theoretical uncertainty in the relation between ${\bar m}_t$, the $\bar{\rm MS}$ top mass, and $m_{t, \rm PV}$, the top pole mass regulated using the PV prescription, is numerically assessed to be $\delta m_{t,\rm PV}= 28\;{\rm MeV}$ for ${\bar m}_t =163$ GeV.

In the framework of potential NRQCD, we obtain the next-to-leading-log renormalization-group running of the matching coefficients for the heavy quarkonium production currents near threshold. This allows to obtain S-wave heavy-quarkonium production/annihilation observables with next-to-leading-log accuracy within perturbative QCD. In particular, we give expressions for the decays of heavy quarkonium to e^+e^- and to two photons. We also compute the O(m\alpha^8\ln^3\alpha) corrections to the Hydrogen spectrum.

We show that some nonrelativistic quantum chromodynamics color-octet matrix elements can be written in terms of (derivatives of) wave functions at the origin and of nonperturbative universal constants once the factorization between the soft and ultrasoft scales is achieved by using an effective field theory where only ultrasoft degrees of freedom are kept as dynamical entities. This allows us to derive a new set of relations between inclusive heavy-quarkonium P-wave decays into light hadrons with different principal quantum numbers and with different heavy flavors. In particular, we can estimate the ratios of the decay widths of bottomonium P-wave states from charmonium data.

Within an effective field theory framework, we obtain an expression, with O(1/m^2) accuracy, for the energies of the gluonic excitations between heavy quarks, which holds beyond perturbation theory. For the singlet heavy quark--antiquark energy, in particular, we also obtain an expression in terms of Wilson loops. This provides, twenty years after the seminal work of Eichten and Feinberg, the first complete expression for the heavy quarkonium potential up to O(1/m^2) for pure gluodynamics. Several errors present in the previous literature (also in the work of Eichten and Feinberg) have been corrected. We also briefly discuss the power counting of NRQCD in the non-perturbative regime.

We compute the hyperfine splitting in a heavy quarkonium composed of different flavors in next-to-leading logarithmic approximation using the nonrelativistic renormalization group. We predict the mass difference of the vector and pseudoscalar charm-bottom mesons to be M(B∗c)−M(Bc)=65±24 (th)+19−16(δαs) MeV.

We determine the 1/m and 1/m 2 spin-independent heavy quarkonium potentials in the unequal mass case with $$ \mathcal{O} $$ (α 3) and $$ \mathcal{O} $$ (α 2) accuracy, respectively. We discuss in detail different methods to calculate the potentials, and show the equivalence among them. In particular we obtain, for the first time, the manifestly gauge invariant 1/m and 1/m 2 potentials in terms of Wilson loops with next-to-leading order (NLO) precision. As an application of our results we derive the theoretical expression for the B c spectrum in the weak-coupling limit through next-to-next-to-next-to-leading order (N3LO).

The next-to-leading nonperturbative contributions to heavy quarkonium systems are calculated. The applicability of the Voloshin-Leutwyler approach to heavy quarkonia systems for the physical cases of Bottomonium and Charmonium is investigated. We study whether the background gluon field correlation time can be considered to be infinity or not, by calculating the leading correction to this assumption and checking whether the expansion is under control. A phenomenological analysis of our results is also performed. The results make us feel optimistic about the $\Upsilon(1S)$ and to a lesser extent about the $J/\psi$ but do not about higher levels. We also briefly discuss the connection with different models where a finite gluon correlation time is introduced.

The standard definition of the electromagnetic radius of a charged particle (in particular the proton) is ambiguous once electromagnetic corrections are considered. We argue that a natural definition can be given within an effective field theory framework in terms of a matching coefficient. The definition of the neutron radius is also discussed. We elaborate on the effective field theory relevant for the hydrogen and muonic hydrogen, specially for the latter. We compute the hadronic corrections to the lamb shift (for the polarizability effects only with logarithmic accuracy) within heavy baryon effective theory. We find that they diverge in the inverse of the pion mass in the chiral limit.

We study the hydrogen and muonic hydrogen within an effective field theory framework. We perform the matching between heavy baryon effective theory coupled to photons and leptons and the relevant effective field theory at atomic scales. This matching can be performed in a perturbative expansion in $\ensuremath{\alpha},{1/m}_{p},$ and the chiral counting. We then compute the ${O(m}_{{l}_{i}}^{3}{\ensuremath{\alpha}}^{5}{/m}_{p}^{2}\ifmmode\times\else\texttimes\fi{}\mathrm{logarithms})$ contribution (including the leading chiral logarithms) to the hyperfine splitting and compare with experiment. They can explain about 2/3 of the difference between experiment and the pure QED prediction when setting the renormalization scale at the $\ensuremath{\rho}$ mass. We give an estimate of the matching coefficient of the spin-dependent proton-lepton operator in heavy baryon effective theory.

In a recent paper, we included two-loop, relativistic one-loop, and second-order relativistic tree level corrections, plus leading nonperturbative contributions, to obtain a calculation of the lower states in the heavy quarkonium spectrum correct up to, and including, $O({\ensuremath{\alpha}}_{s}^{4})$ and leading ${\ensuremath{\Lambda}}^{4}{/m}^{4}$ terms. The results were obtained with, in particular, the value of the two-loop static coefficient due to Peter; this has been recently challenged by Schr\"oder. In our previous paper we used Peter's result; in the present one we now give results with Schr\"oder's, as this is likely to be the correct one. The variation is slight as the value of ${b}_{1}$ is only one among the various $O({\ensuremath{\alpha}}_{s}^{4})$ contributions. With Schr\"oder's expression we now have ${m}_{b}{=5001}_{\ensuremath{-}66}^{+104} \mathrm{MeV},$ ${m}_{b}({m}_{b}^{2}{)=4454}_{\ensuremath{-}29}^{+45} \mathrm{MeV},$ ${m}_{c}{=1866}_{\ensuremath{-}133}^{+215} \mathrm{MeV},$ ${m}_{c}({m}_{c}^{2}{)=1542}_{\ensuremath{-}104}^{+163} \mathrm{MeV}.$ Moreover, $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Upsilon}}{e}^{+}{e}^{\ensuremath{-}})=1.07\ifmmode\pm\else\textpm\fi{}0.28 \mathrm{keV}(\mathrm{expt}=1.320\ifmmode\pm\else\textpm\fi{}0.04 \mathrm{keV})$ and the hyperfine splitting is predicted to be $M(\ensuremath{\Upsilon})\ensuremath{-}M(\ensuremath{\eta}{)=47}_{\ensuremath{-}13}^{+15} \mathrm{MeV}.$

We study the effect of resumming large logarithms in the determination of the bottom quark mass through a nonrelativistic sum rule analysis. Our result is complete at next-to-leading-logarithmic accuracy and includes some known contributions at next-to-next-to-leading logarithmic accuracy. Compared to finite order computations, the reliability of the theoretical evaluation is greatly improved, resulting in a substantially reduced scale dependence and a faster convergent perturbative series. This allows us to significantly improve over previous determinations of the $\overline{\mathrm{MS}}$ bottom quark mass, $\overline{{m}_{b}}$, from nonrelativistic sum rules. Our final figure reads $\overline{{m}_{b}}(\overline{{m}_{b}})=4.19\ifmmode\pm\else\textpm\fi{}0.06\text{ }\text{ }\mathrm{GeV}$.

We investigate the effects produced by the three-momentum scale $\sqrt{m\Lambda_{QCD}}$ in the strong coupling regime of heavy quarkonium. We compute the leading non-vanishing contributions due to this scale to the masses and inclusive decay widths. We find that they may provide leading corrections to the S-wave decay widths but only subleading corrections to the masses.

We consider a different power counting in potential NRQCD by incorporating the static potential exactly in the leading order Hamiltonian. We compute the leading relativistic corrections to the inclusive electromagnetic decay ratios in this new scheme. The effect of this new power counting is found to be large (even for top). We produce an updated value for the ηb decay to two photons. This scheme also brings consistency between the weak coupling computation and the experimental value of the charmonium decay ratio.

We obtain a model-independent expression for the Lamb shift in muonic hydrogen. This expression includes the leading logarithmic ${\cal O}(m_{\mu}\alpha^{6})$ terms, as well as the leading ${\cal O}(m_{\mu}\alpha^{5}\frac{m_{\mu}^{2}}{m_{\rho}^{2}})$ hadronic effects. The latter are controlled by the chiral theory, which allows for their model-independent determination. In this paper we give the missing piece for their complete expression including the pion and Delta particles. Out of this analysis, and the experimental measurement of the Lamb shift in muonic hydrogen, we determine the electromagnetic proton radius: $ r_{p}=0.8412(15)$ fm. This number is at $ 6.8\sigma$ variance with respect to the CODATA value. The accuracy of our result is limited by uncomputed terms of ${\cal O}\left(m_{\mu}\alpha^{5}\frac{m_{\mu}^{3}}{m_{\rho}^{3}},m_{\mu}\alpha^{6}\right)$ . This parametric control of the uncertainties allows us to obtain a model-independent estimate of the error, which is dominated by hadronic effects.

We compute the heavy quarkonium mass of $l\not= 0$ (angular momentum) states, with otherwise arbitrary quantum numbers, with next-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. This constitutes the first observable in heavy quarkonium for which two orders of the weak-coupling expansion sensitive to the ultrasoft scale are known and the resummation of ultrasoft logarithms is made. We also obtain, for the first time, resummed N$^3$LL expressions for the different fine and hyperfine energy splittings of these states, which are not sensitive to the ultrasoft scale but still require resummation of (hard) logarithms. We do this analysis for the equal and non-equal mass cases. We also study an alternative computational scheme that treats the static potential exactly. We then perform a comprehensive phenomenological analysis: we apply these results to the $n=2$, $l=1$ bottomonium, $B_c$ and charmonium systems and study their convergence.

We compute the energy of a static hybrid, i.e., of a hybrid quarkonium with static quark and antiquark, at short distances in $D=4,3$, dimensions. The soft contribution to this energy is the static potential of a color-octet quark-antiquark pair at short distances, which is known at two loops for arbitrary $D$. We have checked this expression employing thermal field theory methods. Using the effective field theory potential nonrelativistic QCD we calculate the ultrasoft contributions to the hybrid (and singlet) static energy at the two-loop level. We then present new results for the static hybrid energy/potential and the hybrid decay width in three and four dimensions. Finally we comment on the meaning of the perturbative results in two space-time dimensions, where the hybrid does not exist.

We compute the static potential associated with the locally $1/2$ BPS Wilson loop in $\mathcal{N}=4$ supersymmetric Yang-Mills theory with $\mathcal{O}({\ensuremath{\lambda}}^{2}/r)$ accuracy. We also resum the leading logarithms, of $\mathcal{O}({\ensuremath{\lambda}}^{n+1}{ln}^{n}\ensuremath{\lambda}/r)$, and show the structure of the renormalization group equation at next-to-leading order in the multipole expansion. In order to obtain these results it is crucial to use an effective theory for the ultrasoft degrees of freedom. We develop this theory up to next-to-leading order in the multipole expansion. Using the same formalism we also compute the leading logarithms, of $\mathcal{O}({\ensuremath{\lambda}}^{n+1}{ln}^{n}\ensuremath{\lambda}/r)$, of the static potential associated with an ordinary Wilson loop in the same theory.

Received 1 December 2009DOI:https://doi.org/10.1103/PhysRevLett.104.199901©2010 American Physical Society

We update our perturbative determination of MSbar bottom quark mass mb(mb), by including the recently obtained four-loop coefficient in the relation between the pole and MSbar mass. First the renormalon subtracted (RS or RS') mass is determined from the known mass of the Upsilon(1S) meson, where we use the renormalon residue Nm obtained from the asymptotic behavior of the coefficient of the 3-loop static singlet potential. MSbar mass is then obtained using the 4-loop renormalon-free relation between the RS (RS') and MSbar mass. We argue that the effects of the charm quark mass are accounted for by effectively using Nf=3 in the mass relations. The extracted value is mb(mb) = 4222(40) MeV, where the uncertainty is dominated by the renormalization scale dependence.

We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. Subleading effects are also considered. The perturbative series is regulated using the principal value prescription for its Borel integral. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: $\langle G^2 \rangle_{\rm PV} (n_f=0)=3.15(18)\; r_0^{-4}$.

We study the constraints that the operator product expansion imposes on large $N_c$ inspired QCD models for current-current correlators. We focus on the constraints obtained by going beyond the leading-order parton computation. We explicitly show that, assumed a given mass spectrum: linear Regge behavior in $n$ (the principal quantum number) plus corrections in $1/n$, we can obtain the logarithmic (and constant) behavior in $n$ of the decay constants within a systematic expansion in $1/n$. Our example shows that it is possible to have different large $n$ behavior for the vector and pseudo-vector mass spectrum and yet comply with all the constraints from the operator product expansion.

We compute the next-to-leading logarithmic (NLL) ultrasoft running of the spin-independent singlet potentials up to ${\cal O}(1/m^2)$, and the corresponding contribution to the spectrum. This includes the static energy at next-to-next-to-next-to-leading logarithmic (NNNLL) order. As a byproduct of these results one could obtain the heavy quarkonium spectrum with N$^3$LL accuracy for $l\not=0$ (angular momentum) and $s=0$ (spin) states, setting the stage for the full analytic and numerical N$^3$LL analysis of such quantity. We also compute the next-to-next-to-next-to-next-to-leading order (N$^4$LO) ultrasoft spin-independent contribution to the heavy quarkonium mass and static energy.

We obtain the renormalization group improved expressions of the Wilson coefficients of the heavy quark effective theory Lagrangian with leading logarithmic approximation to $\mathcal{O}(1/{m}^{3})$ for the spin-independent sector, which includes the heavy quark chromopolarizabilities. Our analysis includes the effects induced by spectator quarks. We observe that the numerical impact of these logarithms is very large in most cases.

We compute hadronic transitions between heavy quarkonium states with two, or one, pion/eta particles in the final state. We use the multipole expansion but not the twist expansion. The latter cannot be justified for the energy release of hadronic transitions between heavy quarkonium states with different principal quantum numbers. Instead, we use a counting based on the dimension of the interpolating field of the hybrid. This alternative counting allows us to still use chiral low-energy theorems to compute the pion production by local gluonic operators. We explore the phenomenological impact of this counting. Remarkably enough, for the two-pion transitions, we obtain the same predictions for the normalized differential decay rate as those obtained assuming the twist expansion. We implement this computational scheme using the hadronic representation of the effective theory potential NRQCD. We assume that the inverse Bohr radius of the heavy quarkonium is much larger than ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$ but do not impose any constraint on the relative size of ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$ and the typical kinetic energy of the bound state.

We study the operator product expansion of the plaquette (gluon condensate) and the self-energy of an infinitely heavy quark. We first compute their perturbative expansions to order α35 and α20, respectively, in the lattice scheme. In both cases we reach the asymptotic regime where the renormalon behavior sets in. Subtracting the perturbative series, we obtain the leading non-perturbative corrections of their respective operator product expansions. In the first case we obtain the gluon condensate and in the second the binding energy of the heavy quark in the infinite mass limit. The results are fully consistent with the expectations from renormalons and the operator product expansion.

We obtain an improved determination of the normalization of the leading infrared renormalon of the Bjorken sum rule: $Z_B (n_f=3)= -0.407\pm 0.119 $. Estimates of higher order terms of the perturbative series are given. We compute the Bjorken sum rule with hyperasymptotic precision by including the leading terminant, associated with the first infrared renormalon. We fit the experimental data to the operator product expansion theoretical prediction with $\hat f_{3}^{\rm PV}$ as the free parameter. We obtain a good agreement with the experiment with $\hat f_{3}^{\rm PV}\times 10^3=32^{+187}_{-196}\;{\rm GeV}^{2}$ for $Q^2 \geq 1$ GeV$^2$.

We study the large order behaviour in perturbation theory of the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules. In particular, we consider their first infrared renormalons, for which we obtain their analytic structure with logarithmic accuracy and also an approximate determination of their normalization constant. Estimates of higher order terms of the perturbative series are given. The Renormalon subtracted scheme is worked out for these observables and compared with experimental data. Overall, good agreement with experiment is found. This allows us to obtain {\hat a}_0 and some higher-twist non-perturbative constants from experiment: {\hat a}_0=0.141\pm 0.089; f_{3,RS}(1 GeV)=-0.124^{+0.137}_{-0.142} GeV^2.

We obtain the next-to-next-to-leading-logarithmic renormalization-group improvement of the spectrum of hydrogenlike atoms with massless fermions by using potential NRQED. These results can also be applied to the computation of the muonic hydrogen spectrum where we are able to reproduce some known double logarithms at $O(m{\ensuremath{\alpha}}_{s}^{6}).$ We compare with other formalisms dealing with logarithmic resummation available in the literature.

We review weakly-bound heavy quarkonium systems using effective field theories of QCD. We concentrate on potential non-relativistic QCD, which provides with a well founded connection between QCD and descriptions of the heavy quarkonium dynamics in terms of Schrödinger-like equations. This connection is obtained using standard quantum field theory techniques such as dimensional regularization, which is used throughout, and renormalization. Renormalization group equations naturally follow. Certain effort is made to illustrate how computations are performed, and the necessary techniques, providing some examples. Finally, we briefly review a selected set of applications, which include spectroscopy, radiative transitions, non-relativistic sum rules, inclusive decays, and electromagnetic threshold production.

The ratio of the photon mediated production or annihilation rates of spin triplet and spin singlet heavy quarkonium states is computed to the next-to-next-to-leading logarithmic accuracy within the nonrelativistic renormalization group approach. The result is presented in analytical form and applied to the phenomenology of $t\bar{t}$, $b\bar{b}$ and $c\bar{c}$ systems. The use of the nonrelativistic renormalization group considerably improves the behaviour of the perturbative expansion and is crucial for accurate theoretical analysis. For bottomonium decays we predict $\Gamma(\eta_b(1S) \to \gamma\gamma)=0.659\pm 0.089 ({\rm th.}) {}^{+0.019}_{-0.018} (\delta \alpha_{\rm s})\pm 0.015 ({\rm exp.}) {\rm keV}$. Our results question the accuracy of the existing extractions of the strong coupling constant from the bottomonium annihilation. As a by-product we obtain novel corrections to the ratio of the ortho- and parapositronium decay rates: the corrections of order $\alpha^4\ln^2\alpha$ and $\alpha^5\ln^3\alpha$.

We study the static potential of a color singlet quark-antiquark pair with (fixed) distance $r$ in $D=3$ and $D=2$ space-time dimensions at weak coupling ($\ensuremath{\alpha}r\ensuremath{\ll}1$ and $gr\ensuremath{\ll}1$, respectively). Using the effective theory potential nonrelativistic QCD (pNRQCD) we determine the ultrasoft contributions, which cannot be computed in conventional perturbative QCD. We show in detail how the ultrasoft renormalization in pNRQCD is carried out. In three dimensions the precision of our results reaches $\mathcal{O}({\ensuremath{\alpha}}^{3}{r}^{2})$, i.e. next-to-next-to-leading order (NNLO) in the multipole expansion, and next-to-next-to-leading logarithmic order (NNLL) in a $\ensuremath{\alpha}/\ensuremath{\Delta}V$ expansion, where $\ensuremath{\Delta}V\ensuremath{\sim}\ensuremath{\alpha}\mathrm{ln}(\ensuremath{\alpha}r)$. We even present results up to partly ${\mathrm{N}}^{4}\mathrm{LL}$ order and compare them to existing lattice data. Finally we discuss the relevance of the perturbative calculation in two dimensions, where the exact result is known.

We obtain the corrections in 1/n and in 1/ln n (n is the principal quantum number of the bound state) of the decay constants of scalar and pseudoscalar currents in two and four dimensions in the large Nc. We obtain them from the operator product expansion provided a model for the large n mass spectrum is given. In the two-dimensional case the spectrum is known and the corrections obtained in this paper are model independent. We confirm these results by confronting them with the numerical solution of the 't Hooft model. We also consider a model at finite Nc and obtain the associated decay constants that are consistent with perturbation theory. This example shows that that the inclusion of perturbative corrections, or finite Nc effects, to the OPE does not constrain the slope of the Regge trajectories, which remain a free parameter for each different channel.

These proceedings review recent work on hyperasymptotic constructions to the operator product expansion. Quantities we consider are the static potential and the pole mass.

We study QCD in 1+1 dimensions in the large Nc limit using light-front Hamiltonian perturbation theory in the 1/Nc expansion. We use this formalism to exactly compute hadronic transition matrix elements for arbitrary currents at leading order in 1/Nc. We compute the semileptonic differential decay rate of a heavy meson, dΓ/dx, and its moments, MN, using the hadronic matrix elements obtained previously. We put some emphasis in trying to understand parity invariance. We also study with special care the kinematic region where the operator product expansion (1/N ∼ 1−x ∼ 1) or non-local effective field theories (1/N ∼ 1−x ∼ ΛQCD/mQ) can be applied. We then compare with the results obtained using an effective field theory approach based on perturbative factorization, with the focus to better understand quark-hadron duality. At the end of the day, using effective field theories, we have been able to obtain expressions for the moments with relative accuracy of O(ΛQCD2/mQ2) in the kinematic region where the operator product expansion can be applied, and with relative accuracy of O(ΛQCD/mQ) in the kinematic region where non-local effective field theories can be applied. These expressions agree, within this precision, with those obtained from the hadronic result using the layer-function approximation plus Euler-McLaurin expansion. Very good numerical agreement for the moments is obtained between the exact result and the result using effective field theories.

We consider the $${\mathcal {O}}(1/m)$$ and the spin-independent momentum-dependent $${\mathcal {O}}(1/m^2)$$ quasi-static energies of heavy quarkonium (with unequal masses). They are defined nonperturbatively in terms of Wilson loops. We determine their short-distance behavior through $$\mathcal{O}(\alpha ^3)$$ and $$\mathcal{O}(\alpha ^2)$$ , respectively. In particular, we calculate the ultrasoft contributions to the quasi-static energies, which requires the resummation of potential interactions. Our results can be directly compared to lattice simulations. In addition, we also compare the available lattice data with the expectations from effective string models for the long-distance behavior of the quasi-static energies.

We argue that the lattice data of the static potential can be explained by perturbation theory up to energies of the order of 1 GeV once renormalons effects are taken into account.

Recent results of the ATLAS experiment at LHC on decay properties of b-hadrons are reviewed. The time-dependent CP asymmetry parameters have been measured in Bs0→J/ψϕ decays using flavour tagging. The parity-violating decay asymmetry parameter αb and the helicity amplitudes have been measured for the decay Λb0→J/ψΛ0. The branching fraction B(B+→χc1K+) has been measured with χc1 reconstruction in the decay χc1→J/ψγ. An excited Bc± state has been observed through its decays to the ground Bc± state and two oppositely charged pions. The mass and decay of this state are consistent with expectations for the second S -wave state of the Bc± meson, Bc±(2S).

We obtain the potential nonrelativistic quantum chromodynamics Lagrangian relevant for $S$-wave states with next-to-next-to-next-to-leading logarithmic accuracy. We compute the heavy quarkonium mass of spin-averaged $l=0$ (angular momentum) states, with otherwise arbitrary quantum numbers, with next-to-next-to-next-to-leading logarithmic accuracy. These results are complete up to a missing contribution of the two-loop soft running.

We complete the computation of the Yang–Mills vacuum wave functional in three dimensions at weak coupling with O(e2) precision. We use two different methods to solve the functional Schrödinger equation. One of them generalizes to O(e2) the method followed by Hatfield at O(e) [1]. The other uses the weak coupling version of the gauge invariant formulation of the Schrödinger equation and the ground-state wave functional followed by Karabali, Nair, and Yelnikov [2]. These methods need to be carefully regularized to yield correct results. This is done in this paper with full detail.

tolerances, with standard drift chamber resolutions ({approximately} 100{mu}m), and with no reliance on the performance of an inner tracking system. Robustness is provided by additional momentum measurements in the inner tracker and in a solid iron spectrometer utilizing the magnet`s return yoke. The total cost of the system, including proper magnetic shielding for the magnet and a forward-backward iron-core toroid muon detection system with {Delta}p/p {approx_equal} 9%, is comparable to that of the low-field L*/GEM approach that does not provide a magnetic flux return nor a forward-backward iron system. The magnet leaves the same amount of space for inner detector items as does the large, low-field L*-type system, while providing a substantially higher magnetic field in the inner tracking volume.

Leading nonperturbative effects to fine and hyperfine splittings were calculated some time ago. Recently, they have been used in order to obtain realistic numerical results for the lower levels in bottomonium systems. We point out that a contribution of the same order $O({\ensuremath{\Lambda}}_{\mathrm{QCD}}^{4}{/m}^{3}{\ensuremath{\alpha}}_{s}^{2})$ has been overlooked. We calculate it in this paper.

We compute the Yang-Mills vacuum wave functional in three dimensions at weak coupling with $\mathcal{O}({e}^{2})$ precision. We use two different methods to solve the functional Schr\"odinger equation. One of them generalizes to $\mathcal{O}({e}^{2})$ the method followed by Hatfield at $\mathcal{O}(e)$ [Phys. Lett. B 147, 435 (1984)]. The other uses the weak coupling version of the gauge invariant formulation of the Schr\"odinger equation and the ground state wave functional followed by Karabali, Nair, and Yelnikov [Nucl. Phys. B824, 387 (2010)]. We compare both results and discuss the differences between them.

Received 27 August 2018DOI:https://doi.org/10.1103/PhysRevD.98.059902Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasPerturbation theoryQuantum chromodynamicsRenormalization groupResummation methodsParticles & Fields

We study some general aspects of the formalism of potential NRQCD (pNRQCD), an effective field theory that deals with ultrasoft degrees of freedom in Heavy Quarkonium systems. Specific attention is paid to its effective Lagrangian that it is displayed at the present level of accuracy.

We study in detail deep inelastic scattering in the 't Hooft model. We are able to analytically check current conservation and to obtain analytic expressions for the matrix elements with relative precision O(1/Q^2) for 1-x >> \beta^2/Q^2. This allows us to compute the electron-meson differential cross section and its moments with 1/Q^2 precision. For the former we find maximal violations of quark-hadron duality, as it is expected for a large N_c analysis. For the latter we find violations of the operator product expansion at next-to-leading order in the 1/Q^2 expansion.

The leading nonperturbative effects to the fine and hyperfine splitting were calculated some time ago. Recently, they have been used in order to obtain realistic numerical results for the lower levels in bottomonium systems. We point out that a contribution of the same order $O(\Lambda_{QCD}^4/m^3 \alpha_s^2)$ has been overlooked. We calculate it in this paper.

We consider deep inelastic scattering in the 't Hooft model. Being solvable, this model allows us to directly compute the moments associated with the cross section at next-to-leading order in the $1/{Q}^{2}$ expansion. We perform the same computation using the operator-product expansion. We find that all the terms match in both computations except for one in the hadronic side, which is proportional to a nonlocal operator. The basics of the result suggest that a similar phenomenon may occur in four dimensions in the large ${N}_{c}$ limit.

Antecedentes: La enfermedad por coronavirus 2019 (COVID-19) representa mayores riesgos para personas con diabetes, pero se desconoce si el riesgo percibido de COVID-19 afecta la adherencia a la medicación de pacientes con diabetes.Objetivo: Explorar la asociación entre percepción del riesgo de COVID-19 y adherencia a la medicación.Material y método: El estudio fue transversal, con 365 pacientes atendiéndose en un hospital público para tratar su diabetes tipo 2. Resultados: La percepción de riesgo de COVID-19 no se asoció con las intenciones de adherencia (β = 0.002, p = 0.477) ni adherencia (β = -0.001,p = 0.736).Conclusiones: Los resultados sugieren que la toma de decisión relacionada con la medicación para la diabetes permanece igual, sin importar la menor o mayor percepción de riesgo de COVID-19.

Abstract Despite the development of novel therapies for acute myeloid leukemia (AML), outcomes remain poor for most patients, and therapeutic improvements are an urgent unmet need. Although treatment regimens promoting differentiation have succeeded in the treatment of acute promyelocytic leukemia (APL), their role in other AML subtypes needs to be explored. Here we identified and characterized two lysine (K) deacetylase inhibitors (DACi), CM-444 and CM-1758, exhibiting capacity to promote myeloid differentiation in all AML subtypes at low non-cytotoxic doses unlike other commercial HDACi. Analyzing the acetylome after CM-444 and CM-1758 treatment revealed modulation of non-histone proteins involved in the enhancer–promoter chromatin regulatory complex, including bromodomain proteins (BRDs). This acetylation was essential for enhancing the expression of key transcription factors directly involved in the differentiation therapy induced by CM-444/CM-1758 in AML. In summary, these compounds may represent effective differentiation-based therapeutic agents across AML subtypes with a novel mechanism for treatment of AML.

Abstract In this talk, we briefly review work which led to the numerical demonstration of the existence of renormalons in four dimensional gauge theories with marginal operators.

Abstract Resistance mechanisms compromise response to single targeted therapies, favoring the idea that combinatorial strategies are key to circumvent this clinical problem. Combinatorial strategies for cancers driven by oncogenic KRAS based on MEK1/2 or KRASG12C inhibitors have so far incorporated abrogation of KRAS proximal effectors involved in oncogenesis or treatment resistance. However, the antitumor effect is highly determined by compensatory mechanisms specifically arising in certain cell types or tumor subgroups. A potential strategy to find drug combinations spanning a large percentage of mutant KRAS lung cancers may capitalize on the common, distal gene expression output elicited by oncogenic KRAS. Here, integrating a signature-driven drug repurposing approach and a pairwise pharmacological screen, we identify a synergistic drug combination consisting of multityrosine kinase PKC and MEK1/2 inhibitors. The drug combination functions in a genotype specific manner, elicits a cytotoxic response both in vitro and in vivo models, and in part involves inhibition of AURKB. Furthermore, we show that the KRASG12C inhibitor Sotorasib can replace the MEK inhibitor with similar cellular and molecular results, including antitumor effect in a genetically engineered mouse model of lung cancer driven by KRasG12C . Proteome profiling links dysregulation of MYC expression to the effect of PKC inhibitor-based drug combinations. Furthermore, we demonstrate that MYC overexpression functions as a resistance mechanism to MEK1/2 and KRASG12C inhibitors. Our study provides a rational framework to nominate drugs entering combinatorial strategies and unveils novel MEK1/2- and KRASG12C-based therapies for lung cancer.

New variants of the Padé approximants (PA) are defined aiming to reproduce the correct hierarchy of the renormalon behavior. These types of PAs are motivated by the appearance of branch cuts instead of poles in the Borel plane of the perturbative series. The first variant of PAs wants to highlight dominant cuts in the Borel plane and it is called D-Log Padé approximant. This method converts the original branch cut into poles through derivatives, where we implement the PA to finally return to the original function. The second method is named Confluent Padé approximant and takes the approximants to the subdominant confluent singularities in the Borel plane which must be considered before moving to the other singular values. We apply the method to the Bjorken Sum Rule, giving a prediction of the next coefficient in the perturbation series.

We show that the infinite imaginary anomalous dimensions of certain heavy quark-antiquark currents in the HQET arise due to an inappropriate commutation of two limits, namely coinciding velocities and infinite cut-off. This commutation is not apparent when dimensional regularization is used, but it can be made manifest in a cut-off regularization. We argue that operators containing heavy quark and antiquark fields with the same velocity in the HQET must not be matched to perturbative QCD but to Coulomb-type bound state contributions. We show how to do so at one loop level.

In Refs. [1,2] we determined the infinite volume coefficients of the perturbative expansions of the self-energies of static sources in the fundamental and adjoint representations in SU(3) gluodynamics to order $\alpha^{20}$. We used numerical stochastic perturbation theory [3], where we employed a new second order integrator and twisted boundary conditions. The expansions were obtained in lattice regularization with the Wilson action and two different discretizations of the covariant time derivative within the Polyakov loop. Overall, we obtained four different perturbative series. For all of them the high order coefficients displayed the factorial growth predicted by the conjectured renormalon picture, based on the operator product expansion. This enabled us to determine the normalization constants of the leading infrared renormalons of heavy quark and heavy gluino pole masses. Here we present improved determinations of the normalization constants and the perturbative coefficients by incorporating the four-loop beta-function coefficient (which we also determine) in the fit function.

We review recent model independent determinations of the radiative transitions of heavy quarkonium obtained using potential NRQCD.

Recently the muonic hydrogen lamb shift has been measured with unprecedented accuracy, allowing for a precise determination of the proton radius. This determination is 5 sigma away from the previous CODATA value obtained from (mainly) the hydrogen lamb shift and the electron-proton scattering. Within an effective field theory formalism, I will define the proton radius and briefly review some aspects of the theoretical prediction for the muonic hydrogen lamb shift, studying both the pure QED-like computation and the hadronic effects.

This experimental work reports the results obtained on the effect of two different zinc precursors (zinc nitrate and zinc acetate), using sodium hydroxide as precipitant agent and different parameters on the synthesis of zinc oxide powders, applying the Taguchi method. The zinc oxide powders were synthesized by the homogeneous precipitation technique. All the resultant precipitates in the process were dried and calcined to produce zinc oxide powders. The powders were characterized by X-ray diffraction and scanning electron microscopy. The characterization results revealed a hexagonal wurtzite structure with an average particular size of 34.4 to 53.5 nanometers. All the synthesized particles presented different sizes with an irregular geometry.

Recently the muonic hydrogen lamb shift has been measured with unprecedented accuracy, allowing for a precise determination of the proton radius. This determination is 5 sigma away from the previous CODATA value obtained from (mainly) the hydrogen lamb shift and the electron-proton scattering. Within an effective field theory formalism, I will define the proton radius and briefly review some aspects of the theoretical prediction for the muonic hydrogen lamb shift, studying both the pure QED-like computation and the hadronic effects.