L. Lyons

Experiments to measure a single physical quantity often produce several estimates based on the same data, and which are hence correlated. We describe how to combine these correlated estimates in order to provide the best single answer, and also how to check whether the correlated estimates are mutually consistent. We discuss the properties of our technique, and illustrate its application by using it for a specific experiment which measured the lifetime of charmed particles.

This book, written by a non-statistician for non-statisticians, emphasises the practical approach to those problems in statistics which arise regularly in data analysis situations in nuclear and high-energy physics experiments. Rather than concentrating on formal proofs of theorems, an abundant use of simple examples illustrates the general ideas which are presented, showing the reader how to obtain the maximum information from the data in the simplest manner. Possible difficulties with the various techniques, and pitfalls to be avoided, are also discussed. Based on a series of lectures given by the author to both students and staff at Oxford, this common-sense approach to statistics will enable nuclear physicists to understand better how to do justice to their data in both analysis and interpretation.

It is usually straightforward to calculate the result of a practical experiment in the laboratory. Estimating the accuracy of that result is often regarded by students as an obscure and tedious routine, involving much arithmetic. An estimate of the error is, however, an integral part of the presentation of the results of experiments. This textbook is intended for undergraduates who are carrying out laboratory experiments in the physical sciences for the first time. It is a practical guide on how to analyse data and estimate errors. The necessary formulas for performing calculations are given, and the ideas behind them are explained, although this is not a formal text on statistics. Specific examples are worked through step by step in the text. Emphasis is placed on the need to think about whether a calculated error is sensible. At first students should take this book with them to the laboratory, and the format is intended to make this convenient. The book will provide the necessary understanding of what is involved, should inspire confidence in the method of estimating errors, and enable numerical calculations without too much effort. The author's aim is to make practical classes more enjoyable. Students who use this book will be able to complete their calculations quickly and confidently, leaving time to appreciate the basic physical ideas involved in the experiments.

The inclusive cross section for larger pTπ0 production near 90° in p-p collisions at the CERN ISR is presented for centre-of-mass energies 30.7, 53.1 and 62.4 GeV. The data are inconsistent with scaling of the form pT−nF(xT), with constant n or with n allowed to depend on xT = 2pT/s. For s = 53.1 and 62.4 GeV, the value of n found for 3.5 < pT < 7.0 GeV/c is n = 8.0 ± 0.5, in agreement with previous experiments. However, for 7.5 < pT < 14.0 GeV/c the value becomes n = 5.1 ± 0.4.

A study has been made of some of the quasi-two-body final states (in which one of the particles is a hyperon) produced by 3.5-GeV/c K− mesons on protons. The analysis has been performed with 310 000 photographs taken in the 81-cm Saclay hydrogen bubble chamber. The cross sections for most of the reactions are lower than have been observed at lower incident momenta. Many of the reactions are characterized by a forward peaking of the production angular distribution of the final-state meson, but in a few cases a significant backward peak has been observed. Decay distributions of unstable particles have been investigated to obtain more information about the production processes. The Y1*+(1385) decay is consistent with the Y*π− final state being produced by K* exchange, but in the case of the production of vector mesons, it is difficult to draw any conclusion concerning the spin of the exchanged particle. An enhancement was observed at 1645 MeV in the Σ±π∓ system. It is difficult to interpret this in terms of the decay of the neutral Y1*(1660).Received 4 April 1966DOI:https://doi.org/10.1103/PhysRev.152.1148©1966 American Physical Society

After an introductory discussion of the history of substructure and of the motivations for examining the possible compositeness of quarks and leptons, experiments which could be relevant to the non-point-like nature of these fermions are reviewed. Where possible the data are used to deduce limits on the substructure energy scale. Starting with very early ideas about quark and lepton substructure, we go on to summarise some of the specific models which have recently been proposed. They are very varied, but a general discussion is given about common topics which such models consider (e.g. the nature of the binding mechanism, the problem of the masses of the composite systems, the way in which fermion generations arise, whether to make weak intermediate bosons composite, etc.). In considering individual models, emphasis is placed on what specific predictions can be tested experimentally. We conclude that experiments in the near future could significantly increase the energy range in which substructure can be probed. This may then provide a more realistic basis on which to judge whether quarks and leptons are composite.

Many statistical issues arise in the analysis of Particle Physics experiments.We give a brief introduction to Particle Physics, before describing the techniques used by Particle Physicists for dealing with statistical problems, and also some of the open statistical questions.

Results are presented of a 12 event/μb bubble-chamber experiment; the reactions discussed in detail are K−p → K∗ (890)−p, K∗ (1420)−p and K∗ (890)−Δ+.The K∗ (890)−p channel is dominated by the forward peak. The suggestion of flattering at cos θ = 1 is more pronounced in (ϱ11 + ϱ1−1) dσdt; which is mainly natural-parity exchange. Pseudoscalar exchange contributes to ϱ00Jdσdt; this is more sharply peaked in t. The value of (ϱ11 − ϱ1−1) dσdt is somewhat larger than the upper limit from the dominant natural-parity exchange. There is significant structure in ϱ00H dσdt at t ≈ −0.6 (GeV/c)2.The K∗ (1420)−p channel is much more pronounced at 3.3 GeV/c than at 3.13 GeV/c, but is not markedly peripheral. The width of the K∗ (1420) in the 3.3 GeV/c data is 42 ± 12 MeV/c2.The cross section for K∗− Δ+ agrees with that expected from K+p → K∗Δ, assuming a single t-channel exchange. Our measured density matrix elements are consistent with a strong pseudoscalar exchange.

The inclusive cross sections for forward D meson production at s=26 GeV in π−p interactions have been measured to be: σ(π−p→D0/D0+X)xF>0 = (10.1±2.2)μb, σ(π−p→D±+X)xF>0 = (5.7±1.6)μb. The distribution in xF for all D and for xF>0 has the form dσ/dxF=107−37+39(1−xF)7.5−1.7+2.5+5.4−3.8+6.0(1−xF)0.7−0.71.0μ b, with evidence for leading D production. The pT2 distribution is exponential with slope parameter [−1.18−0.16+0.18](GeV/ c)−2. The data are compared with predictions from first-order quark/gluon fusion calculations.

A study of the properties of charm particles produced in 400 GeV/cpp interactions is reported. The experiment was performed using the high resolution hydrogen bubble chamber LEBC in association with the European Hybrid Spectrometer at the CERN SPS. Details of the experimental set-up and operational procedures are given and the methods to extract samples of charm decays are discussed. Results are presented on the intrinsic properties of charm particles (masses, lifetimes, decay modes and branching ratios), adding, whenever appropriate, the relevant information obtained in a similar study made with 360 GeV/cπ − p interactions. The hadroproduction properties of charm states (total and differential cross sections, correlations) are presented and discussed in the context of current QCD inspired phenomenology.

This book, written by a non-statistician for non-statisticians, emphasises the practical approach to those problems in statistics which arise regularly in data analysis situations in nuclear and high-energy physics experiments. Rather than concentrating on formal proofs of theorems, an abundant use of simple examples illustrates the general ideas which are presented, showing the reader how to obtain the maximum information from the data in the simplest manner. Possible difficulties with the various techniques, and pitfalls to be avoided, are also discussed. Based on a series of lectures given by the author to both students and staff at Oxford, this common-sense approach to statistics will enable nuclear physicists to understand better how to do justice to their data in both analysis and interpretation.

A study of the properties of charm particles produced in 360 GeV/c π- p interactions is reported. The experiment was performed using the high resolution hydrogen bubble chamber LEBC in association with the European Hybrid Spectrometer at the CERN SPS. Details of the exposure and operation of the spectrometer are given and the methods used to extract the charm data are presented. The essential physics results on the decay properties (lifetime, branching ratios) as well as on the hadroproduction properties (cross sections forD, $$\bar D$$ ,F, Λ c ,D, correlations between charm particles) are given.

To introduce the ideas of statistical and systematic errors, this review first describes a simple pendulum experiment. We follow with a brief discussion of the Bayesian and frequentist approaches. Two widely used applications of statistical techniques in particle physics data include extracting ranges for parameters of interest (e.g., mass of the W boson, cross section for top production, neutrino mixing angles, etc.) and assessing the significance of possible signals (e.g., is there evidence for Higgs boson production?). These two topics are first discussed in the absence of systematics, and then methods of incorporating systematic effects are described. We give a detailed discussion of a Bayesian approach to setting upper limits on a Poisson process in the presence of background and/or acceptance uncertainties. The relevance of the choice of priors and how this affects the coverage properties of the method are described.

Cross sections are given for the main processes contributing to the final states ppπ+π−, ppπ+π−π0 and pnπ+π+π−. In all reactions N∗(1238) is observed to be strongly produced. For these three reactions the baryons are strongly forward/backward peaked in the c.m. The reaction pp → N∗++(1238)pπ− has been examined in some detail, and compared with the predictions of various peripheral models. As is already well known, the Ferrari-Selleri model is inadequate, but when some of the effects of absorption are included, the agreement with the data is considerably improved. The alternative of replacing the propagator corresponding to elementary pion exchange by that for a Regge exchange also gives good agreement with experiment. Finally we have tested a double-Regge-exchange model, and found that its prediction for one of the Treiman-Yang angles is unsatisfactory. A discussion is also given of a classification in which events are divide into categories depending on which particles are emitted in the same hemisphere. The two groupings p(pπ+π−) and (pπ+)(pπ−) each accounts for approximately half of the ppπ+π− final state. The final states ppω, ppη and possibly ppϱ0 are observed, and cross sections are compared with values obtained at other momenta. An attempt to deduce the reaction mechanism from the longitudinal momentum plot is discussed in an appendix.

The undoubted successes of the quark model in the fields of hadron spectroscopy and hard scattering processes have raised the question of whether free quarks exist. We review those recent experiments that have looked for quarks in experiments at accelerators, and in cosmic rays. The accelerator experiments include heavy ion reactions, pp and e+e− collisions, and deep inelastic scattering of leptons. Some of the cosmic ray experiments search for fractional charge, while others look for unusual mass particles, which need not necessarily be quarks; an example of the latter type is the delayed air shower search. A brief mention is also made of stable matter searches, future experiments, and various ideas and speculations concerning quarks, which may be of relevance to the experimental search for them.

Charm D-meson production in 360 GeV π−p interactions has been studied using the high-resolution hydrogen bubble chamber LEBC and the European Hybrid Spectrometer. The data show evidence for leading quark effects both in the number of D-meson types and in the Feynman x distributions. The production cross section is of the form d2δdxdpT2∞(1-x)nexp(-apT2) with n = 2.8±0.8 and a = 1.1±0.3 (GeV/c)−2. The x distribution is, however, compatible with the presence of both central (n = 6) and leading (n = 1) D/Dproduction. The fraction of D-messons in the leading component is estimated to be ≈30%. The rapidity gap between members of reconstructed charm pairs is small compared to the available rapidity range. The inclusive cross section for single D-messons in the forward direction is: δ(D/D)=(408+15)μb (forx>0).

Charm D-meson production in 360 GeV pp interactions has been studied using the high-resolution hydrogen bubble chamber LEBC and the European Hybrid Spectrometer. D-mesons are produced with a differential cross section of the form d2σdx dpT2δ(1-x)n exp (-apT2), withn=1.8± 0.8 and a=1.1±0.03 GeV/c−2 for the Feynman x and Transverse momentum pT behaviour. The inclusive partle prticle crossssection for D and D̄;measured to be: σ(D/D̄) = (56−12 25μb (for all x). The ΛcD̄ cross section can be estimated to be ≈20μb. No strong correlation is observed between DD̄ pairs. The results are compared with results from a study of D-meaon production in 360 GeV/c π−p interactions also using LEBC-EHS.

The vector meson production, hypercharge exchange reactions K−p → (φ, ω, ϱ) Λ and (φ, ϱ) Σ0 are studied at 4.2 GeV/c incident momentum. The data come from a high statistics bubble chamber experiment with a sensitivity of ∼ 120 events/μb. Total and differential cross sections are presented. The vector meson density matrix elements and hyperon polarization are investigated as functions of momentum transfer. Amplitude analyses are performed for all five reactions. The results are compared with duality and quark model predictions, as well as used to test current ideas in two-body phenomenology.

A large solid-angle apparatus consisting of a superconducting solenoid magnet, cylindrical drift chambers, and two arrays of lead-glass counters is used to examine particles associated with a high transverse momentum trigger in pp interactions at the CERN ISR.

The Oxford 12 cm deuterium bubble chamber has been used to examine the reactions p+d→p+d, p+d→p+p+n, at an incident proton energy of 77 MeV. The total cross-section (excluding elastic scattering below 10° c.m.) is found to be 146±8 mb. The elastic differential cross-section, measured over the angular range 5°–180° (c.m.) is compared with the impulse approximation theory. The low statistical accuracy of the experiment does not allow a detailed examination of the inelastic events to be made, but some general features are discussed. Chew-Low extrapolations have been performed to determine the free p-p and n-p cross sections.

Abstract An enhancement is observed in Λ 0 π + effective mass in the reaction K − + p → Λ 0 + π + + π − at 6 GeV/ c . The lack of any large enhancements in other final states, as well as the shape and position of the peak, suggest that it is due to the new hyperon resonance, the Y 1 ∗ (1700), since it cannot be explained in terms of the known Y 1 ∗ (1660) and Y 1 ∗ (1765).

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Charm-charm correlation properties are studied in detail for the first time using a sample of DD pairs produced in 360 GeV/c π−p interactions. The data are compared with various models of charm production.

The inclusive reactions pn → ps + x and π+n → ps + x at incident momentum of 195 GeV/c have been studied in an exposure of the Fermilab 30 inch deuterium filled bubble chamber to a mixed (π+, p) beam. Analysing the t and M2 dependence of our data within the framework of triple-Regge models we conclude that pion exchange yields a dominating contribution. Comparing our data with the pp results we conclude that isoscalar Regge exchange, ω, is much larger than isovector, ϱ, Regge exchange. We observe significant leading π− emission from the recoiling mass x, comparable to that observed in on-mass-shell π−p → π− experiments. This verifies our conclusions about pion-exchange dominance in the above reactions.

A bubble chamber experiment has been performed to study the deuteron-deuteron interaction in the momentum range 270 to 507 MeV/c. Results are presented for elastic scattering, the stripping reactions and the inelastic reactions. The elastic scattering differential cross-section for the incident momentum range 433 to 507 MeV/c is compared with impulse approximation calculations.

Recently, much attention has been focused on the replicability of scientific results, causing scientists, statisticians, and journal editors to examine closely their methodologies and publishing criteria.Experimental particle physicists have been aware of the precursors of nonreplicable research for many decades and have many safeguards to ensure that the published results are as reliable as possible.The experiments require large investments of time and effort to design, construct, and operate.Large collaborations produce and check the results, and many papers are signed by more than 3,000 authors.This article gives an introduction to what experimental particle physics is and to some of the tools that are used to analyze the data.It describes the procedures used to ensure that results can be computationally reproduced, both by collaborators and by noncollaborators.It describes the status of publicly available data sets and analysis tools that aid in reproduction and recasting of experimental results.It also describes methods particle physicists use to maximize the reliability of the results, which increases the probability that they can be replicated by other collaborations or even the same collaborations with more data and new personnel.Examples of results that were later found to be false are given, both with failed replication attempts and one with alarmingly successful replications.While some of the characteristics of particle physics experiments are unique, many of the procedures and techniques can be and are used in other fields.

A superconducting solenoid at the CERN ISR has been equipped with a system of high accuracy cylindrical drift chambers. This detector consists of eight layers of field shaped drift cells with a delay line opposite each sense wire to provide coupled two dimensional readout. The design, construction, and operation of this system are discussed. The resolution and performance of the delay lines and sense wires under ISR running conditions are shown.

The reaction pn → Δ++Δ− with σ = 1.1 ± 0.2 mb is studied at 6.98 GeV/c. Comparison with the reactions pp → ΔΔ and pp → ΔΔ at different incident momenta shows that their cross section behaves like Plab−2.5±0.3, consistent with one-pion exchange. The production and decay of Δ++Δ− at small momentum transfer agrees with the OPE model with sharp cut-off at R = 1.3 fm. The decay correlations are also compared with some quark-model predictions.

The current estimate of the $B$ lifetime is obtained by averaging the results of six experiments. We point out problems connected with the conventional approach to combining data and discuss ways of overcoming them. Our recommended value is 1.13\ifmmode\pm\else\textpm\fi{}0.15 ps. Our discussion is relevant to a wide range of problems in which data are combined.

The experimental data on the production of μ+μ− and e+e− pairs in hadronic interactions are reviewed. The region above ∼ 3 GeV in lepton pair mass is considered, with continuum and resonance contributions being dealt with separately. The continuum is compared critically with the predictions of the naive Drell-Yan model of qq annihilation, and its limitations are discussed. To the extent that the simple model is applicable, quark distributions in hadrons can be extracted; these supplement information from other sources. Embellishments to the simplest Drell-Yan picture, and their degree of success in explaining the data, are considered. Higher order QCD processes may be the dominant mechanism, especially at large transverse momentum. Resonance production (of the ψ and γ families) differs from the continuum. Various mechanisms, differing at the level of which partons contribute, have been proposed. None of these on its own seems adequate, but a picture of what sort of mixture is required is emerging. The aim for the future is to check in more detail the higher order corrections to the Drell-Yan process for the continuum, and to test more stringently whether a mechanism involving subprocesses whose relative magnitudes are derived theoretically really does describe well all aspects of resonance production. This may then enable us to use lepton pair data to probe in greater detail the parton structure of hadrons, and to understand better the relevance of higher order QCD phenomena to hard scattering processes.

We discuss the traditional criterion for discovery in Particle Physics of requiring a significance corresponding to at least 5 sigma; and whether a more nuanced approach might be better.

Many analyses of data in High Energy Physics are concerned with searches for New Physics. We review the statistical issues that arise in such searches, and then illustrate these using the specific example of the recent successful search for the Higgs boson, produced in collisions between high energy protons at CERN's Large Hadron Collider.

Charm data from 360 GeV/c π− p interactions are used to give results on D-meson branching ratios. The analysis is based on 114 charm events containing 183 observed charm particle decays. We present topological branching ratios and decay multiplicities, as well as the following inclusive branching ratios of D-mesons: B(D± → K∓ + anything) = 0.16−0.07 +0.08, if B(D0 → K ± + anything) = 0.44−0.10+0.11, ifB(D± → e± + 2,4 (rmcharged hadrons) = 0.07−0.05++0.08, B(D0 → e ± + anything) = 0.17−0.06+0.08.

Results of fitting the differential distributions in xF and pT2 of D mesons produced in 400 GeV/c p-p interactions to the form d2σdxFdpT2∝(1−xF)nexp[−(pT2/〈pT2〉)] are discussed. The D+ distribution is found to be relatively hard [n=3.1±0.8〈Pt2〉=1.32±0.27 (GeV/c)2] and the D̄0 distribution relatively soft [n=8.1±1.9,〈pT2〉=0.62±0.14 (GeV/c)2] compared to the average for all D's [n=4.9±0.5,〈pT2〉=0.99±0.10 (GeV/c)2]. It is suggested that these distributions could reflect contribution of leading di-quarks in pp collisions. Comparison is made with evidence for leading quarks in charm production in 360 GeV/cπ−p interactions.

Results are reported of a successful test of ISIS 1 in a particle beam. ISIS 1 is a full aperture (4m × 2m) prototype of the particle identifier ISIS (Identification of Secondaries by Ionisation Sampling), proposed for the European Hybrid Spectrometer (EHS) at the SPS at CERN. Using the “relativistic rise” of the ionisation loss, electrons and pions at 500 MeV/c were identified with better than 99% confidence, the data containing typically 5–10 tracks per “picture” drifted by up to 2 m. The ionisation resolution was 12–14% fwhm on 1m of track and the two track resolution was 2 cm. These results, which agree with our predictions, indicate that ISIS 2 with 5 m of useful track length will be able to distinguish uniquely kaons and protons from pions of known momentum in high multiplicity interactions up to 50 and 100 GeV/c respectively.

We present results on single-particle inclusive distributions in p(π+)n reactions from a Fermilab experiment using the hybrid 30″ bubble chamber and PWC facility. Distributions in rapidity, y, Feynman x and p2T for π+ and π− are presented and compared with other experiments. The effects of different targets and projectiles (neutrons, protons and pions) on the distributions are demonstrated and discussed in terms of projectile and target fragmentation. The average transverse momentum 〈PT〉 is studied as a function of x, y and multiplicity.

Abstract Fits are made to new K − p → K 0 π − p data at 3.3 GeV/ c with a generalized Veneziano model that includes both vector and pseudoscalar exchanges. Tests of the exchange degeneracy properties of the Regge trajectories show that the model prefers exchange degeneracy of the K ∗ (890) and non-exchange degeneracy of the Δ(1238). Several defects in the model are noted.

In almost every scientific field, an experiment involves collecting data and then analysing it. The analysis stage will often consist in trying to extract some physical parameter and estimating its uncertainty; this is known as Parameter Determination. An example would be the determination of the mass of the top quark, from data collected from high energy proton-proton collisions. A different aim is to choose between two possible hypotheses. For example, are data on the recession speed s of distant galaxies proportional to their distance d, or do they fit better to a model where the expansion of the Universe is accelerating? There are two fundamental approaches to such statistical analyses - Bayesian and Frequentist. This article discusses the way they differ in their approach to probability, and then goes on to consider how this affects the way they deal with Parameter Determination and Hypothesis Testing. The examples are taken from every-day life and from Particle Physics.

Abstract The difference between two forms of likelihood approach is discussed, and their relative merits are described. The methods are illustrated by two examples: (1) estimating rates for forward or backward particles in an observed angular distribution; and (2) assigning tracks as pions or kaons using the information from a particle identifier. In the latter case, real data from decays of neutral charmed mesons are analysed by the two likelihood methods.

The non-strange four-prong events of π+p interactions at 3.5 GeV/c are studied. Cross sections are calculated for all resonance productions in the channels π+p → pπ+π+π− (σT = 3.18 ± 0.13 mb) and π+p → pπ+π+π−πo (σT = 4.03 ± 0.16 mb). The dominant two body reactions Δ++ϱo and Δ++ ωo are investigated in detail, and production and decay distributions are presented as well as joint decay density matrix elements and joint correlation terms. The Δ++ϱo reaction is compared to predictions of OPE with absorption and the Δ++ωo is compared to rho-exchange with sharp cutoff.

When you’re searching for elusive manifestations of new physics, it’s easy to be fooled by statistical fluctuations or instrumental quirks.

The quark model is successful in the fields of hadronic spectroscopy and high energy scattering processes, but the question of whether free quarks exist remains of fundamental importance. The experimental situation was reviewed in 1977 by Jones who concluded that there was little evidence for free quarks. Developments since then are presented, with special emphasis on whether experiments claiming positive results are compatible with others seeing no effect. Some suggestions for the future are made.

Compilation of information about the structure of A = 3 systems. This review mainly summarizes the work presented in (2010Pu04) and has updates of mass, lifetime and nuclear moment data as noted in the text.

Abstract A bellows expanded bubble chamber, 12 cm in diameter, 9 cm deep, has been designed for use with liquid deuterium. Good quality electron tracks have been observed over the temperature range 31.2° to 34.1°K, with a minimum volume expansion ratio of 1.6 per cent. It has been used with the Harwell synchrocyclotron to study the interaction of 80 MeV protons with deuterons. The results are being analysed with a modified rectangular coordinate plotter.

We present the final results on the D-meson liftime measurements obtained by the NA27 experiment. From a sample of 145 D0D0and149D± decays, we have measured τ(D0)=(4.6+0.6−0.5)×10−13 s, τ(D±)=(11.2+1.4−1.1)×10−13 s, with a ratio R=τ(D±)τ(D0)=2.4±0.4.

The first data on the production of D∗(2010) are presented as observed in π− -proton interactions at √s = 27 GeV. It is found that D∗(2010) dominates the total charm D-meson production, without a significant non-central component.

In a 2.5 events/μb exposure of a small 20 cm diameter, rapid cycling hydrogen bubble chamber equipped with high resolution optics, clear evidence is observed for the first time of the associated production of charmed particles, identified by their short decays. A significant excess of 12 events which we interpret as charm pairs corresponding to a total cross section of ∼ 40 μb is seen above the expected strange particle background. In addition, 8 charged 3 prong events consistent with D± decay are observed with an expected background of ∼ 2 events

The reactions K−p→pKoπ+π−π−, pKoπ+π−π− πo and nKoπ+π+π−π− have been studied at 6 GeV/c incident momentum. Cross sections are given for the various resonances produced in each channel. In the first two channels, resonance production dominates. A detailed analysis has been performed on the simultaneous resonance production K−p→ Δ++K∗−π−, and evidence is given for a vector-ex-change mechanism. A Veneziano-model calculation has been attempted for this quasi three-body final state, and the predictions are found to be in good agreement with the experimental results.

The measurement of 12D 0 and 10D ± exclusive branching ratios are presented. The analysis is based on 608 spatially resolved charm particle decays produced in 360 GeV/c π− p and 400 GeV/cpp interactions.

PHYSTAT2003 was a Conference held at SLAC on September 8th-11th, 2003. Its theme was ''Statistical Problems in Particle Physics, Astrophysics and Cosmology''. It followed on from the Confidence Limits Workshops held at CERN and Fermilab in 2000, and a conference in 2002 at the Institute for Particle Physics Phenomenology in Durham, UK. PHYSTAT2003 differed from the earlier meetings in two important respects. While the first three meetings had been attended largely by particle physicists, at SLAC there was also involvement of astrophysicists and cosmologists. Secondly, the SLAC meeting really benefited from a strong presence of statisticians. They enhanced the usefulness of the Conference in many ways: they were involved in the planning stage, gave invited and contributed talks, and were simply ''there'' to discuss statistical issues with physicists in the breaks between the sessions.

We present new data on the reactions K−p → Λϱ, Σoϱ, Λω, Λφ, Σoφ, Y∗ϱ and Y∗φ. All the reactions are characterised by forward-peaked production angular distributions. Fits of the form exp(At′) to the momentum transfer distributions result in values of A ∼ 1 (GeV/c)−2. We have examined the decay distributions of the vector mesons with respect to an axis normal to the production plane. The data are compared with the quark model predictions for the ϱ/ω, Λ/Σo and Λ/Y∗ ratios. The most serious contradiction is for the Λ/Σo ratio, which is experimentally too small.

Various three-body final states produced in 6 GeV/c K−p interactions show peripheral features. These are examined in some detail, and it is found that a double peripheral mechanism is consistent with the data. For each reaction when interpreted in this way the most important double peripheral process is one in which the final state pion is produced at the central vertex. Two-dimensional transfer distributions are analysed; it is found that the strongest dependence on momentum transfer occurs when the relevant initial and final state particles are identical.

The Oxford 12-cm deuterium bubble chamber was used to study interactions in the d-d system in the energy range 20--70 Mev. A preliminary analysis of 1000 interactions was presented that listed the possible reactions, their cross sections, and branching ratios. (C.E.S.)

A comparative analysis of the global properties of 400 GeV/c proton-proton interactions with and without charm production is presented. Multiplicities, momentum distributions, sphericity and thrust of these interactions are compared.

Abstract π − ω interference is studied in the reactions K − p → π + π − (Λ 0 , ϵ) at 4.2 GeV/ c using data from a high statistics experiments in the CERN 2m HBC. The phenomenon is analysed in terms of the conventional formalism as well as in terms of a new model for π − ω interference proposed by Earles and Srivastava. Satisfactory agreement with the data is found for both models. The rate of ω → 2π obtained in the latter model is in agreement with the VMD (Vector Meson Dominance) prediction for ω → γ → ϱ → 2π.

New experimental data is presented on the reaction K−p → Λω from a bubble chamber experiment at 3.13 and 3.3 GeV/c. The cross section, production angular distribution, Λ-polarization, and ω-density matrix elements are determined. We also investigate the joint decay distribution of the Λ and ω together; this contains sufficient information for us to perform an almost complete amplitude analysis for the reaction. These amplitudes are used to test a duality + absorption hypothesis.

We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we study is that of inferring the rate of a Poisson process when there are uncertainties on the acceptance and the background. Limit calculating software associated with this work is available in the form of C functions.

We consider the relative merits of two different approaches to discovery or exclusion of new phenomena, a raster scan or a 2-dimensional approach.

This book, written by a non-statistician for non-statisticians, emphasises the practical approach to those problems in statistics which arise regularly in data analysis situations in nuclear and high-energy physics experiments. Rather than concentrating on formal proofs of theorems, an abundant use of simple examples illustrates the general ideas which are presented, showing the reader how to obtain the maximum information from the data in the simplest manner. Possible difficulties with the various techniques, and pitfalls to be avoided, are also discussed. Based on a series of lectures given by the author to both students and staff at Oxford, this common-sense approach to statistics will enable nuclear physicists to understand better how to do justice to their data in both analysis and interpretation.

We present evidence for δ production in the reactions K−p→Σ(1385)+δ−; δ−→η0π−, and K−p → Λδ+π−; δ+ → η0π+, in a bubble chamber experiment with beam momentum in the range 3.1 to 3.6 GeV/c. The η0 from the δ decay is seen both as a missing mass effect, and in its charged decay modes. The δ− has a mass of 989 ± 4 MeV, and width a of 16−16+25 MeV (after allowing for experimental resolution). The cross section for Σ(1385)−δ− production is 7±3μb; the reaction is produced at small momentum transfers. The mass and width of the δ+ are consistent with those of the δ−, and the cross section for the Λ0π−δ+ final state is about 5 μb. Neither δ appears to be produced as a result of D0 decay.

ϱ0 is produced in the final state pn π+π− with a cross-section of σ = 100 ± 30 μb. The ϱ0 is observed only when the neutron in pnπ+π− is emitted in the forward direction and the proton is emitted in the backward direction in the c.m.s. Single ϱ0 production in nucleon-nucleon collisions is discussed in terms of two I = 1 meson exchange diagram, and is compared to ϱ0 production in pion-nucleon collisions.

The authors discuss the techniques of measuring lifetimes in the picosecond range; the relevant particles are the tau lepton, and charm and beauty hadrons. The different types of vertex detectors used to recognise decays and to measure decay distances are described. Lifetimes are generally determined from decay distances; problems caused by experimental cuts, resolution, backgrounds, and unknown momenta are discussed. The measurement of the b lifetime is presented as an example. They conclude by describing decay vertex tagging at present and future colliders.

Theπ 0 andη 0 production is studied inπ − p interactions at 360 GeV/c. The cross section forπ 0 production in the forward hemisphere (X>0) isσ(π 0)=(49.7 ± 1.0 ± 1.1) mb and for η withX>0.1,N ch>2,σ(η 0)=(3.1 ± 0.5) mb. The ratio of theπ 0 toη 0 cross section forX>0.1,N ch>2 isσ(π 0)/σ(η 0). Results on FeynmanX andp T distributions are presented. The data were obtained using the European Hybrid Spectrometer EHS and the bubble chamber LEBC at CERN.

By measuring 121 000 2-prong interactions on the Oxford PEPR, we obtained 9 543 events of the type K−p → K−π+n. The cuts to improve the quality of the data and to reduce ambiguities with other final states are described in detail. Strong signals corresponding to the final states K∗o (890)n and K∗o (1420)n are observed. The masses and widths of these resonances are determined. The differential cross section for K∗o (890)n is less steep than that for the reaction K+ n → K∗o (890)p. The decay of the K−π+ system in the 890 MeV region is analysed as a coherent mixture of spins 0+ and 1−, and the density matrix elements extracted. The combination ϱooH dσ/dt' has the sharpest t' dependence. A comparison is made with the reaction K− p → K∗− (890)p to study the t-channel isospin contributions to the various helicity substates. The K− π+ mass spectrum appears distorted on the low side of the K∗o (1420) at low momentum transfers, thus complicating a study of this region. The K∗o (1420)n final state has a shallower t' dependence than for K∗o (890)n; this is in contrast with K±N data at higher energies. Finally we study the moments of the K− π+ system's decay distribution as a function both of mass and of momentum transfer.

Results are presented of a 12 event/μb bubble-chamber experiment; the reactions discussed in detail are K−p → K∗ (890)−p, K∗ (1420)−p and K∗ (890)−Δ+. The K∗ (890)−p channel is dominated by the forward peak. The suggestion of flattering at cos θ = 1 is more pronounced in (ϱ11 + ϱ1−1) dσdt; which is mainly natural-parity exchange. Pseudoscalar exchange contributes to ϱ00Jdσdt; this is more sharply peaked in t. The value of (ϱ11 − ϱ1−1) dσdt is somewhat larger than the upper limit from the dominant natural-parity exchange. There is significant structure in ϱ00H dσdt at t ≈ −0.6 (GeV/c)2. The K∗ (1420)−p channel is much more pronounced at 3.3 GeV/c than at 3.13 GeV/c, but is not markedly peripheral. The width of the K∗ (1420) in the 3.3 GeV/c data is 42 ± 12 MeV/c2. The cross section for K∗− Δ+ agrees with that expected from K+p → K∗Δ, assuming a single t-channel exchange. Our measured density matrix elements are consistent with a strong pseudoscalar exchange.

For situations where we are trying to decide which of two hypotheses $H_{0}$ and $H_{1}$ provides a better description of some data, we discuss the usefulness of plots of $p_{0}$ versus $p_{1}$, where $p_{i}$ is the $p$-value for testing $H_{i}$. They provide an interesting way of understanding the difference between the standard way of excluding $H_{1}$ and the $CL_{s}$ approach; the Punzi definition of sensitivity; the relationship between $p$-values and likelihood ratios; and the probability of observing misleading evidence. They also help illustrate the Law of the Iterated Logarithm and the Jeffreys-Lindley paradox.

We describe two different approaches for incorporating systematics into analyses for parameter determination in the physical sciences. We refer to these as the Pragmatic and the Full methods, with the latter coming in two variants: Full Likelihood and Fully Bayesian. By the use of a simple and readily understood example, we point out the advantage of using the Full Likelihood and Fully Bayesian approaches; a more realistic example from Astrophysics is also presented. This could be relevant for data analyses in a wide range of scientific fields, for situations where systematic effects need to be incorporated in the analysis procedure. This note is an extension of part of the talk by van Dyk at the PHYSTAT-Systematics meeting.

Abstract Background Efficiently identifying the social risks of patients with serious illnesses (SIs) is the critical first step in providing patient-centered and value-driven care for this medically vulnerable population. Objective To apply and further hone an existing natural language process (NLP) algorithm that identifies patients who are homeless/at risk of homeless to a SI population. Methods Patients diagnosed with SI between 2019 and 2020 were identified using an adapted list of diagnosis codes from the Center for Advance Palliative Care from the Kaiser Permanente Southern California electronic health record. Clinical notes associated with medical encounters within 6 months before and after the diagnosis date were processed by a previously developed NLP algorithm to identify patients who were homeless/at risk of homelessness. To improve the generalizability to the SI population, the algorithm was refined by multiple iterations of chart review and adjudication. The updated algorithm was then applied to the SI population. Results Among 206 993 patients with a SI diagnosis, 1737 (0.84%) were identified as homeless/at risk of homelessness. These patients were more likely to be male (51.1%), age among 45-64 years (44.7%), and have one or more emergency visit (65.8%) within a year of their diagnosis date. Validation of the updated algorithm yielded a sensitivity of 100.0% and a positive predictive value of 93.8%. Conclusions The improved NLP algorithm effectively identified patients with SI who were homeless/at risk of homelessness and can be used to target interventions for this vulnerable group.

Discusses various methods for estimating the bias from a repeated set of measurements that exhibit a spread larger than expected on the basis of their statistical errors. Monte Carlo simulations are used to test how well the methods perform.

New data for the reaction K−p → ΛK+K− at 3.3 GeV/c have been used to investigate the five-particle generalized Veneziano model. The amplitude is constrained by symmetry properties of the crossed channels and by non-exchange degeneracy of the Nα∗ trajectory. The Harari-Rosner dual quark model determines the trajectories which couple to the K+K− system. Reasonable choices for the other trajectories lead to good agreement with these data as well as data at higher and lower beam momentum. The pomeron exchange contribution to the reaction is shown to be small; however, both pseudoscalar and vector kinematic factors are required for detailed agreement with the angular distributions. The model fails to account for the crossing-symmetric reaction K+p → ΛK+K+.

The centre-of-mass angular distributions of the Λo produced in final states with three, four, five and six particles are compared with those of other baryons in final states with the same multiplicity. A forward Λo peak, consistent with a baryon-exchange mechanism contribution, is found in all Λo final states we have studied. The polarisation of the Λ° as a function of the λo production angle is studied for each final state.

A bstract The determination of the infection fatality rate (IFR) for the novel SARS-CoV-2 coronavirus is a key aim for many of the field studies that are currently being undertaken in response to the pandemic. The IFR together with the basic reproduction number R 0 , are the main epidemic parameters describing severity and transmissibility of the virus, respectively. The IFR can be also used as a basis for estimating and monitoring the number of infected individuals in a population, which may be subsequently used to inform policy decisions relating to public health interventions and lockdown strategies. The interpretation of IFR measurements requires the calculation of confidence intervals. We present a number of statistical methods that are relevant in this context and develop an inverse problem formulation to determine correction factors to mitigate time-dependent effects that can lead to biased IFR estimates. We also review a number of methods to combine IFR estimates from multiple independent studies, provide example calculations throughout this note and conclude with a summary and “best practice” recommendations. The developed code is available online.

D-meson lifetimes have been determined from decays observed in an exposure of the high resolution hydrogen bubble chamber LEBC in association with the European Hybrid Spectrometer (EHS) to an incident 360 GeV π− beam. Various techniques for lifetime determination are presented and the results compared. A new model-independent analysis based on the distribution in transverse decay length is introduced and preferred over other techniques. Best values are found to be: $$\begin{gathered} \tau (D^0 ) = \left( {4.1_{ - 0.3}^{ + 0.7} } \right) \times 10^{ - 13} s (60 decays) \hfill \\ \tau (D^ \pm ) = \left( {10.7_{ - 1.8}^{ + 2.8} } \right) \times 10^{ - 13} s (40 decays) \hfill \\ \end{gathered} $$ . The lifetime ratio is: $$T = \frac{{\tau (D^ \pm )}}{{\tau (D^0 )}} = 2.6_{ - 0.6}^{ + 0.8} $$ .

This document is part of Part 1 'Principles and Methods' of Subvolume B 'Detectors for Particles and Radiation' of Volume 21 'Elementary Particles' of Landolt-Börnstein - Group I 'Elementary Particles, Nuclei and Atoms'. It contains the Section '4.5 Statistical Issues in Particle Physics' of Chapter '4 Data Treatment and Analysis Methods' with the content: Get Access PDF

Pshenin and Voinov have noted a possible source of bias in mean free path estimates. We find their suggestion that this could provided an explantion for the phenomenon of anomalons is unlikely.

Abstract The well-known class-A quark-model relations of Bialas and Zalewski are parametrised in a particular form, where one can compare the data with the predictions separately for the meson non-flip and flip parts, defined in the transversity frame. A 3-parameter fit to the joint decay angular distribution is performed on the experimental data, and the results are compared with the quark-model predictions for various regions of the four-momentum transfer. The effect of an s -wave state under the ρ 0 is discussed.

Some aspects of the reaction pp → N∗ (1238) pπ− at 6 GeV/c are compared with the predictions of a one-pion-exchange process in which some of the effects of absorption have been taken into account. The agreement between theory and ex experiment is encouraging.

We review the methods to combine several measurements, in the form of parameter values or $p$-values.

Charm data from 360 GeV/c π− p and 400 GeV/cpp interactions are used to give results onD-meson branching ratios. The analysis is based on 438 charm events containing 608 spatially resolved charm particle decays. We present topological branching ratios, as well as the following inclusive branching ratios ofD-mesons into kaons: $$\begin{gathered} B(D^ \pm \to K^ \mp + anything) = 0.17 \pm 0.07, \hfill \\ B(D^ \pm \to K^ \pm + anything) = 0.08_{ - 0.05}^{ + 0.06} , \hfill \\ B(D^0 \to K^ \pm + anything) = 0.42 \pm 0.08, \hfill \\ B(D^0 \to K^ + + anything) = 0.03_{ - 0.02}^{ + 0.05} , \hfill \\ \end{gathered} $$ and the following semi-electronic branching ratios ofD-mesons: $$\begin{gathered} B(D^ \pm \to e^ \pm + anything) = 0.20_{ - 0.07}^{ + 0.09} , \hfill \\ B(D^0 \to e^ \pm + anything) = 0.15 \pm 0.05. \hfill \\ \end{gathered} $$

We present data on the five final states Λω, Λφ, Λϱ0, Σ0⊘ and Σ0ϱ0 produced in 3.1–3.6 GeV/c K−p interactions. These data are from a bubble chamber experiment with 18 events/μb. For all reactions the data consist of the overall and differetial cross sections, and the hyperon polarisation and the vector meson's density matrix elements as a function of momentum transfer. For Λω and Λ⊘, an almost complete amplitude analysis is performed in several regions of momentum transfer. The data are examined from the point of view of various exchange models.

The dependence of the average charged multiplicity, 〈nX〉, of the system X on |t| and M2X is studied for the reactions p(π+)n→pfast(p+fast) + X and p(π+)n→pslow + X at 195 GeV/c. For a fixed M2X, 〈nX〉 changes significantly among these reactions, yielding a systematic hierarchy of mean multiplicities. The results indicate that a proton emits on the average less charged particles than a pion and more than a neutron.

In classification problems, the usual way of estimating systematic errors consists of first deciding on an algorithm for determining the quantity of interest, and then seeing the effect on the answer of varying the relevant (Monte Carlo) input constants by suitable amounts. A better way of analysing the data, which can result in reduced systematic errors, is described. Its effect on a toy example is presented; the improvement is striking.