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Review of Particle Physics

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,062 new measurements from 721 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 117 reviews are many that are new or heavily revised, including those on Pentaquarks and Inflation. The complete Review is published online in a journal and on the website of the Particle Data Group (http://pdg.lbl.gov). The printed PDG Book contains the Summary Tables and all review articles but no longer includes the detailed tables from the Particle Listings. A Booklet with the Summary Tables and abbreviated versions of some of the review articles is also available. Contents Abstract, Contributors, Highlights and Table of ContentsAcrobat PDF (150 KB) IntroductionAcrobat PDF (456 KB) Particle Physics Summary Tables Gauge and Higgs bosonsAcrobat PDF (155 KB) LeptonsAcrobat PDF (134 KB) QuarksAcrobat PDF (84 KB) MesonsAcrobat PDF (871 KB) BaryonsAcrobat PDF (300 KB) Searches (Supersymmetry, Compositeness, etc.)Acrobat PDF (91 KB) Tests of conservation lawsAcrobat PDF (330 KB) Reviews, Tables, and Plots Detailed contents for this sectionAcrobat PDF (37 KB) Constants, Units, Atomic and Nuclear PropertiesAcrobat PDF (278 KB) Standard Model and Related TopicsAcrobat PDF (7.3 MB) Astrophysics and CosmologyAcrobat PDF (2.7 MB) Experimental Methods and CollidersAcrobat PDF (3.8 MB) Mathematical Tools or Statistics, Monte Carlo, Group Theory Acrobat PDF (1.3 MB) Kinematics, Cross-Section Formulae, and PlotsAcrobat PDF (3.9 MB) Particle Listings Illustrative key and abbreviationsAcrobat PDF (235 KB) Gauge and Higgs bosonsAcrobat PDF (2 MB) LeptonsAcrobat PDF (1.5 MB) QuarksAcrobat PDF (1.2 MB) Mesons: Light unflavored and strangeAcrobat PDF (4 MB) Mesons: Charmed and bottomAcrobat PDF (7.4 MB) Mesons: OtherAcrobat PDF (3.1 MB) BaryonsAcrobat PDF (3.97 MB) Miscellaneous searchesAcrobat PDF (2.4 MB) IndexAcrobat PDF (160 KB)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A fast exact simulation method for a class of Markov jump processes

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On control of continuous dynamical polysystems in discrete times

This paper considers control systems with a finite number of control parameters, i.e. dynamical polysystems. It is assumed that control switchings can occur only at certain discrete times. Statistical methods in number theory are used to investigate the controllability of these systems. Existence of control switching times is established through analysis of Diophantine equations. The values of control switching times are found through suitable numerical methods. Certain assertions on the controllability of the polysystems of the class under consideration are proved. Some examples are considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Intrinsic alignment in redMaPPer clusters – II. Radial alignment of satellites towards cluster centres

We study the orientations of satellite galaxies in redMaPPer clusters constructed from the Sloan Digital Sky Survey at 0.1 < z < 0.35 to determine whether there is any preferential tendency for satellites to point radially towards cluster centres. Here, we analyse the satellite alignment (SA) signal based on three shape measurement methods (re-Gaussianization, de Vaucouleurs, and isophotal shapes), which trace galaxy light profiles at different radii. The measured SA signal depends on these shape measurement methods. We detect the strongest SA signal in isophotal shapes, followed by de Vaucouleurs shapes. While no net SA signal is detected using re-Gaussianization shapes across the entire sample, the observed SA signal reaches a statistically significant level when limiting to a subsample of higher luminosity satellites. We further investigate the impact of noise, systematics, and real physical isophotal twisting effects in the comparison between the SA signal detected via different shape measurement methods. Unlike previous studies, which only consider the dependence of SA on a few parameters, here we explore a total of 17 galaxy and cluster properties, using a statistical model averaging technique to naturally account for parameter correlations and identify significant SA predictors. We find that the measured SA signal is strongest for satellites with the following characteristics: higher luminosity, smaller distance to the cluster centre, rounder in shape, higher bulge fraction, and distributed preferentially along the major axis directions of their centrals. Finally, we provide physical explanations for the identified dependences and discuss the connection to theories of SA.

79 ASTRONOMY AND ASTROPHYSICS↗

Robust verification analysis

We introduce a new methodology for inferring the accuracy of computational simulations through the practice of solution verification. We demonstrate this methodology on examples from computational heat transfer, fluid dynamics and radiation transport. Our methodology is suited to both well- and ill-behaved sequences of simulations. Our approach to the analysis of these sequences of simulations incorporates expert judgment into the process directly via a flexible optimization framework, and the application of robust statistics. The expert judgment is systematically applied as constraints to the analysis, and together with the robust statistics guards against over-emphasis on anomalous analysis results. We have named our methodology Robust Verification. Our methodology is based on utilizing multiple constrained optimization problems to solve the verification model in a manner that varies the analysis' underlying assumptions. Constraints applied in the analysis can include expert judgment regarding convergence rates (bounds and expectations) as well as bounding values for physical quantities (e.g., positivity of energy or density). This approach then produces a number of error models, which are then analyzed through robust statistical techniques (median instead of mean statistics). This provides self-contained, data and expert informed error estimation including uncertainties for both the solution itself and order of convergence. Our method produces high quality results for the well-behaved cases relatively consistent with existing practice. The methodology can also produce reliable results for ill-behaved circumstances predicated on appropriate expert judgment. We demonstrate the method and compare the results with standard approaches used for both code and solution verification on well-behaved and ill-behaved simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A statistical approach to combining multisource information in one-class classifiers

A new method is introduced in this paper for combining information from multiple sources to support one-class classification. The contributing sources may represent measurements taken by different sensors of the same physical entity, repeated measurements by a single sensor, or numerous features computed from a single measured image or signal. The approach utilizes the theory of statistical hypothesis testing, and applies Fisher's technique for combining p-values, modified to handle nonindependent sources. Classifier outputs take the form of fused p-values, which may be used to gauge the consistency of unknown entities with one or more class hypotheses. The approach enables rigorous assessment of classification uncertainties, and allows for traceability of classifier decisions back to the constituent sources, both of which are important for high-consequence decision support. Application of the technique is illustrated in two challenge problems, one for skin segmentation and the other for terrain labeling. Finally, the method is seen to be particularly effective for relatively small training samples.

97 MATHEMATICS AND COMPUTING↗

A Python Multiscale Thermochemistry Toolbox (pMuTT) for thermochemical and kinetic parameter estimation

Estimating the thermochemical properties of systems is important in many fields such as material science and catalysis. The Python multiscale thermochemistry toolbox (pMuTT) is a Python software library developed to streamline the conversion of ab-initio data to thermochemical properties using statistical mechanics, to perform thermodynamic analysis, and to create input files for kinetic modeling software. Its open-source implementation in Python leverages existing scientific codes, encourages users to write scripts for their needs, and allows the code to be expanded easily. The core classes developed include a statistical mechanical model in which energy modes can be included or excluded to suit the application, empirical models for rapid thermodynamic property estimation, and a reaction model to calculate kinetic parameters or changes in thermodynamic properties. In addition, pMuTT supports other features, such as Brønsted–Evans–Polanyi (BEP) relationships, coverage effects, and ab-initio phase diagrams.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Activation of Water by Thorium Cation: A Guided Ion Beam and Quantum Chemical Study

The reaction of atomic thorium cations with deuterated water as a function of kinetic energy from thermal to 10 eV was studied using guided ion beam tandem mass spectrometry. At thermal energies, both ThO{sup +} + D{sub 2} and DThO{sup +} + D are formed in barrierless exothermic processes and reproduce results in the literature obtained using ion cyclotron resonance mass spectrometry. As the energy is increased, the branching ratio between these two channels changes such that the dominant product changes from ThO{sup +} to DThO{sup +} and back to ThO{sup +}, until ThD{sup +} + OD is energetically available and is the dominant product channel. To help understand these experimental results, a variety of theoretical approaches were tried and used to establish a potential energy surface, which compares well with previous theoretical studies. Utilizing the theoretical results, the kinetic energy dependent branching ratio between the ThO{sup +} + D{sub 2} and DThO{sup +} + D channels was calculated using both RRKM and phase space theory (PST). The results indicate that consideration of angular momentum conservation (as in PST) and spin-orbit corrected energies are needed to reproduce experimental results quantitatively. The PST modeling also provides relative energies for the two competing transition states that lead to the primary products, for which theory provides reasonable agreement. .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Lattice QCD Calculation of Nucleon Structure

It is emphasized in the 2015 NSAC Long Range Plan that "understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large-scale computer simulation. We started out by calculating the nucleon form factors -- electromagnetic, axial-vector, πNN, and scalar form factors, the quark spin contribution to the proton spin, the strangeness magnetic moment, the quark orbital angular momentum, the quark momentum fraction, and the quark and glue decomposition of the proton momentum and angular momentum. The first round of calculations were done with Wilson fermions in the `quenched' approximation where the dynamical effects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge configurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at ~ 300 MeV and obtained the strange form factors, charm and strange quark masses, the charmonium spectrum and the D s meson decay constant f D s , the strangeness and charmness, the meson mass decomposition and the strange quark spin from the anomalous Ward identity. Recently, we have started to include multiple lattices with different lattice spacings and different volumes including large lattices at the physical pion mass point. We are getting quite close to being able to calculate the hadron structure at the physical point and to do the continuum and large volume extrapolations, which is our ultimate aim. We have now finished several projects which have included these systematic corrections. They include the leptonic decay width of the ρ, the πN sigma and strange sigma terms, and the strange quark magnetic moment. Over the years, we have also studied hadron spectroscopy with lattice calculations and in phenomenology. These include Roper resonance, pentaquark state, charmonium spectrum, glueballs, scalar mesons a 0 (1450) and σ(600) and other scalar mesons, and the 1 -+ meson. In addition, we have employed the canonical approach to explore the first-order phase transition and the critical point at finite density and finite temperature. We have also discovered a new parton degree of freedom -- the connected sea partons, from the path-integral formulation of the hadronic tensor, which explains the experimentally observed Gottfried sum rule violation. Combining experimental result on the strange parton distribution, the CT10 global fitting results of the total u and d anti-partons and the lattice result of the ratio of the momentum fraction of the strange vs that of u or d in the disconnected insertion, we have shown that the connected sea partons can be isolated. In this final technical report, we shall present a few representative highlights that have been achieved in the project.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Development of a statistically based access delay timeline methodology.

The charter for adversarial delay is to hinder access to critical resources through the use of physical systems increasing an adversary s task time. The traditional method for characterizing access delay has been a simple model focused on accumulating times required to complete each task with little regard to uncertainty, complexity, or decreased efficiency associated with multiple sequential tasks or stress. The delay associated with any given barrier or path is further discounted to worst-case, and often unrealistic, times based on a high-level adversary, resulting in a highly conservative calculation of total delay. This leads to delay systems that require significant funding and personnel resources in order to defend against the assumed threat, which for many sites and applications becomes cost prohibitive. A new methodology has been developed that considers the uncertainties inherent in the problem to develop a realistic timeline distribution for a given adversary path. This new methodology incorporates advanced Bayesian statistical theory and methodologies, taking into account small sample size, expert judgment, human factors and threat uncertainty. The result is an algorithm that can calculate a probability distribution function of delay times directly related to system risk. Through further analysis, the access delay analyst or end user can use the results in making informed decisions while weighing benefits against risks, ultimately resulting in greater system effectiveness with lower cost.

Rivera, W. Gary↗

Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q-statistics. Starting from the q-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy preserves a scaling property of this equation. The q-statistical approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q is traced. It is found that the q-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length. -- Highlights: •Thomas–Fermi approach for self-gravitating fermions. •A generalized Thomas–Fermi equation is derived. •Nonextensivity preserves a scaling property of this equation. •Nonextensive approach to Jeans’ instability of self-gravitating fermions. •It is found that nonextensivity makes the Fermionic system unstable at shorter scales.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Muon $g-2$ Experiment at Fermilab

The current ~ 3.5σ discrepancy between the experimental measurement and theoretical prediction of the muon magnetic anomaly, a µ , stands as a potential indication of the existence of new physics. The Muon g - 2 experiment at Fermilab is set to measure aµ with a four-fold improvement in the uncertainty with respect to previous experiment, with an aim to determine whether the g - 2 discrepancy is well established. The experiment recently completed its first physics run and a summer programme of essential upgrades, before continuing on with its experimental programme. The Run-1 data alone are expected to yield a statistical uncertainty of 350 ppb and the publication of the first result is expected in late-2019.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. Our analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [ J. Appl. Phys. (1948), 19 , 742–753] appears as a special case, limited to large crystallite sizes, here. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystalline powder samples.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The Effect of Satellite Observing System Changes on MERRA Water and Energy Fluxes

Because reanalysis data sets offer state variables and fluxes at regular space / time intervals, atmospheric reanalyses have become a mainstay of the climate community for diagnostic purposes and for driving offline ocean and land models. Although one weakness of these data sets is the susceptibility of the flux products to uncertainties because of shortcomings in parameterized model physics, another issue, perhaps less appreciated, is the fact that continual but discreet changes in the evolving observational system, particularly from satellite sensors, may also introduce artifacts in the time series of quantities. In this paper we examine the ability of the NASA MERRA (Modern Era Retrospective Analysis for Research and Applications) and other recent reanalyses to determine variability in the climate system over the satellite record (approximately the last 30 years). In particular we highlight the effect on the reanalysis of discontinuities at the junctures of the onset of passive microwave imaging (Special Sensor Microwave Imager) in late 1987 as well as improved sounding and imaging with the Advanced Microwave Sounding Unit, AMSU-A, in 1998. We first examine MERRA fluxes from the perspective of how physical modes of variability (e.g. ENSO events, Pacific Decadal Variability) are contaminated by artificial step-like trends induced by the onset of new moisture data these two satellite observing systems. Secondly, we show how Redundancy Analysis, a statistical regression methodology, is effective in relating these artifact signals in the moisture and temperature analysis increments to their presence in the physical flux terms (e.g. precipitation, radiation). This procedure is shown to be effective greatly reducing the artificial trends in the flux quantities.

Robertson, Franklin R.↗

The Effect of Satellite Observing System Changes on MERRA Water and Energy Fluxes

Because reanalysis data sets offer state variables and fluxes at regular space / time intervals, atmospheric reanalyses have become a mainstay of the climate community for diagnostic purposes and for driving offline ocean and land models. Although one weakness of these data sets is the susceptibility of the flux products to uncertainties because of shortcomings in parameterized model physics, another issue, perhaps less appreciated, is the fact that continual but discreet changes in the evolving observational system, particularly from satellite sensors, may also introduce artifacts in the time series of quantities. In this paper we examine the ability of the NASA MERRA (Modern Era Retrospective Analysis for Research and Applications) and other recent reanalyses to determine variability in the climate system over the satellite record (approx. the last 30 years). In particular we highlight the effect on the reanalysis of discontinuities at the junctures of the onset of passive microwave imaging (Special Sensor Microwave Imager) in late 1987 and, more prominently, with improved sounding and imaging with the Advanced Microwave Sounding Unit, AMSU-A, in 1998. We first examine MERRA fluxes from the perspective of how physical modes of variability (e.g. ENSO events, Pacific Decadal Variability) are contained by artificial step-like trends induced by the onset of new moisture data these two satellite observing systems. Secondly, we show how Redundancy Analysis, a statistical regression methodology, is effective in relating these artifact signals in the moisture and temperature analysis increments to their presence in the physical flux terms (e.g. precipitation, radiation). This procedure is shown to be effective greatly reducing the artificial trends in the flux quantities.

Robertson, Franklin R.↗

Improved profile fitting and quantification of uncertainty in experimental measurements of impurity transport coefficients using Gaussian process regression

The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, yet the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We demonstrate that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. Moreover, we discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Sensitive Detection of Structural Differences using a Statistical Framework for Comparative Crystallography

Chemical and conformational changes underlie the functional cycles of proteins. Comparative crystallography can reveal these changes over time, over ligands, and over chemical and physical perturbations in atomic detail. A key difficulty, however, is that the resulting observations must be placed on the same scale by correcting for experimental factors. We recently introduced a Bayesian framework for correcting (scaling) X-ray diffraction data by combining deep learning with statistical priors informed by crystallographic theory. To scale comparative crystallography data, we here combine this framework with a multivariate statistical theory of comparative crystallography. By doing so, we find strong improvements in the detection of protein dynamics, element-specific anomalous signal, and the binding of drug fragments.

Hekstra, Doeke R. [Harvard Univ., Cambridge, MA (U↗

Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains

The nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain-wall state, in which the two half lattices are prepared in equilibrium with distinct parameters. Here, we analyse the Riemann problem for the corresponding Euler equations and, in specific cases, compare with molecular dynamics. Additionally, the fluctuations of time-integrated currents are investigated. In analogy with the KPZ equation, their typical fluctuations should be of size t 1/3 and have a Tracy–Widom GUE distributed amplitude. The proper extension to anharmonic chains is explained and tested through molecular dynamics. Our results are calibrated against the stochastic LeRoux lattice gas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗