We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \rightarrow \pi $ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi $ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha _s$. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

FLAG Review 2019

Dyson-Schwinger equations: Density, temperature and continuum strong QCD

A method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the 0(3) non-linear if-model on a simple square lattice. We also compute the isospin current form factor in this model and compare our results with the known exact expressions for the S-matrix and the form factor in the continuum limit. As a technical improvement, we introduce a two-cluster simulation algorithm which leads to significantly reduced statistical errors in the calculation of four-point correlation functions.

https://physics.ucsd.edu/students/courses/spring2013/physics142/labs/finalprojects/luscherwolff.pdf

HOW TO CALCULATETHE ELASTICSCATFERINGMATRiX IN TWO-DIMENSIONALQUANTUMFIELD THEORIES BY NUMERICAL SIMULATION

I review recent results on the infrared properties of QCD from Dyson-Schwinger equations. The topics include infrared exponents of one-particle irreducible Green's functions, the fixed point behaviour of the running coupling at zero momentum, the pattern of dynamical quark mass generation and properties of light mesons.

http://iopscience.iop.org/article/10.1088/0954-3899/32/8/R02/pdf

Infrared properties of QCD from Dyson-Schwinger equations

https://www.ge.infn.it/jlab12/IT/files/0612014-C.F..pdf

Nucleon electromagnetic form factors

We extend to quenched QCD an earlier investigation of the chiral structure of the masses of the nucleon and the delta in lattice simulations of full QCD. Even after including the meson-loop self-energies which give rise to the leading and next-to-leading nonanalytic behavior (and hence the most rapid variation in the region of light quark mass), we find surprisingly little curvature in the quenched case. Replacing these meson-loop self-energies by the corresponding terms in full QCD yields a remarkable level of agreement with the results of the full QCD simulations. This comparison leads to a very good understanding of the origins of the mass splitting between these baryons.

/pdf/chiral-analysis-of-quenched-baryon-masses-1oetn375yr.pdf

Chiral analysis of quenched baryon masses

Consideration of the analytic properties of pion-induced baryon self-energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral perturbation theory, the correct non-analytic behavior at the $N\ensuremath{\pi}$ threshold and the appropriate heavy-quark limit. They involve only three unknown parameters, which may be obtained by fitting to lattice data. Recent dynamical fermion results from CP-PACS and UKQCD are extrapolated using these new functional forms. We also use these functions to probe the limit of applicability of chiral perturbation theory to the extrapolation of lattice QCD results.

/pdf/baryon-masses-from-lattice-qcd-beyond-the-perturbative-q797gflrch.pdf

Baryon masses from lattice QCD: Beyond the perturbative chiral regime

Detailed investigations of the structure of hadrons are essential for understanding how matter is constructed from the quarks and gluons of Quantum chromodynamics (QCD), and amongst the questions posed to modern hadron physics, three stand out. What is the rigorous, quantitative mechanism responsible for confinement? What is the connection between confinement and dynamical chiral symmetry breaking? And are these phenomena together sufficient to explain the origin of more than 98% of the mass of the observable universe? Such questions may only be answered using the full machinery of nonperturbative relativistic quantum field theory. This contribution provides a perspective on progress toward answering these key questions. In so doing it will provide an overview of the contemporary application of Dyson-Schwinger equations in Hadron Physics, additional information on which may be found in Refs. [1, 2, 3, 4, 5, 6]. The presentation assumes that the reader is familiar with the concepts and notation of relativistic quantum mechanics, with the functional integral formulation of quantum field theory and with regularization and renormalization in its perturbative formulation. For these topics, in order of appearance, Refs. [7, 8, 9, 10] are useful. In addition, Chaps. 1 and 2 of Ref. [5] review the bulk ofmore » the necessary concepts. Hadron physics is a key part of the international effort in basic science. For example, in the USA we currently have the Thomas Jefferson National Accelerator Facility (JLab) and the Relativistic Heavy Ion Collider (RHIC) while in Europe hadron physics is studied at the Frascati National Laboratory and is an important part of a forthcoming pan-European initiative; namely, the Facility for Antiproton and Ion Research (FAIR) at GSI-Darmstadt. Progress in this field is gauged via the successful completion of precision measurements of fundamental properties of hadrons; e.g., the pion, proton and neutron, and simple nuclei, for comparison with theoretical calculations to provide a quantitative understanding of their quark substructure.« less

Aspects of hadron physics

The axial-vector Ward-Takahashi identity places constraints on particular properties of every pseudoscalar meson. For example, in the chiral limit all pseudoscalar mesons, except the Goldstone mode, decouple from the axial-vector current. Nevertheless, all neutral pseudoscalar mesons couple to two photons. The strength of the ${\ensuremath{\pi}}_{n}^{0}\ensuremath{\gamma}\ensuremath{\gamma}$ coupling, where $n=0$ denotes the Goldstone mode, is affected by the Abelian anomaly's continuum contribution. The effect is material for $n\ensuremath{\ne}0$. The ${\ensuremath{\gamma}}^{*}{\ensuremath{\pi}}_{n}{\ensuremath{\gamma}}^{*}$ transition form factor, ${\mathcal{T}}_{{\ensuremath{\pi}}_{n}}({Q}^{2})$, is nonzero $\ensuremath{\forall}n$, and ${\mathcal{T}}_{{\ensuremath{\pi}}_{n}}({Q}^{2})\ensuremath{\approx}(4{\ensuremath{\pi}}^{2}/3)({f}_{{\ensuremath{\pi}}_{n}}/{Q}^{2})$ at large ${Q}^{2}$. For all pseudoscalars but the Goldstone mode, this leading contribution vanishes in the chiral limit. In this instance the ultraviolet power-law behavior is $1/{Q}^{4}$ for $n\ensuremath{\ne}0$, and we find numerically ${\mathcal{T}}_{{\ensuremath{\pi}}_{1}}({Q}^{2})\ensuremath{\simeq}(4{\ensuremath{\pi}}^{2}/3)(\ensuremath{-}\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}/{Q}^{4})$. This subleading power-law behavior is always present. In general its coefficient is not simply related to ${f}_{{\ensuremath{\pi}}_{n}}$. The properties of $n\ensuremath{\ne}0$ pseudoscalar mesons are sensitive to the pointwise behavior of the long-range piece of the interaction between light quarks.

S. V. Wright

Papers

Chiral analysis of quenched baryon masses

Baryon masses from lattice QCD: Beyond the perturbative chiral regime

Aspects of hadron physics

Electromagnetic properties of ground-state and excited-state pseudoscalar mesons

In-medium kaon and antikaon properties in the quark-meson coupling model