We study the effects of different "fat link" actions for Kogut-Susskind quarks on flavor symmetry breaking. Our method is mostly empirical - we compute the pion spectrum with different valence quark actions on common sets of sample lattices. Different actions are compared, as best we can, at equivalent physical points. We find significant reductions in flavor symmetry breaking relative to the conventional or to the "link plus staple" actions, with a reasonable cost in computer time. We also develop and test a scheme for approximate unitarization of the fat links. While our tests have concentrated on the valence quark action, our results will be useful in designing simulations with dynamical quarks.Comment: 16 pages, LaTeX, PostScript figures include

We demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element M(P z3, z 2 3 ) as a function of the Ioffe time ν = P z3 and the distance z3. The next step is to divide M(P z3, z 2 3 ) by the rest-frame density M(0, z 2 3 ). Our lattice calculation shows a linear exponential z3-dependence in the rest-frame function, expected from the Z(z 2 3 ) factor generated by the gauge link. Still, we observe that the ratio M(P z3, z 2 3 )/M(0, z 2 3 ) has a Gaussian-type behavior with respect to z3 for 6 values of P used in the calculation. This means that Z(z 2 3 ) factor was canceled in the ratio. When plotted as a function of ν and z3, the data are very close to z3-independent functions. This phenomenon corresponds to factorization of the x-and k ⊥ -dependence for the TMD F(x, k 2 ⊥ ). For small z3 ≤ 4a, the residual z3-dependence is explained by perturbative evolution, with αs/π = 0.1.

We present results from a lattice hadron spectrum calculation using three flavors of dynamical quarks -two light and one strange, and quenched simulations for comparison. These simulations were done using a one-loop Symanzik improved gauge action and an improved Kogut-Susskind quark action. The lattice spacings, and hence also the physical volumes, were tuned to be the same in all the runs to better expose differences due to flavor number. Lattice spacings were tuned using the static quark potential, so as a byproduct we obtain updated results for the effect of sea quarks on the static quark potential. We find indications that the full QCD meson spectrum is in better agreement with experiment than the quenched spectrum. For the 0 ++ (a 0 ) meson we see a coupling to two pseudoscalar mesons, or a meson decay on the lattice. 11.15Ha,12.38.GcTypeset using REVT E X

The axial coupling of the nucleon, g, is the strength of its coupling to the weak axial current of the standard model of particle physics, in much the same way as the electric charge is the strength of the coupling to the electromagnetic current. This axial coupling dictates the rate at which neutrons decay to protons, the strength of the attractive long-range force between nucleons and other features of nuclear physics. Precision tests of the standard model in nuclear environments require a quantitative understanding of nuclear physics that is rooted in quantum chromodynamics, a pillar of the standard model. The importance of g makes it a benchmark quantity to determine theoretically-a difficult task because quantum chromodynamics is non-perturbative, precluding known analytical methods. Lattice quantum chromodynamics provides a rigorous, non-perturbative definition of quantum chromodynamics that can be implemented numerically. It has been estimated that a precision of two per cent would be possible by 2020 if two challenges are overcome: contamination of g from excited states must be controlled in the calculations and statistical precision must be improved markedly. Here we use an unconventional method inspired by the Feynman-Hellmann theorem that overcomes these challenges. We calculate a g value of 1.271 ± 0.013, which has a precision of about one per cent.

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and globalanalysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.The detailed understanding of the inner structure of nucleons is an active research field with phenomenological implications in high-energy, hadron, nuclear and astroparticle physics. Within quantum chromodynamics (QCD), information on this structure -specifically on how the nucleon's momentum and spin are divided among quarks and gluons -is encoded in parton distribution functions (PDFs).There exist two main methods to determine PDFs. 1 The first method is the global QCD analysis [3][4][5][6][7][8][9][10][11][12]. It is based on QCD factorization of physical observables, i.e. the fact that a class of hard-scattering cross-sections can be expressed as a convolution between short-distance, perturbative, matrix elements and long-distance, nonperturbative, PDFs. By combining a variety of available hard-scattering experimental data with state-of-the-art perturbative calculations, complete PDF sets, including the gluon and various combinations of quark flavors, are currently determined for protons, in both the unpolarized [13][14][15][16][17] and the polarized [18][19][20][21] case.Recent progress in global QCD analyses has been driven, on the one hand, by the increasing availability of a wealth of high-precision measurements from Jefferson Lab, HERA, RHIC, the Tevatron and the LHC and, on the other hand, by the advancement in perturbative calculations of QCD and electroweak (EW) higher-order corrections. Parton distributions are now determined with unprecedented precision, in many cases at the few-percent level. A paradigmatic illustration of this progress is provided by both the unpolarized and polarized gluon PDFs, which were affected by rather large uncertainties until recently, due to the limited experimental information available. In the unpolarized case, the gluon PDF is now constrained quite accurately from small to large x thanks to the inclusion of processes such a...

We present the first exploratory lattice QCD calculation of the pion valence quark distribution extracted from spatially separated current-current correlations in coordinate space. We show that an antisymmetric combination of vector and axial-vector currents provides direct information on the pion valence quark distribution. Using the collinear factorization approach, we calculate the perturbative tree-level kernel for this current combination and extract the pion valence distribution. The main goal of this article is to demonstrate the efficacy of this general lattice QCD approach in the reliable extraction of parton distributions. With controllable power corrections and a good understanding of the lattice systematics, this method has the potential to serve as a complementary to the many efforts to extract parton distributions in global analyses from experimentally measured cross sections. We perform our calculation on an ensemble of 2+1 flavor QCD using the isotropicclover fermion action, with lattice dimensions 32 3 × 96 at a lattice spacing a = 0.127 fm and the quark mass equivalent to a pion mass mπ 416 MeV.

The nuclear matrix element determining the pp → de þ ν fusion cross section and the Gamow-Teller matrix element contributing to tritium β decay are calculated with lattice quantum chromodynamics for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3) flavor-symmetric value of the quark masses, corresponding to a pion mass of m π ∼ 806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within 2σ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated pp → de þ ν transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be L 1;A ¼ 3.9ð0.2Þð1.0Þð0.4Þð0.9Þ fm 3 at a renormalization scale set by the physical pion mass, also agreeing within the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics. DOI: 10.1103/PhysRevLett.119.062002 Weak nuclear processes play a central role in many settings, from the instability of the neutron to the dynamics of core-collapse supernova. In this work, the results of the first lattice quantum chromodynamics (LQCD) calculations of two such processes are presented, namely, the pp → de þ ν e fusion process and tritium β decay. The pp → de þ ν process is centrally important in astrophysics as it is primarily responsible for initiating the proton-proton fusion chain reaction that provides the dominant energy production mechanism in stars like the Sun. Significant theoretical effort has been expended in refining calculations of the pp → de þ ν cross section at the energies relevant to solar burning, and progress continues to be made with a range of techniques [1][2][3][4][5][6][7][8][9][10], as summarized in Ref. [11]. This process is related to the νd → nne þ neutrino-induced deuteron-breakup reaction [12][13][14], relevant to the measurement of neutrino oscillations at the Sudbury Neutrino Observatory [15,16], and to the muon capture reaction μ − d → nnν μ , which is the focus of current investigation in the MuSun experiment [17]. The second process studied in this work, tritium β decay, is a powerful tool for investigating the weak interactions of the Standard Model and plays an important role in the search for new physics. The superallowed process 3 H → 3 He e − ν is theoretically clean and is the simplest semileptonic weak decay of a nuclear system. In contrast to pp fusion, this decay has been very precisely studied in the laboratory (see Ref.[18...

A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the nn → ppeeν e ν e transition is described in detail, expanding on the results presented in Ref.[1]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-β decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-β decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-β decay rates in heavy nuclei.