Lattice QCD Techniques Research Articles

First lattice QCD calculation of semileptonic decays of charmed-strange baryons Ξ c * *Supported in part by Natural Science Foundation of China (11735010, U2032102, 11653003, 12005130, 11521505, 12070131001, 11975127, 11935017, 12005130, 12125503), Natural Science Foundation of Shanghai (15DZ2272100), the China Postdoctoral Science Foundation and the National Postdoctoral Program for Innovative Talents (BX20190207), National Key Research and Development Program of China

While the standard model is the most successful theory to describe all the interactions and constituents of elementary particle physics, it has been constantly scrutinized for over four decades. Weak decays of charm quarks can be used to measure the coupling strength between quarks in different families and serve as an ideal probe for CP violation. As the lowest charm-strange baryons with three different flavors, baryons (composed of or ) have been extensively studied in experiments. In this study, we use state-of-the-art lattice QCD techniques to generate 2+1 clover fermion ensembles with two lattice spacings, . Then, we present the first ab-initio lattice QCD calculation of the form factors. Our theoretical results for the decay widths are consistent with and approximately two times more precise than the latest measurements by the ALICE and Belle collaborations. Based on the latest experimental measurements, we independently obtain the quark-mixing matrix element , which is in good agreement with results from other theoretical approaches.

Breakdown of Chiral Perturbation Theory for the Axion Hot Dark Matter Bound.

We show that the commonly adopted hot dark matter bound on the axion mass m_{a}≲1 eV is not reliable, since it is obtained by extrapolating the chiral expansion in a region where the effective field theory breaks down. This is explicitly shown via the calculation of the axion-pion thermalization rate at the next-to-leading order in chiral perturbation theory. We finally advocate a strategy for a sound extraction of the axion hot dark matter bound via lattice QCD techniques.

Elastic form factors of nucleon excitations in lattice QCD

First principles calculations of the form factors of baryon excitations are now becoming accessible through advances in Lattice QCD techniques. In this paper, we explore the utility of the parity-expanded variational analysis (PEVA) technique in calculating the Sachs electromagnetic form factors for excitations of the proton and neutron. We study the two lowest-lying odd-parity excitations and demonstrate that at heavier quark masses, these states are dominated by behaviour consistent with constituent quark models for the $N^*(1535)$ and $N^*(1650)$, respectively. We also study the lowest-lying localised even-parity excitation, and find that its form factors are consistent with a radial excitation of the ground state nucleon. A comparison of the results from the PEVA technique with those from a conventional variational analysis exposes the necessity of the PEVA approach in baryon excited-state studies.

News from the Lattice: example of the pion distribution amplitude

In this contribution I present a brief summary of recent progress in selected Lattice QCD techniques and subsequently illustrate them using the example of the current calculations of moments of meson distribution amplitude as well as of a direct evaluation of meson distribution amplitude.

Lattice QCD spectroscopy for hadronic CP violation

The interpretation of nuclear electric dipole moment (EDM) experiments is clouded by large theoretical uncertainties associated with nonperturbative matrix elements. In various beyond-the-Standard Model scenarios nuclear and diamagnetic atomic EDMs are expected to be dominated by CP-violating pion-nucleon interactions that arise from quark chromo-electric dipole moments. The corresponding CP-violating pion-nucleon coupling strengths are, however, poorly known. In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calculating the pion-nucleon coupling constants, a challenging task, we use chiral symmetry relations that link the pion-nucleon couplings to nucleon sigma terms and mass splittings that are significantly easier to calculate. In this work, we show that these relations are reliable up to next-to-next-to-leading order in the chiral expansion in both SU(2) and SU(3) chiral perturbation theory. We conclude with a brief discussion about practical details regarding the required lattice QCD calculations and the phenomenological impact of an improved understanding of CP-violating matrix elements.

Applications of lattice QCD techniques for condensed matter systems

We review the application of lattice QCD techniques, most notably the Hybrid Monte Carlo (HMC) simulations, to first-principle study of tight-binding models of crystalline solids with strong inter-electron interactions. After providing a basic introduction into the HMC algorithm as applied to condensed matter systems, we review HMC simulations of graphene, which in the recent years have helped to understand the semimetal behavior of clean suspended graphene at the quantitative level. We also briefly summarize other novel physical results obtained in these simulations. Then we comment on the applicability of hybrid Monte Carlo to topological insulators and Dirac and Weyl semimetals and highlight some of the relevant open physical problems. Finally, we also touch upon the lattice strong-coupling expansion technique as applied to condensed matter systems.

Neutron electric dipole moment usingNf=2+1+1twisted mass fermions

We evaluate the neutron electric dipole moment $\vert \vec{d}_N\vert$ using lattice QCD techniques. The gauge configurations analyzed are produced by the European Twisted Mass Collaboration using $N_f{=}2{+}1{+}1$ twisted mass fermions at one value of the lattice spacing of $a \simeq 0.082 \ {\rm fm}$ and a light quark mass corresponding to $m_{\pi} \simeq 373 \ {\rm MeV}$. Our approach to extract the neutron electric dipole moment is based on the calculation of the $CP$-odd electromagnetic form factor $F_3(Q^2)$ for small values of the vacuum angle $\theta$ in the limit of zero Euclidean momentum transfer $Q^2$. The limit $Q^2 \to 0$ is realized either by adopting a parameterization of the momentum dependence of $F_3(Q^2)$ and performing a fit, or by employing new position space methods, which involve the elimination of the kinematical momentum factor in front of $F_3(Q^2)$. The computation in the presence of a $CP$-violating term requires the evaluation of the topological charge ${\cal Q}$. This is computed by applying the cooling technique and the gradient flow with three different actions, namely the Wilson, the Symanzik tree-level improved and the Iwasaki action. We demonstrate that cooling and gradient flow give equivalent results for the neutron electric dipole moment. Our analysis yields a value of $\vert \vec{d}_N\vert=0.045(6)(1)\ \bar{\theta} \ e \cdot {\rm fm}$ for the ensemble with $m_\pi=373$ MeV considered.

Developments in lattice quantum chromodynamics for matter at high temperature and density

A brief overview of the QCD phase diagram at nonzero temperature and density is provided. It is explained why standard lattice QCD techniques are not immediately applicable for its determination, due to the sign problem. A selection of recent lattice approaches that attempt to evade the sign problem are then discussed and classified according to the underlying principle: constrained simulations (density of states, histograms), holomorphicity (complex Langevin, Lefschetz thimbles), partial summations (clusters, subsets, bags) and change in integration order (strong coupling, dual formulations).

Some exact results on the QCD critical point

We show, in a model-independent manner, that the QCD critical point can appear only inside the pion condensation phase of the phase-quenched QCD as long as the contribution of flavor-disconnected diagrams is negligible. The sign problem is known to be maximally severe in this region, implying that the QCD critical point is reachable by the present lattice QCD techniques only if there is an enhancement of the flavor-disconnected contribution at finite baryon chemical potential.

Determination of the [formula omitted] and [formula omitted] quark masses from [formula omitted] decay

For a precise determination of the m_u and m_d quark masses, it is useful to combine isospin symmetric results of lattice or sum rules QCD techniques with some isospin breaking study performed in chiral perturbation theory (ChPT). The most promising process for the later is $\eta \to 3\pi$ decay. However, this process is affected by large chiral corrections and there are observed discrepancies between the values of Dalitz plot parameters stemming from the standard ChPT computation of its amplitude and those experimentally measured. We describe here the method based on analytic dispersive representation which attempts to obtain the information on the masses by taking this discrepancy into account independently of its exact origin. Together with the results of this analysis we present a review of some other constraints on the light quark masses and conclude with values of the masses compatible with them.

Magnetic moments of vector, axial, and tensor mesons in lattice QCD

We present a calculation of magnetic moments for selected spin-1 mesons using the techniques of lattice QCD. This is carried out by introducing a progressively small static magnetic field on the lattice and measuring the linear response of a hadron's mass shift. The calculations are done on ${24}^{4}$ quenched lattices using standard Wilson actions, with $\ensuremath{\beta}=6.0$ and pion mass down to 500 MeV. The results are compared to those from the form factor method.

Study of the gluon-quark-antiquark static potential in SU(3) lattice QCD

We study the long distance interaction for hybrid hadrons, with a static gluon, a quark and an antiquark with lattice QCD techniques. A Wilson loop adequate to the static hybrid three-body system is developed and, using a ${24}^{3}\ifmmode\times\else\texttimes\fi{}48$ periodic lattice with $\ensuremath{\beta}=6.2$ and $a\ensuremath{\sim}0.072\text{ }\text{ }\mathrm{fm}$, two different geometries for the gluon-quark segment and the gluon-antiquark segment are investigated. When these segments are perpendicular, the static potential is compatible with confinement realized with a pair of fundamental strings, one linking the gluon to the quark and another linking the same gluon to the antiquark. When the segments are parallel and superposed, the total string tension is larger and agrees with the Casimir scaling measured by Bali. This can be interpreted with a type-II superconductor analogy for the confinement in QCD, with repulsion of the fundamental strings.

Gluon flux-tube distribution and linear confinement in baryons

We have observed the formation of gluon flux-tubes within baryons using lattice QCD techniques. A high-statistics approach, based on translational and rotational symmetries of the four-dimensional lattice, enables us to observe correlations between vacuum action density and quark positions in a completely gauge independent manner. This contrasts with earlier studies which used gauge-dependent smoothing techniques. We used 200 O(a^2) improved quenched QCD gauge-field configurations on a 16^3x32 lattice with a lattice spacing of 0.123 fm. In the presence of static quarks flux tubes representing the suppression of gluon-field fluctuations are observed. We have analyzed 11 L-shapes and 8 T and Y shapes of varying sizes in order to explore a variety of flux-tube topologies, including the ground state. At large separations, Y-shape flux-tube formation is observed. T-shaped paths are observed to relax towards a Y-shaped topology, whereas L-shaped paths give rise to a large potential energy. We do not find any evidence for the formation of a Delta-shaped flux-tube (empty triangle) distribution. However, at small quark separations, we observe an expulsion of gluon-field fluctuations in the shape of a filled triangle with maximal expulsion at the centre of the triangle. Having identified the precise geometry of the flux distribution, we are able to perform quantitative comparison between the length of the flux-tube and the associated static quark potential. For every source configuration considered we find a universal string tension, and conclude that, for large quark separations, the ground state potential is that which minimizes the length of the flux-tube. The flux tube radius of the baryonic ground state potential is found to be 0.38 \pm 0.03 fm, with vacuum fluctuations suppressed by 7.2 \pm 0.6 %.

Magnetic polarizability of hadrons from lattice QCD in the background field method

We present a calculation of hadron magnetic polarizability using the techniques of lattice QCD. This is carried out by introducing a uniform external magnetic field on the lattice and measuring the quadratic part of a hadron's mass shift. The calculation is performed on a 24{sup 4} lattice with standard Wilson actions at beta=6.0 (spacing a=0.1 fm) and pion mass down to about 500 MeV. Results are obtained for 30 particles covering the entire baryon octet (n, p, {sigma}{sup 0}, {sigma}{sup -}, {sigma}{sup +}, {xi}{sup -}, {xi}{sup 0}, {lambda}) and decuplet ({delta}{sup 0}, {delta}{sup -}, {delta}{sup +}, {delta}{sup ++}, {sigma}*{sup 0}, {sigma}*{sup -}, {sigma}*{sup +}, {xi}*{sup 0}, {xi}*{sup -}, {omega}{sup -}), plus selected mesons ({pi}{sup 0}, {pi}{sup +}, {pi}{sup -}, K{sup 0}, K{sup +}, K{sup -}, {rho}{sup 0}, {rho}{sup +}, {rho}{sup -}, K*{sup 0}, K*{sup +}, K*{sup -}). The results are compared with available values from experiments and other theoretical calculations.

Baryons on the lattice

I comment on progress of lattice QCD techniques and calculations. Recent results on pentaquark masses as well as of the spectrum of excited baryons are summarizned and interpreted. The present state of calculations of quantities related to the nucleon structure and of electromagnetic transition form factors is surveyed.

Understanding hadron structure using lattice QCD

An elementary introduction is presented to the study of hadron structure using lattice QCD. Following a brief review of relevant aspects of path integrals, the discrete lattice path integral is presented for gluon and quark fields and used to calculate physical observables. Essential aspects of instanton physics are reviewed, and it is shown how the instanton content is extracted from lattice gluon configurations. Finally, both comparison of results including all gluons with those including only instantons and the study of quark zero modes associated with instantons and their contributions to hadronic observables are used to show the dominant role of gluons in hadron structure. MIT CTP# 2701 hep-lat/9804017 1. – Introduction and Motivation Although a quarter of a century has passed since the experimental discovery of quarks and the formulation of QCD, we are only now beginning to understand the essential physics of the structure of light hadrons. To truly understand hadron structure, one must solve rather than model QCD, and the only known means to do so is the numerical solution of lattice field theory. But obtaining accurate numerical results for observables from a computer is not enough — we also need to obtain physical insight. Hence, our strategy is to use numerical evaluation of the QCD path integral on a lattice to identify the configurations that dominate the action as well as to calculate observables. In recent years, the algorithms and techniques of lattice QCD and the performance of massively parallel computers have developed to the point that we are now on the threshold of reliable, quantitative calculations of QCD observables. Furthermore, there is strong evidence from lattice calculations that the topological excitations of the gluon field corresponding in the semiclassical limit to instantons play a dominant role in the structure of light hadrons. The purpose of these lectures is to describe at an elementary level the basic elements of lattice QCD and how numerical solution of QCD on a lattice is elucidating the role of instantons in light hadrons. To appreciate the significance of the current lattice results, it is useful to recall the wide range of disparate physical pictures that have arisen from the different QCD inspired models introduced to model hadrons. For example, non-relativistic quark models focus on constituent quarks interacting via an adiabatic potential. Bag models postulate a

Weak interaction matrix elements in strong coupling lattice QCD

Amplitude of many non-leptonic processes require a non-perturbative calculation of matrix elements between pseudo-Goldstone boson states, after the standard perturbation theory in the Electro-Weak sector. Several such matrix elements are estimated using the techniques of strong coupling lattice QCD.

Charge radii from lattice relative charge distributions

Electromagnetic charge radii values are extracted from relative charge distribution data for pseudoscalars using lattice QCD techniques. This is done with Wilson fermions and SU(2) color at five values of the hopping parameter.