Constantia Alexandrou
Recent progress in hadron structure calculations within lattice QCD is reviewed. Results on key observables such as the axial charge, the quark momentum fraction and the spin content of the nucleon are discussed with focus on open issues. Lattice QCD studies of the $γ^* N\rightarrow Δ$ transition as well as the $Δ$ form factors are also presented.
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I describe recent progress toward calculating hadronic interactions with Lattice QCD.
This article reviews lattice QCD results for the light hadron spectrum. We give an overview of different formulations of lattice QCD, with discussions on the fermion doubling problem and improvement programs. We summarize recent developments in algorithms and analysis techniques, that render calculations with light, dynamical quarks feasible on present day computer resources. Finally, we summarize spectrum results for ground state hadrons and resonances using various actions.
Since the numerical path integration in the lattice QCD involves quark and gluon fields (not hadron fields) the lattice QCD cannot calculate any hadronic observable. Because of this reason the hadronic properties are extracted in the lattice QCD method by inserting complete set of hadron states $\sum_n |n><n|=1$ in between the partonic operators by assuming $H_{\rm QCD}|n>=E_n|n>$ where $E_n$ is the energy of the hadron. However, in this paper we find $H_{\rm QCD}|n>\neq E_n|n>$ because the QCD hamiltonian $H_{QCD}$ is unphysical but the $E_n$ and $|n>$ of the hadron are physical. We show that…
Following our previous proposal [1], we construct a class of good "lattice cross sections" (LCSs), from which we could study partonic structure of hadrons from ab initio lattice QCD calculations. These good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. We also show that proposed functions for la…
We compare the trace anomaly, strangeness and baryon number fluctuations calculated in lattice QCD with expectations based on hadron resonance gas model. We find that there is a significant discrepancy between the hadron resonance gas and the lattice data. This discrepancy is largely reduced if the hadron spectrum is modified to take into account the larger values of the quark mass used in lattice calculations as well as the finite lattice spacing errors. We also give a simple parametrization of QCD equation of state, which combines hadron resonance gas at low temperatures with lattice QCD at …
Lattice Gauge Theory enables an ab initio study of the low-energy properties of Quantum Chromodynamics, the theory of the strong interaction. I begin these lectures by presenting the lattice formulation of QCD, and then outline the benchmark calculation of lattice QCD, the light-hadron spectrum. I then proceed to explore the predictive power of lattice QCD, in particular as it pertains to hadronic physics. I will discuss the spectrum of glueballs, exotics and excited states, before investigating the study of form factors and structure functions. I will conclude by showing how lattice QCD can b…
We address the issue of hadron deformation within the framework of lattice QCD. For hadrons with spin greater than 1/2 the deformation can be determined by evaluating the charge and matter distributions. Deviation of the nucleon shape from spherical symmetry is determined by evaluating the quadrupole strength in the transition $γN \to Δ(1232)$ both in the quenched and in the unquenched theory.
Progress on the potential method, recently proposed to investigate hadron interactions in lattice QCD, is reviewed. The strategy to extract the potential in lattice QCD is explained in detail. The method is applied to extract $NN$ potentials, hyperon potentials and the meson-baryon potentials. A theoretical investigation is made to understand the origin of the repulsive core using the operator product expansion. Some recent extensions of the method are also discussed.
A survey of recent lattice QCD simulations for the mass spectrum of bottom and charmed hadrons is presented.
Model analysis on the effectiveness of the HAL QCD method for hadron-hadron interactions
本文通过推导公式，结合弹性散射简单模型及$\bar{K}N$散射分析，检验HAL QCD方法在强子-强子相互作用中的有效性，明确其定域势可定量再现散射相移并指示束缚态，还探讨了$\bar{K}N$势奇异行为的成因。
The determination of the pattern of hadronic resonances as predicted by Quantum Chromodynamics requires the use of non-perturbative techniques. Lattice QCD has emerged as the dominant tool for such calculations, and has produced many QCD predictions which can be directly compared to experiment. The concepts underlying lattice QCD are outlined, methods for calculating excited states are discussed, and results from an exploratory Nucleon and Delta baryon spectrum study are presented.
Hadron-Hadron Interactions from Lattice QCD: Theory meets Experiments
本文总结了基于HAL QCD方法在物理π质量附近研究强子-强子相互作用的最新进展，重点关注若干关键相互作用道及双π交换机制对长程相互作用的支配作用。
We review progress on hadron structure using lattice QCD simulations at or near to physical values of the QCD parameters. In particular, we discuss recent results on hadron masses, the nucleon charges, spin, gluon and quark unpolarized moments, the axial charge of hyperons, and the pion unpolarized moment.
A review of recent lattice QCD hadron structure calculations is presented. Important hadronic properties such as the axial charge and spin content of the nucleon, as well as, the mass and axial charge of hyperons and charmed baryons are discussed.
We propose a new method to extract hadron interactions above inelastic threshold from the Nambu-Bethe-Salpter amplitude in lattice QCD. We consider the scattering such as $A+B\rightarrow C+D$, where $A,B,C,D$ are names of different 1-particle states. An extension to cases where particle productions occur during scatterings is also discussed.
I discuss recent results of the NPLQCD Collaboration regarding the calculation of hadronic interactions with lattice QCD. A particular emphasis will be spent on pi-pi scattering and other meson interactions.
We compare lattice QCD results for appropriate combinations of net strangeness fluctuations and their correlations with net baryon number fluctuations with predictions from two hadron resonance gas (HRG) models having different strange hadron content. The conventionally used HRG model based on experimentally established strange hadrons fails to describe the lattice QCD results in the hadronic phase close to the QCD crossover. Supplementing the conventional HRG with additional, experimentally uncharted strange hadrons predicted by quark model calculations and observed in lattice QCD spectrum ca…
I review recent results from lattice QCD calculations on the in-medium hadron properties. I discuss the thermal dilepton rates, heavy quarkonium properties as well as the chiral and $U(1)_A$ symmetries at finite temperature.
Finite temperature lattice simulations of quantum chromodynamics (QCD) are sensitive to the hadronic mass spectrum for temperatures below the "critical" temperature T_c ~ 160 MeV. We show that a recent precision determination of the QCD trace anomaly shows evidence for the existence of a large number of hadron states beyond those known from experiment. The lattice results are well represented by an exponentially growing hadron mass spectrum up to a temperature T = 155 MeV. Using simple parametrizations we show how one may estimate the total spectral weight in these yet undermined states.
We review the potential method in lattice QCD, which has recently been proposed to extract nucleon-nucleon interactions via numerical simulations. We focus on the methodology of this approach by emphasizing the strategy of the potential method, the theoretical foundation behind it, and special numerical techniques. We compare the potential method with the standard finite volume method in lattice QCD, in order to make pros and cons of the approach clear. We also present several numerical results for the nucleon-nucleon potentials.
These are the proceedings of the workshop on ``Lattice QCD, Chiral Perturbation Theory and Hadron Phenomenology'' held at the European Centre for Theoretical Studies in Nuclear Physics and Related Areas from October 2 to 6, 2006. The workshop concentrated on bringing together researchers working in lattice QCD and chiral perturbation theory with the aim of improving our understanding how hadron properties can be calculated and analyzed from first principles. Included are a short contribution per talk.
Recent progress on charmed hadron interactions from lattice QCD
本研究针对实验发现奇特态推动下的粲强子物理研究需求，综述了利用格点QCD开展粲强子相互作用研究的最新进展，重点介绍了三个代表性系统的相关研究。
The use of lattice QCD to understand hadron structure is described, with particular emphasis on exploring the role of glue.
Recent progress in unquenched lattice QCD simulations is reviewed with emphasis on understanding of chiral behavior for light quark masses.
We present results on the spin carried by quarks and gluons in the nucleon using lattice QCD simulations with physical values of the light, strange and charm quark masses. We also discuss selective results on the x-dependence of parton distribution functions computed in lattice QCD employing the quasi-parton distribution approach and the large momentum effective theory.
Lattice QCD can give direct information on OZI-violating contributions to mesons. Here we explore the contributions that split flavour singlet and non-singlet meson masses. I discuss in detail the spectrum and decays for scalar mesons (ie including glueball effects). I also review the status of hybrid mesons and their decays.
A review of QCD-based theory approaches to study the heavy-flavor and exotic hadrons is given. The focus is on the results from lattice QCD and from lattice QCD complemented by effective field theories. Both approaches are first briefly introduced and applied in few examples. Then the status of various hadrons sectors is presented.
Spectroscopy of hadrons with heavy quarks from lattice QCD
本文综述了格点QCD对重夸克强子光谱的研究，涵盖常规与奇异强子，并探讨了部分常规强子的结构。
Lattice QCD calculations of hadron structure are a valuable complement to many experimental programs as well as an indispensable tool to understand the dynamics of QCD. I present a focused review of a few representative topics chosen to illustrate both the challenges and advances of our community: the momentum fraction, axial charge and charge radius of the nucleon. I will discuss the current status of these calculations and speculate on the prospects for accurate calculations of hadron structure from lattice QCD.
We report on calculations of the hadronic coupling constants $g_{ρππ}$ and $g_{nnπ}$ based on lattice QCD with four flavors of dynamical staggered fermions. By computing 2--point and 3--point Green's functions we have been able to determine these coupling constants ab initio from QCD; the results are compatible with the experimental values.
The ability to reliably measure the energy of an excited hadron in Lattice QCD simulations hinges on the accurate determination of all lower-lying energies in the same symmetry channel. These include not only single-particle energies, but also the energies of multi-hadron states. This talk deals with the determination of multi-hadron energies in Lattice QCD. The group-theoretical derivation of lattice interpolating operators that couple optimally to multi-hadron states is described. We briefly discuss recent algorithmic developments which allow for the efficient implementation of these operato…
Hadron spectroscopy and few-body dynamics from lattice QCD
本文回顾了利用格点QCD研究强子谱及其与少体动力学关系的最新方法，以应对QCD非微扰性质带来的挑战。
We present a summary of our results for the light hadron spectrum in quenched lattice QCD and preliminary ones in two-flavor full QCD. For the quenched hadron spectrum we find that the mass formulae predicted by quenched chiral perturbation theory(QChPT) give a good description of our results. Employing the QChPT mass formulae for chiral extrapolations we conclude that the mass spectrum in the continuum limit deviates unambiguously and systematically from experiment. For our two-flavor full QCD results we focus on the dynamical quark effects on the light hadron spectrum.
QCD spectral functions of hadrons in the pseudo-scalar and vector channels are extracted from lattice Monte Carlo data of the imaginary time Green's functions. The maximum entropy method works well for this purpose, and the resonance and continuum structures in the spectra are obtained in addition to the ground state peaks.
We summarize recent results on the hadron resonance gas description of QCD. In particular, we apply this approach to describe the equation of state and the vacuum expectation value of the Polyakov loop in several representations. Ambiguities related to exactly which states should be included are discussed.
Cooling is used as a filter on a set of gluon fields sampling the Wilson action to selectively remove essentially all fluctuations of the gluon field except for the instantons. The close agreement between quenched lattice QCD results with cooled and uncooled configurations for vacuum correlation functions of hadronic currents and for density-density correlation functions in hadronic bound states provides strong evidence for the dominant role of instantons in determining light hadron structure and quark propagation in the QCD vacuum.
Cooling is used as a filter on a set of gluon fields sampling the Wilson action to selectively remove essentially all fluctuations of the gluon field except for the instantons. The close agreement between quenched lattice QCD results with cooled and uncooled configurations for vacuum correlation functions of hadronic currents and for density-density correlation functions in hadronic bound states provides strong evidence for the dominant role of instantons in determining light hadron structure and quark propagation in the QCD vacuum.
Lattice QCD approach to study the hadronic resonances and exotic hadrons is described at an introductory level. The main challenge is that these states decay strongly via one or more decay channels, and they often lie near thersholds. Specific results for conventional and exotic hadrons are shown to illustrate the current status.
We present the QCD hadron spectrum for the cases of both quenched and two-flavor dynamical domain wall fermions. We compare the results obtained using the Wilson gauge action and a renormalization group improved gauge action. Finite volume effects and the dependence on the finite extent of the fifth dimension are discussed.
I present recent developments in the lattice QCD calculations of the light hadron spectrum. Emphasis is placed on the limitation of the quenched approximation in reproducing the observed spectrum and indications that the discrepancy is reduced by introducing two flavors of light dynamical quarks.
Approaching the Inverse Problem: Toward Lattice QCD Calculations of Inclusive Hadronic Quantities
该报告探讨格点QCD中包容性强子量计算的谱重建逆问题，并提出利用复分析技术严格界定不确定性的新方法。
The experimental value of g-2 of the muon is larger by $4.2 σ$ than the Standard Model prediction based on the hadronic vacuum polarization contribution (HVP) determined from the measured R-ratio, $σ(e^+e^- \! \rightarrow \! \mathit{hadrons})/σ(e^+e^- \! \rightarrow \!μ^+ μ^-)$; the HVP calculated in lattice QCD also significantly exceeds the measured R-ratio value. We show here that these discrepancies can be explained by an undetected contribution to $e^+e^- \! \rightarrow \! \mathit{hadrons}$ as could arise from production of neutral, long-lived hadrons which have not previously been identi…
Method of calculating hadron multi-point functions and disconnected quark loop contributions which are not readily accessible through conventional techniques is proposed. Results are reported for pion-pion, pion-nucleon and nucleon-nucleon scattering lengths and the flavor singlet-non singlet meson mass splitting estimated in quenched QCD.
Lattice QCD has matured to a degree where it is now possible to study excited hadrons as they truly appear in nature, as short-lived resonant enhancements decaying into multiple possible final states. Through variational analysis of matrices of correlation functions computed with large bases of interpolating fields it has proven possible to extract many excited state energy levels, and these can be used to constrain the hadron-hadron scattering amplitudes in which hadron resonances can be observed. Recent progress is illustrated with several examples including coupled-channel scattering in the…
Various suggestions exist for incorporating the strange quark into twisted mass QCD. One option for quenched simulations is to employ two twisted doublets, (u,d) and (c,s), with separate twist angles. Working in the isospin limit, preliminary results for the quenched spectrum of strange hadrons are presented, with both twist angles tuned to pi/2. Splittings within the mass multiplets provide some insight into the symmetry breaking effects of twisted mass lattice QCD.
The nonperturbative approach to soft high-energy hadron-hadron scattering, based on the analytic continuation of Wilson-loop correlation functions from Euclidean to Minkowskian theory, allows to investigate the asymptotic energy dependence of hadron-hadron total cross sections in lattice QCD. In this paper we will show, using best fits of the lattice data with proper functional forms satisfying unitarity and other physical constraints, how indications emerge in favor of a universal asymptotic high-energy behavior of the kind B log^2 s for hadronic total cross sections.
We report on the first large-scale study of two flavor QCD with domain wall fermions (DWF). Simulation has been carried out at three dynamical quark mass values about 1/2, 3/4, and 1 $m_{strange}$ on $16^3\times 32$ volume with $L_s=12$ and $a^{-1}\approx 1.7$ GeV. After discussing the details of the simulation, we report on the light hadron spectrum and decay constants.
The aim of the GRAL project is to simulate full QCD with standard Wilson fermions at light quark masses on small to medium-sized lattices and to obtain infinite-volume results by extrapolation. In order to establish the functional form of the volume dependence we study systematically the finite-size effects in the light hadron spectrum. We give an update on the status of the GRAL project and show that our simulation data for the light hadron masses depend exponentially on the lattice size.
A brief review is given of the lattice QCD calculation of the hadron spectrum. The status of current attempts toward inclusion of dynamical up, down and strange quarks is summarized focusing on our own work. Recent work on the possible existence of pentaquark states are assessed. We touch upon the PACS-CS Project for building our next machine for lattice QCD, and conclude with a near-term physics and machine prospects.
Progress in determining the spectrum of excited baryons and mesons in lattice QCD is described. Large sets of carefully-designed hadron operators have been studied and their effectiveness in facilitating the extraction of excited-state energies is demonstrated. A new method of stochastically estimating the low-lying effects of quark propagation is proposed which will allow reliable determinations of temporal correlations of single-hadron and multi-hadron operators.
Gauge-invariant equal-time correlation functions are calculated in lattice QCD within the quenched approximation and with two dynamical quark species. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the $Δ$.
We report progress on calculating the contribution to the anomalous magnetic moment of the muon from the disconnected hadronic diagrams with light and strange quarks and the valence QED contribution to the connected diagrams. The lattice QCD calculations use the highly-improved staggered quark (HISQ) formulation. The gauge configurations were generated by the MILC Collaboration with four flavors of HISQ sea quarks with physical sea-quark masses.
We evaluate the infinite volume, continuum limits of eight hadron mass ratios predicted by lattice QCD with Wilson quarks in the valence (quenched) approximation. Each predicted ratio differs from the corresponding observed value by less than 6\%.
The status and prospects for investigations of exotic and conventional hadrons with lattice QCD are discussed. The majority of hadrons decay strongly via one or multiple decay-channels, including most of the experimentally discovered exotic hadrons. Despite this difficult challenge, the properties of several hadronic resonances have been determined within lattice QCD. To further discern the spectroscopic properties of various hadrons and to help resolve their nature we present our suggestions for future analytic and lattice studies.
I suggest a new approach to the determination of the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon $a_μ^{\rm HVP}$ in lattice QCD. It is based on properties of the Mellin transform of the hadronic spectral function and their relation to the HVP self energy in the Euclidean. I show how $a_μ^{\rm HVP}$ is very well approximated by a few moments associated to this Mellin transform and how these moments can be evaluated in lattice QCD, providing thus a series of tests when compared with the corresponding determinations using experimental data.
By means of a nonperturbative approach to soft high-energy hadron-hadron scattering, based on the analytic continuation of Wilson-loop correlation functions from Euclidean to Minkowskian theory, we shall investigate the asymptotic energy dependence of hadron-hadron total cross sections in lattice QCD: we will show, using best fits of the lattice data with proper functional forms satisfying unitarity and other physical constraints, how indications emerge in favor of a universal asymptotic high-energy behavior of the kind $B \log^2 s$ for hadronic total cross sections.
We perform a lattice QCD calculation of the hadronic light-by-light scattering amplitude in a broad kinematical range. At forward kinematics, the results are compared to a phenomenological analysis based on dispersive sum rules for light-by-light scattering. The size of the pion pole contribution is investigated for momenta of typical hadronic size. The presented numerical methods can be used to compute the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Our calculations are carried out in two-flavor QCD with the pion mass in the range of 270 to 450MeV, and c…
After a brief self-contained introduction to the muon anomalous magnetic moment, (g-2), we review the status of lattice calculations of the hadronic vacuum polarization contribution and present first results from lattice QCD for the hadronic light-by-light scattering contribution. The signal for the latter is consistent with model calculations. While encouraging, the statistical error is large and systematic errors are mostly uncontrolled. The method is applied first to pure QED as a check.
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