A Review of Nucleon Spin Calculations in Lattice QCD
Huey-Wen Lin
本文综述了核子自旋结构的晶格计算的最新进展，包括部分子分布函数、形状因子、广义部分子分布以及晶格技术的最新发展。
We review recent progress on lattice calculations of nucleon spin structure, including the parton distribution functions, form factors, generalization parton distributions, and recent developments in lattice techniques.
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It has proven a significant challenge to experiment and phenomenology to extract precise values of the nucleon sigma terms. This difficulty opens the window for lattice QCD simulations to lead the field in resolving this aspect of nucleon structure. Here we report on recent advances in the extraction of nucleon sigma terms in lattice QCD. In particular, the strangeness component is now being resolved to a precision that far surpasses best phenomenological estimates.
We study the three nucleon force in Nf=2 dynamical clover fermion lattice QCD, utilizing the Nambu-Bethe-Salpeter wave function of the three nucleon system. Since parity-odd two nucleon potentials are not available in lattice QCD at this moment, we develop a new formulation to extract the genuine three nucleon force which requires only the information of parity-even two nucleon potentials. In order to handle the extremely expensive calculation cost, we consider a specific three-dimensional coordinate configuration for the three nucleons. We find that the linear setup is advantageous, where nuc…
In this paper we review recent progress in hadron structure using lattice QCD simulations, with main focus in the evaluation of nucleon matrix elements. We highlight developments that may guide new Physics searches, such as the scalar and tensor charges, as well as, the neutron electric dipole moment.
Calculation of the nucleon axial charge in lattice QCD
质子和中子有着丰富的结构，就它们的组成成分夸克和胶子而言。理解这种结构需要解决量子色动力学（QCD）。然而QCD是极其复杂的，所以我们必须用一种称为格点量子色动力学的方法来数值求解QCD方程。在这里，我们描述了一个典型的格点量子色动力学计算检查我们最近的核子轴荷的计算。
New Developments in Lattice QCD: Calculation of Flavor Singlet Nucleon Matrix Elements and Hadron Scattering Lengths
评述了味单重态核子矩阵元的格点量子色动力学计算的最新进展。在$π$ - $N\ σ$项和核子的夸克自旋含量中发现了大量的海夸克贡献，使得包括价贡献的总幅度与实验合理一致。指出了味非单重态核子矩阵元的一些问题。最后讨论了格点量子色动力学计算强子散射长度的最新工作。
In this lattice QCD study we evaluate the nucleon spin decomposition to quarks and gluons contributions. We employ one gauge ensemble of maximally twisted mass fermions with two degenerate light quarks tuned to approximately reproduce the physical pion mass. We find that both spin sum and momentum sum are satisfied within the current statistical and systematic accuracy.
Even parity excitations of the nucleon in lattice QCD
本文研究了猝灭格点量子色动力学中核子偶宇称激发谱。我们扩展了我们以前的分析，包括扩展的基础上的核子插值字段，增加晶格的物理尺寸，包括更多的配置，以提高统计和探测更接近手征极限。通过对世界晶格数据的回顾，我们得出结论：在猝灭的格点量子色动力学中，几乎没有发现Roper共振的证据。
Bayesian approach to the first excited nucleon state in lattice QCD
本文首次尝试用最大熵方法（MEM）从格点量子色动力学数据重建核子和$Δ$通道的谱函数，给出了初步结果。MEM分析的一个优点是使我们能够获得激发态光谱的信息。通过对两个格点体的模拟，我们证实了在轻夸克质量区，第一激发核子态的大有限尺寸效应。
The parity partner of the nucleon in quenched QCD with domain wall fermions
本文利用在有限格点截断下保持手征对称性的畴壁费米子方法，给出了淬灭格点量子色动力学中核子及其低激发态的质谱的初步结果.在核子和它的宇称伙伴之间观察到确定的质量分裂。这种分裂随着价夸克质量的减少而增加。我们还提出了关于第一个正宇称激发态的初步数据。
The three-particle $Nππ$-state contribution to the QCD two-point function of standard nucleon interpolating fields is computed to leading order in chiral perturbation theory. Using the experimental values for two low-energy coefficients the impact of this contribution on lattice QCD calculations of the nucleon mass is estimated. The impact is found to be at the per mille level at most and negligible in practice.
Nucleon sigma terms with a variational analysis from Lattice QCD
本研究基于格点QCD，通过广义特征向量分析结合核子-sigma型插值算符，有效降低了核子三点函数中的激发态污染，从而更准确地确定了核子sigma项。
Polarized Nucleon Structure Functions from Lattice QCD
本文描述了质子和中子极化深度非弹性结构函数g_1和g_2矩的高统计猝灭QCD计算。
We study the sigma term and the strange quark content of nucleon in 2+1-flavor QCD with dynamical overlap fermions. We analyze the lattice data of nucleon mass taken at two different strange quark masses with five values of up and down quark masses each. Using the reweighting technique, we study the strange quark mass dependence of the nucleon and extract the strange quark content.
Quark Mass Dependence of Nucleon Properties and Extrapolation from Lattice QCD
本文综述了核子磁矩和轴矢量耦合常数g_A与夸克质量的关系。目的是探索手征有效场论方法外推格点量子色动力学结果的可行性，从相对较大的夸克质量，可以在这样的计算处理到物理相关的范围。
We determine generalized form factors of the nucleon from lattice simulations with $N_f = 2$ mass-degenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions down to a pion mass of 150 MeV. We also present the resulting isovector quark angular momentum. Possible excited-state contaminations are investigated with correlated simultaneous fits.
The quark-composites approach to QCD: The nucleon-pion interaction
我们推导出一个新的微扰方法QCD的框架内的π-核子相互作用的基础上使用的夸克复合作为基本变量。在定义配分函数的Berezin积分中，假设核子量子数的复合为新的积分变量，而手征介子量子数的复合则用辅助玻色子场代替.通过增加不相关的算子来修改作用，这些算子为这些复合物提供动力学项，夸克作用被视为微扰。由此产生的膨胀具有内置的夸克禁闭。到一阶，我们得到了Yukawa模型的π-核子相互作用。
Nucleon-structure calculations of isovector vector- and axialvector-current form factors, transversity and scalar charge, and quark momentum and helicity fractions are reported from two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD Collaborations with Iwasaki $\times$ dislocation-suppressing-determinatn-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV.
Excited nucleon spectrum from lattice QCD with maximum entropy method
本文用最大熵谱分析方法研究了猝灭格点量子色动力学中核子的激发态。我们的模拟进行三个晶格尺寸$16^3\times 32$，$24^3\times 32$和$32^3\times 32$，在$β=6.0$，以解决有限体积的问题。我们发现对于轻夸克质量，Roper共振的质量存在明显的有限体积效应。在消除了这个系统误差后，它的质量变得相当小，朝着解决罗珀共振$N'(1440)$和负宇称核子$N^*(1535)$之间的能级顺序之谜的方向发展。
Finite Size Effects in Nucleon Masses in Dynamical QCD
对于轻动力学夸克的晶格计算，有限尺寸效应已经成为一个重要的方面。本文研究了1- 2fm的N_f=2动力学格点上核子质量的有限尺寸效应。在单圈手征微扰理论中得到了有限尺寸效应的预言。
Nucleon structure from generalized parton distributions in lattice QCD
本文介绍了QCDSF-UKQCD合作的结果，基于O（a）改进的Wilson费米子，研究了双味格点量子色动力学中的主导扭曲广义部分子分布的矩。我们研究了与螺旋度无关和螺旋度翻转的广义相对论，重点研究了横截面中夸克的密度。
The charmonium-nucleon effective central interactions have been computed by the time-dependent HAL QCD method. This gives an updated result of a previous study based on the time-independent method, which is now known to be problematic because of the difficulty in achieving the ground-state saturation. We discuss that the result is consistent with the heavy quark symmetry. No bound state is observed from the analysis of the scattering phase shift; however, this shall lead to a future search of the hidden-charm pentaquarks by considering channel-coupling effects.
We explore three-nucleon forces (3NF) from lattice QCD simulations. Utilizing the Nambu-Bethe-Salpeter (NBS) wave function, two-nucleon forces (2NF) and 3NF are determined on the same footing. Quantum numbers of the three-nucleon (3N) system are chosen to be (I, J^P)=(1/2,1/2^+) (the triton channel). The enormous computational cost is reduced by employing the simplest geometrical configuration, where 3N are aligned linearly with an equal spacing. We perform lattice QCD simulations using Nf=2 dynamical clover fermion configurations generated by CP-PACS Collaboration, at the lattice spacing of a…
Generalized Parton Distributions from Lattice QCD
我回顾了LHPC协作组的格点量子色动力学计算的广义部分子分布的核子和突出的那些方面的核子结构最好的说明格点量子色动力学，核子的自旋分解和横夸克结构。
Precision measurements on nucleons provide constraints on the Standard Model and can also discern the signatures predicted for particles beyond the Standard Model. Knowing the Standard Model inputs to nucleon matrix elements will be necessary to constrain the couplings of dark matter candidates such as the neutralino, to relate the neutron electric dipole moment to the CP-violating theta parameter, or to search for new TeV-scale particles though non-$V-A$ interactions in neutron beta decay. However, these matrix elements derive from the properties of quantum chromodynamics (QCD) at low energie…
We calculate the strange quark content of the nucleon directly from its disconnected three-point function in N_f=2+1 QCD. Chiral symmetry is crucial to avoid a possibly large contamination due to operator mixing, and is exactly preserved by employing the overlap quark action. We also use the all-to-all quark propagator and the low-mode averaging technique in order to accurately calculate the relevant nucleon correlator. Our preliminary result extrapolated to the physical point is f_{T_s} = 0.013(12)(16). This is in good agreement with our previous estimate in N_f=2 QCD as well as those from ou…
Hyperon-Nucleon Scattering from Fully-Dynamical Lattice QCD
我们首次用全动力学格点量子色动力学研究了超子-核子散射。一个s波相移被确定为n λ散射在两个自旋通道在π介子质量为350，490，和590 MeV，和n σ散射在两个自旋通道在π介子质量为490，和590 MeV。计算是在晶格间距为b ~ 0.125 fm的动态交错规范组态上用畴壁价夸克进行的。
The nucleon to Delta electromagnetic transition form factors in lattice QCD
用两种简并的动力学Wilson费米子和具有畴壁价夸克的动力学海交错费米子计算了电磁核子到Delta跃迁的形状因子。两个次主导的四极形状因子的第一次在全QCD评估到足够的精度，以排除零值，这是作为一个信号的变形的核子三角洲系统。对于库仑四极形状因子，在低q ^2时，未淬灭的结果与淬灭的结果有偏差，这使得动力学晶格结果更接近实验，从而证实了π云对这个量的贡献的重要性。
We present new N_f=2 data for the nucleon generalized form factors, varying volume, lattice spacing and pion mass, down to 150 MeV. We also give an update of our direct calculation of the nucleon sigma term for a range of pion mass values including the lightest one.
Calculation of Finite Size Effects on the Nucleon Mass in Unquenched QCD using Chiral Perturbation Theory
本文用相对论手征微扰理论计算了核子质量的有限尺寸效应。结果进行了比较，与两味格的结果。
The strangeness of the nucleon, <N|ss|N> - <0|ss|0>, is a quantity of interest for interpreting the results of dark matter detection experiments as well as for exploring the structure of the nucleon itself. We present a calculation of this quantity in 2+1 flavor lattice QCD using a range of lattice spacings and quark masses. The method is based on calculating quark-line disconnected contributions on the MILC lattice configurations, which include the effects of dynamical strange quarks. After continuum and chiral extrapolations, the value is <N|ss|N> - <0|ss|0> = 0.69 +/- 0.07(stat) +/- 0.09(sy…
Nucleon and Nucleon to Delta Axial form factors from Lattice QCD
我们给出了在猝灭理论中，利用动力学威尔逊费米子的两种简并形式，在动量转移平方约为0.1 ~ 2 GeV ^2，π介子质量在380 ~ 600 MeV范围内，核子轴向矢量形状因子$G_A(q^2)$和$G_p(q^2)$的结果。我们还提出了相应的N到Delta轴向矢量转换形状因子$C_5^A(q^2)$和$C_6^A(q^2)$的结果，除了威尔逊费米子，域壁价夸克和动力学交错海夸克提供的MILC合作。
What we are learning about the Quark Structure of Hadrons from Lattice QCD?
随着格点场论和计算机技术的发展，利用格点量子色动力学研究强子的夸克结构取得了巨大的进展。这个演讲将描述选定的例子，包括结构函数，电磁形状因子，核子轴向电荷，核子自旋的起源，核子的横向结构，以及核子到Delta跃迁的形状因子。
We discuss a robust projection method for the extraction of excited-state masses of the nucleon from a matrix of correlation functions. To illustrate the algorithm in practice, we present results for the positive parity excited states of the nucleon in quenched QCD. Using eigenvectors obtained via the variational method, we construct an eigenstate-projected correlation function amenable to standard analysis techniques. The method displays its utility when comparing results from the fit of the projected correlation function with those obtained from the eigenvalues of the variational method. Sta…
Nucleon Spin Structures from Lattice QCD: Flavor Singlet Axial and Tensor Charges
在格点量子色动力学中计算了核子的味单重轴荷和张量荷。我们发现$ΔΣ=Δu+Δd+Δs=+0.638(54)-0.347(46)-0.109(30) = +0.18(10)$的轴向电荷和$δΣ=δu+δd+δs=+0.839(60)-0.231(55)-0.046(34) = +0.562(88)$的张量电荷。对轴向电荷的计算结果与实验结果符合较好，而对张量电荷的计算结果是在实验测量之前首次从格点量子色动力学得到的结果。
A determination of the excited energy eigenstates of the nucleon, $s=c{1}{2}$, $I={1}{2}$, $N^{\pm}$, is presented in full QCD using 2+1 flavor PACS-CS gauge configurations. The correlation-matrix method is used and is built using standard nucleon interpolators employing smearings at the fermion sources and sinks. We develop and demonstrate a new technique that allows the eigenvectors obtained to be utilized to track the propagation of the intrinsic nature of energy-states from one quark mass to the next. This approach is particularly useful for larger dimension correlation matrices where more…
The current status is reported of joint lattice numerical calculations by LHP and RBC collaborations of isovector nucleon form factors using 2+1-flavor physical-mass domain-wall fermions ensemble at a lattice cutoff $a^{-1}$ of 1.730(4) GeV and spatial volume of $(La=\mbox{\rm 5.471(13)fm})^3$ generated jointly by RBC and UKQCD collaborations.
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.
Fits of the p^4 covariant SU(2) baryon chiral perturbation theory to lattice QCD nucleon mass data from several collaborations for 2 and 2+1 flavors are presented. We consider contributions from explicit Delta(1232) degrees of freedom, finite volume and finite spacing corrections. We emphasize here our Nf=2+1 study. We obtain low-energy constants of natural size that are compatible with the rather linear pion-mass dependence of the nucleon mass observed in lattice QCD. We report a value for the pion-nucleon sigma term of 41(5)(4) MeV for the 2 flavor case and 52(3)(8) MeV for 2+1 flavors.
Nucleon form factors and structure functions from Lattice QCD
在这次演讲中，我们强调最近的核子形状因子和结构函数的晶格计算。
Electric dipole moments (EDMs) of nucleons and nuclei are actively considered as direct evidence of the CP violation. Calculations of nucleon EDMs on lattice are required to connect the quark- and hadron- level effective CP violating interactions within QCD or other CP violating sources in new physics beyond the standard model. Among them, the theta-induced nucleon EDM, that is the only such renormalizable interaction, has widely been investigated on a lattice. In the report, we review recent developments of the lattice calculations of nucleon EDM induced QCD theta term.
Lattice QCD calculations of resonant meson-meson scattering amplitudes have improved significantly due to algorithmic and computational advances. However, progress in meson-nucleon scattering has been slower due to difficulties in computing the necessary correlation functions, the exponential signal-to-noise problem, and the finite-volume treatment of scattering with fermions. Nonetheless, first benchmark calculations have now been performed. The status of lattice QCD calculations of meson-nucleon scattering amplitudes is reviewed together with comments on future prospects.
Nucleon-Nucleon Scattering From Fully-Dynamical Lattice QCD
本文首次用全动力学格点量子色动力学方法测定了1 S 0和3S 1 - 3D 1耦合道中核子-核子散射长度。计算是在没有电磁相互作用的情况下，在晶格间距b=0.125 fm的MILC交错组态上用畴壁价夸克进行的.
We show that the Aharonov-Bohm effect in the nuclear matrix model derives the statistical nature of nucleons in holographic QCD. For N_c= odd (even), the nucleon is shown to be a fermion (boson).
Chiral extrapolations of nucleon properties from lattice QCD
本文报道了核子磁矩和轴矢耦合常数与夸克质量关系的研究进展。我们研究了手征有效场论方法外推格点量子色动力学数据的可行性。
An Exploratory Study of Nucleon-Nucleon Scattering Lengths in Lattice QCD
本文对具有Wilson夸克作用量的猝灭格点量子色动力学中核子-核子$s$波散射长度进行了探索性研究。为了比较，还计算了$π$ - $N$和$π$ - $π$散射长度。计算是用对应于$m_π/m_ρ\approx 0.73-0.95$的重夸克进行的。结果表明，$N$ - $N$体系在自旋单重态和三重态通道中都存在吸引力，其散射长度明显大于$π$ - $N$和$π$ - $π$的散射长度，这一趋势与实验定性一致.对轻夸克的更现实的计算问题进行了讨论。
Physical Nucleon Properties from Lattice QCD
我们证明，非常准确的格点量子色动力学数据的质量的核子最近获得的CP-PACS，结合现代手征外推技术，导致一个值的质量的物理核子的系统误差小于百分之一。
Flavour singlet contributions to the nucleon spin are elusive due to the fact that they cannot be determined directly in experiment but require extrapolations to the small x region. Direct calculations of these contributions are possible using Lattice QCD, however, they pose a significant computational challenge due to the presence of disconnected quark line diagrams. We report on recent progress in determining these sea quark contributions on the lattice.
The $J/ψ$-nucleon interaction is studied by lattice QCD calculations. At the leading order of the derivative expansion, the interaction consists of four terms: the central, the spin-spin, and two types of tensor forces. We determine these spin-dependent forces quantitatively by using the time-dependent HAL QCD method. We find that the spin-spin force is the main cause of the hyperfine splitting between the $J=1/2$ and the $J=3/2$ states, while the two tensor forces have much smaller effects on the S-wave scattering processes.
We investigate the pion-mass dependence of the nucleon mass within the covariant SU(2) baryon chiral perturbation theory up to order p4 with and without explicit Delta(1232) degrees of freedom. We fit lattice QCD data from several collaborations for 2 and 2+1 flavor ensembles. Here, we emphasize our Nf=2 study where the inclusion the Delta(1232) contributions stabilizes the fits. We correct for finite volume and spacing effects, set independently the lattice QCD scale by a Sommer-scale of r0 = 0.493(23) fm and also include one sigma pi-N lQCD data point near Mpi = 290 MeV. We obtain low-energy…
Nucleon Structure from Lattice QCD
近年来，由于格点场论、计算机技术和手征微扰理论的发展，格点量子色动力学已成为研究强子结构的一个强有力的定量工具。我描述的核子形状因子和部分子分布函数的时刻的计算的最新进展，然后继续描述广义部分子分布（GPD）的晶格研究。特别是，我展示了如何格点的GPD研究有助于建立一个三维的质子图片。最后，我描述了从格点量子色动力学研究共振结构的前景。
The nucleon axial form factor is a dominant contribution to errors in neutrino oscillation studies. Lattice QCD calculations can help control theory errors by providing first-principles information on nucleon form factors. In these proceedings, we present preliminary results on a blinded calculation of $g_A$ and the axial form factor using HISQ staggered baryons with 2+1+1 flavors of sea quarks. Calculations are done using physical light quark masses and are absolutely normalized. We discuss fitting form factor data with the model-independent $z$ expansion parametrization.
The charmonium-nucleon interaction is studied by the time-dependent HAL QCD method. We use a larger lattice volume and the relativistic heavy quark action for charm quark to obtain less systematic errors than those in our previous study. As a result, the sizable J/$ψ$N hyperfine splitting is observed, indicating that the spin-spin interaction is important to understand this system quantitatively. No J/$ψ$N or $η_c$N bound state is observed below the thresholds as in the previous results.
The Nambu-Bethe-Salpeter (NBS) wave function for two nucleons on the lattice has been shown to yield a non-local and energy-independent nucleon-nucleon (NN) potential, U(r,r'). In practice, the derivative expansion of U(r,r') is currently employed to determine the potential at low energies. In this report, we study the magnitude of non-locality to check the convergence of such a derivative expansion. With quenched lattice QCD at m_π= 530MeV, we compare the NN potentials at the center of mass energy E ~ 0 MeV and at E ~ 45 MeV. We also investigate the angular momentum dependence of the spin sin…
Recent Results on the Nucleon Structure Functions from Lattice QCD
本文报道了核子非极化和极化结构函数的高统计格点计算的最新结果。
Hyperon-nucleon interactions serve as basic inputs to studies of hypernuclear physics and dense (neutron) stars. Unfortunately, a precise understanding of these important quantities have lagged far behind that of the nucleon-nucleon interaction due to lack of high precision experimental data. Historically, hyperon-nucleon interactions are either formulated in quark models or meson exchange models. In recent years, lattice QCD simulations and chiral effective field theory approaches start to offer new insights from first principles. In the present work, we contrast the state of art lattice QCD …
Higher-twist corrections to nucleon structure functions from lattice QCD
一个真正的非微扰评价高扭曲贡献的核子的结构功能，与所有的混合效应和重整化不确定性照顾，提出。较高的扭转修正在中等的$q^2$值下是显著的。
We present our recent study on baryon-baryon ($BB$) interactions from lattice QCD with almost physical quark masses corresponding to $(m_π,m_K)\approx(146,525)$ MeV and large volume $(La)^4=(96a)^4\approx$ (8.1 fm)$^4$. In order to perform a comprehensive study of $BB$ interactions based on lattice QCD calculation with almost physical masses and to make better use of such large scale computer resources, a large number of $BB$ interactions from $NN$ to $ΞΞ$ are calculated simultaneously. In this report, we focus on the strangeness $S=-1$ channels of the hyperon interactions by means of HAL QCD …
In this paper we show that for a nucleon at rest if the quarks and/or antiquarks are in motion inside the nucleon producing chromo-magnetic field then the mass sum rule in QCD is violated when the confinement potential energy at large distance $r$ rises linearly with $r$ (or faster). Hence we find that the mass of the nucleon at rest is not equal to the mass-energy of all the quarks plus antiquarks plus gluons inside the nucleon if there exists chromo-magnetic field inside the nucleon and the confinement potential energy at large distance $r$ rises linearly with $r$ (or faster).
By the quenched lattice QCD simulation for two nucleons with finite scattering energy, validity of the delivative expansion of the general nucleon-nucleon potential U(r,r') = V(r, {\nabla}_r) δ^3(r-r') is studied. The relative kinetic energy between two nucleons is introduced through the anti-periodic boundary condition in the spatial directions. On a hypercubic lattice with the lattice spacing a ~ 0.137 fm and the spatial extent L_s ~ 4.4 fm with the pion mass m_π ~ 530 MeV, the local potentials for two different energies (E ~ 0 MeV and 45 MeV) are compared and found to be identical within st…
We discuss the status of current dynamical lattice QCD simulations in connection to the emerging results on the strange and charmed baryon spectrum, excited states of the nucleon and the investigation of the structure of scalar mesons.
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