Parton Distributions from Lattice QCD and Flavor Symmetry Breaking in the Delta Sea

晶格量子色动力学（LQCD）提供了一种通用的、非微扰的方法来求解低能的量子色动力学。它已被用于研究核物理和粒子物理的各个方面，如强子散射和共振现象，电弱衰变中的强子矩阵元素，手性动力学和QCD对新物理搜索贡献的异常和约束，以及强耦合和夸克质量等基本参数。然而，对于部分子分布函数（PDFs）的LQCD计算，仍然存在一个问题，即LQCD是在欧几里得时空上表述的，而PDFs是光锥主导的。2013年，Ji提出，与其直接计算光锥相关性，不如计算纯粹的空间相关性，其傅里叶变换通常被称为准pdf。准pdf和pdf具有相同的红外物理特性，这是允许我们将两个量联系起来的基本观察。因式分解公式使得从准pdf中提取pdf成为可能，这一操作称为匹配，使用摄动理论。这个过程被称为大动量有效理论（LaMET），我们已经用它来首次重建物理点质量系综上核子内的等矢量u(x)-d(x)分布。它也可能提供对核子海中轻夸克味不对称性质的洞察，d′(x)-u′(x)。具体而言，对于风味不对称，虽然可以在LaMET中计算，但由于多种因素的综合，包括：傅里叶变换少量点的问题，以及可能的体积和截止效应，仍然有一些问题妨碍对其得出确切的结论。最近，我们提出了另一种方法来测试味道不对称的起源，使用Δ^+重子。根据这一建议，如果自发的手性对称性破缺是测量不对称的原因，那么与质子的情况相比，Δ^+中的d′(x)- u′(x)应该被强烈增强。计算和理解导致风味不对称的物理机制是我们提案的主要目标。

Lattice Quantum Chromodynamics (LQCD) provides a generic, non-perturbative way to solving QCD at low energies. It has been used to study the various aspects of nuclear and particle physics, e.g. hadron scattering and resonance phenomena, hadronic matrix elements for electroweak decays, chiral dynamics and anomaly and constraints of QCD contributions for new-physics search, as well as fundamental parameters such as the strong coupling and quark masses. However, for a LQCD computation of parton distribution functions (PDFs), a remaining problem is that LQCD is formulated on Euclidean spacetime while the PDFs are light-cone dominated. In 2013, Ji proposed that instead of computing light-cone correlations directly, one should compute purely spatial correlations, whose Fourier transform are usually referred to as quasi-PDFs. Quasi-PDFs and PDFs possess the same infrared physics, which is the fundamental observation that allows us to relate both quantities. A factorization formula then makes it possible to extract the PDFs from the quasi-PDFs, an operation called matching, using perturbation theory. This procedure is known as large-momentum effective theory (LaMET) and it has been used by us to make a first reconstruction of the iso-vector u(x)-d(x) distribution within a nucleon at a physical point mass ensemble. It may, also, offer an insight into the nature of the flavor asymmetry for the light quarks in the nucleon sea, d ̅(x)-u ̅(x). Specifically, for the flavor asymmetry, although it can be computed in LaMET, few issues still prevent firm conclusions on it, because of a combination of factors, including: the problem of Fourier transforming a small number of points, and possible volume and cut-off effects. Recently, we proposed an alternative way to test the origin of the flavor asymmetry, using the Δ^+ baryon. According to this proposal, if spontaneous chiral symmetry breaking is responsible for the measured asymmetry, then d ̅(x)- u ̅(x) should be strongly enhanced in the Δ^+, as compared to the proton case. The computation and the understanding of the physical mechanism responsible for the flavor asymmetry is the main objective of our proposal.