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

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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.