Insights into the Emergence of Mass from Studies of Pion and Kaon Structure

There are two mass generating mechanisms in the standard model of particle physics (SM). One is related to the Higgs boson and fairly well understood. The other is embedded in quantum chromodynamics (QCD), the SMs strong interaction piece; and although responsible for emergence of the roughly 1 GeV mass scale that characterises the proton and hence all observable matter, the source and impacts of this emergent hadronic mass (EHM) remain puzzling. As bound states seeded by a valence-quark and -antiquark, pseudoscalar mesons present a simpler problem in quantum field theory than that associated with the nucleon. Consequently, there is a large array of robust predictions for pion and kaon properties whose empirical validation will provide a clear window onto many effects of both mass generating mechanisms and the constructive interference between them. This has now become significant because new-era experimental facilities, in operation, construction, or planning, are capable of conducting such tests and thereby contributing greatly to resolving the puzzles of EHM. These aspects of experiment, phenomenology, and theory, along with contemporary successes and challenges, are sketched herein, simultaneously highlighting the potential gains that can accrue from a coherent effort aimed at finally reaching an understanding of the character and structure of Natures Nambu-Goldstone modes.

Lattice QCD and Neutrino-Nucleus Scattering

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in neutrino-oscillation physics, which inevitably entails nucleon and nuclear structure. In addition to discussing pertinent lattice-QCD calculations of nucleon and nuclear matrix elements, the interplay with models of nuclei is discussed. This program of lattice- QCD calculations is relevant to current and upcoming neutrino experiments, becoming increasingly important on the timescale of LBNF/DUNE and HyperK.

Weak Neutral Current Axial Form Factor Using $(bar{ u}) u$-Nucleon Scattering and Lattice QCD Inputs

We present a determination of the neutral current weak axial charge $G^Z_A(0)=-0.654(3)_{rm stat}(5)_{rm sys}$ using the strange quark axial charge $G^s_A(0)$ calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region $0.24lesssim Q^2 lesssim 0.71$ GeV$^2$ to determine the neutral current weak axial form factor $G^Z_A(Q^2)$ in the range of $0lesssim Q^2leq 1$ GeV$^2$. This yields a phenomenological value of $G^Z_A(0)=-0.687(89)_{rm stat}(40)_{rm sys}$. The value of $G^Z_A(0)$ constrained by the lattice QCD calculation of $G^s_A(0)$, when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $G^Z_A(Q^2)$ for $Q^2>0$. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near $Q^2=0$ and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G^Z_A(Q^2)$ obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.