Lattice QCD

Lattice QCD (LQCD) allows the solution of QCD in the strong-coupling regime, and therefore, first-principles LQCD calculations comprise an essential component of the QGT Collaboration and will contribute to the goal of understanding the internal structure of hadrons. LQCD is formulated on a four-dimensional Euclidean space-time lattice, which admits the use of importance sampling to sample the path integral and thereby render non-perturbative computations practical. However, the Euclidean nature of LQCD precludes the direct computation of some of the quantities under investigation in this proposal, such as the matrix elements of operators separated along the light cone. The recent realization that such matrix elements can, in fact, be related to quantities calculable on a Euclidean lattice in a systematically improvable way has transformed the potential of LQCD to study the structure of hadrons. The advent of exascale computing will not only allow the calculation of key measures of hadron structure, such as the x-dependent PDFs, with controlled uncertainties, but enable us to address the three-dimensional distributions at the heart of this proposal.

There has been tremendous progress in the calculation of physical observables connected to hadron structure. Recent highlights include the calculation of the axial charge of the nucleon with controlled statistical uncertainties and in full agreement with the experimental value. This progress has stimulated intense activity in the field of hadron structure, with the study of a large class of observables, some of which are known experimentally, but many that are still unexplored, or difficult to measure. Therefore, LQCD results will provide valuable input to the activities of the QGT Collaboration.

Our team brings together wide-ranging and extensive expertise in the field of LQCD related to hadron structure and beyond. Our contributions range from algorithmic developments for lattice calculations and the introduction and implementation of novel data analysis techniques, to significant theoretical developments, both in the context of lattice field theory and the connection between LQCD and phenomenology. Members of our team have pioneered calculations of three-dimensional hadron structure, collinear distributions, generalized form factors, and various other measures of hadron structure, including the spin decomposition of the nucleon.

Our investigations in the context of this proposal cover twist-2 and twist-3 measures of hadron structure in both the meson and baryon sectors, and will initiate calculations for SU(Nc) gauge theories to better understand the mechanisms of confinement and chiral symmetry breaking in QCD. A focus of the later stages of the program will be the incorporation of lattice calculations of hadron structure in global analysis frameworks, a program that requires expertise from, and collaboration between, the global fitting and LQCD communities.