Abstract
Quark bilinear operators with staple-shaped Wilson lines are used to study transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice quantum chromodynamics (QCD). Here, the renormalization factors for the isovector operators, including all mixings between operators with different Dirac structures, are computed nonperturbatively in the regularization-independent momentum subtraction scheme for the first time. This study is undertaken in quenched QCD with three different lattice spacings. With Wilson flow applied to the gauge fields in the calculations, the operator mixing pattern due to chiral symmetry breaking with the lattice regularization is found to be significantly different from that predicted by one-loop lattice perturbation theory calculations. These results constitute a critical step towards the systematic extraction of TMDPDFs from lattice QCD.
Highlights
Building a quantitative description of the structure of the proton in terms of its fundamental parton constituents is a defining goal of hadronic physics research
transverse-momentum-dependent parton distribution functions (TMDPDFs), which are relevant to scattering processes such as Drell-Yan and semi-inclusive deep inelastic scattering (SIDIS), can be expressed in terms of beam functions which describe the incoming collinear partons in the scattering process, and soft functions, which encode the effects of soft gluon radiation by partons
Mixing between nonlocal quark bilinears with different Dirac operator structures is observed to be larger than the corresponding mixing between local quark bilinears; this mixing cannot be neglected in studies of nonlocal quark bilinears targeting precision better than the 10% level
Summary
Building a quantitative description of the structure of the proton in terms of its fundamental parton constituents is a defining goal of hadronic physics research. The subset of the nonperturbative RI0=MOM renormalization factors required to calculate renormalized quark-bilinear operators with Dirac structure γ4 are matched to the MS scheme using matching coefficients computed in one-loop perturbation theory [30], and their lattice-spacing dependence is studied. This completes the nonperturbative renormalization prescription for quasi beam functions needed to study TMDPDFs from lattice QCD. The key result is that, for the action considered here, and with Wilson flow applied to the gauge fields in the calculations, the operator mixing pattern due to chiral symmetry breaking with the lattice regularization is found to be significantly different from that predicted by one-loop lattice perturbation theory. Complete calculations of renormalized quasiTMDPDFs in this framework will require the computation of a larger set of operator structures than one might naively expect from perturbative studies
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