Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized TMDPDFs at Physical Quark Masses

Abstract: We present the first lattice QCD calculations of the isovector helicity transverse momentum-dependent parton distribution function (TMDPDF) and the flavor-dependent unpolarized TMDPDFs for up and down quarks in the proton. Our computations utilize domain-wall fermion discretization with physical quark masses. Employing Coulomb-gauge-fixed bilocal quark correlation functions within the large-momentum effective theory framework, we access nonperturbative transverse quark separations $b_T$ up to approximately 1~fm, corresponding to low transverse momentum scales. We present renormalization and factorization scale-independent ratios of these TMDPDFs as functions of $b_T$ and longitudinal momentum fraction $x$, allowing direct comparisons with phenomenological parameterizations from global experimental fits. Our results demonstrate remarkably similar $b_T$ dependence between helicity and unpolarized TMDPDFs at moderate $x$, in agreement with phenomenology. In contrast to certain phenomenological models, we observe mild flavor dependence in the $b_T$ distributions at moderate values of $x$.