Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses

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 quark correlation functions within the large-momentum effective theory framework, we access nonperturbative transverse quark separations <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>b</a:mi> <a:mi>T</a:mi> </a:msub> </a:math> up to approximately 1 fm, corresponding to transverse momenta as low as 200 MeV. Based on the quasi-TMD factorization theorem, we construct renormalization-group–invariant ratios that are equal to the corresponding light-cone TMDPDF ratios. At moderate <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>x</c:mi> </c:math> , our results reveal that the isovector helicity and unpolarized TMDPDFs exhibit nearly identical transverse structure up to a normalization factor, and the unpolarized distributions display only mild flavor dependence. These findings not only support key trends observed in recent global analyses but also provide robust, nonperturbative constraints that can distinguish between different parameterizations. This Letter establishes a first-principles benchmark for TMDPDFs, offering valuable input for ongoing and future experimental efforts to map the proton’s three-dimensional structure.