Flavor decomposition for the proton helicity parton distribution functions

Abstract

We present, for the first time, an \textit{ab initio} calculation of the individual up, down and strange quark helicity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD using one ensemble of dynamical up, down, strange and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are non-perturbatively renormalized and the final results are presented in the $\overline{\mathrm{MS}}$ scheme at a scale of 2 GeV. We give results on the $\Delta u^{+}(x)$ and $\Delta d^{+}(x)$, including disconnected quark loop contributions, as well as on the $\Delta s^{+}(x)$. For the latter we achieve unprecedented precision compared to the phenomenological estimates.

Comments: 6 pages, 3 figures