Flavor Decomposition for the Proton Helicity Parton Distribution Functions
Constantia Alexandrou, Martha Constantinou, Kyriakos Hadjiyiannakou, Karl Jansen, Floriano Manigrasso
Abstract
We present, for the first time, an 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. The analysis is performed using one ensemble of dynamical up, down, strange, and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are nonperturbatively renormalized and the final results are presented in the $\overline{\mathrm{MS}}$ scheme at a scale of 2 GeV. We give results for $\mathrm{\ensuremath{\Delta}}{u}^{+}(x)$, $\mathrm{\ensuremath{\Delta}}{d}^{+}(x)$ $\mathrm{\ensuremath{\Delta}}{u}^{\ensuremath{-}}(x)$, $\mathrm{\ensuremath{\Delta}}{d}^{\ensuremath{-}}(x)$, including disconnected quark loop contributions, as well as for $\mathrm{\ensuremath{\Delta}}{s}^{+}(x)$ and $\mathrm{\ensuremath{\Delta}}{s}^{\ensuremath{-}}(x)$. For the latter we achieve unprecedented precision compared to the phenomenological estimates.