Lattice QCD Determination of the Bjorken-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math> Dependence of Parton Distribution Functions at Next-to-Next-to-Leading Order
Xiang Gao, Andrew D. Hanlon, Swagato Mukherjee, Peter Petreczky, Philipp Scior, Sergey Syritsyn, Yong Zhao
Abstract
We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings a=0.04 and 0.06 fm and valence pion mass m_{π}=300 MeV, at boost momentum as large as 2.42 GeV. As a crucial step to control the systematics, we renormalize the pion valence quasidistribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the MS[over ¯] scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-x space yield a reliable determination of the valence quark distribution for 0.03≲x≲0.80 with 5%-20% uncertainties.