Quark Transverse Spin-Momentum Correlation of the Nucleon from Lattice QCD: The Boer-Mulders Function

Abstract

We present the first lattice QCD calculation of the quark transverse spin-momentum correlation, i.e., the naive time-reversal-odd Boer-Mulders function, of the nucleon, using large-momentum effective theory (LaMET). The calculation is carried out on an ensemble with lattice spacing $a=0.098$ fm and pion mass $338$ MeV, at various proton momenta up to $2.11$ GeV. We have implemented perturbative matching up to the next-to-next-to-leading order together with a renormalization-group resummation improvement. The result exhibits a decay behavior with increasing transverse separation $b_{\perp }$. We also compare the results in the nucleon and pion.

Comments: 18 pages, 14 figures, 2 tables