Transversity parton distribution functions from lattice QCD

Abstract

We present the first direct calculation of the transversity parton distribution function within the nucleon from lattice QCD. The calculation is performed using simulations with the light quark mass fixed to its physical value and at one value of the lattice spacing. Novel elements of the calculations are non-perturbative renormalization and extraction of a formula for the matching to light-cone PDFs. Final results are presented in the $\overline{\rm MS}$ scheme at a scale of $\sqrt{2}$ GeV.

Figures (3)

• Figure 1: Real (upper) and imaginary part (lower) of the bare $M_{h_1}(P,z)$ at 5 stout steps, for $P{=}\frac{6\pi}{L}$ (blue), $P{=}\frac{8\pi}{L}$ (red) and $P{=}\frac{10\pi}{L}$ (green), as a function of the Wilson line length, $z/a$.
• Figure 2: Renormalized quasi-PDF, $\widetilde{h}_1^{u-d}$ (green), PDF after matching, ${h'_1}^{u-d}$ (orange) and after TMCs, $h_1^{u-d}$ (blue), as a function of Bjorken-$x$ for $P{=}\frac{10\pi}{L}$.
• Figure 3: Transversity PDF for $P{=}\frac{10\pi}{L}$ (blue) as a function of Bjorken-$x$. The phenomenological fits have been obtained using SIDIS data (grey) Lin:2017stx and SIDIS data constrained using $g_T^{\rm lattice}$ (purple) Lin:2017stx.