Target mass effects in polarized deep-inelastic scattering

TL;DR

The paper addresses target-mass corrections in polarized deep-inelastic scattering by deriving the polarized operator-product-expansion corrections to the structure-function moments $g_1^n(Q^2)$ and $g_2^n(Q^2)$ to first order in $m^2/Q^2$. It extends the unpolarized Georgi-Politzer formalism to the polarized case, expressing the moments in terms of reduced matrix elements $a_n$ and $d_n$ and showing that the Wandzura-Wilczek relation emerges when $d_n=0$, with explicit first-order corrections. A phenomenological analysis of existing data at NLO-QCD demonstrates that these mass corrections are generally small and within the prior higher-twist uncertainties, slightly shifting quantities such as the axial coupling $g_A$ by ~$+0.03$ and $oldsymbol{\a_S(m_Z)}$ by ~$+0.004$, while leaving quark distributions largely intact. Overall, the work provides a practical, reliable framework to account for kinematic target-mass effects in polarized DIS without compromising the extraction of polarized parton densities.

Abstract

We present a computation of nucleon mass corrections to nucleon structure functions for polarized deep-inelastic scattering. We perform a fit to existing data including mass corrections at first order in $m^2/Q^2$ and we study the effect of these corrections on physically interesting quantities. We conclude that mass corrections are generally small, and compatible with current estimates of higher twist uncertainties, when available.

Figures (5)

• Figure 1: The structure function $g_1$ for the proton at $Q^2=1,10$ GeV$^2$ in fits A and B, with and without target mass corrections (parameters fixed at the $m=0$ values).
• Figure 2: The structure function $g_1$ for the proton at $Q^2=1,10$ GeV$^2$ in fits A and B, with and without target mass corrections (fitted parameters).
• Figure 3: The quark singlet distribution at $Q^2=10$ GeV$^2$ in fits A and B, with and without target mass corrections.
• Figure 4: The quark nonsinglet distribution for the proton at $Q^2=10$ GeV$^2$ in fits A and B, with and without target mass corrections.
• Figure 5: The gluon distribution at $Q^2=10$ GeV$^2$ in fits A and B, with and without target mass corrections.