Symmetry Constraints on Pion Valence Structure

Abstract

The profile of the pion valence quark distribution function (DF) remains controversial. Working from the concepts of QCD effective charges and generalised parton distributions, we show that since the pion elastic electromagnetic form factor is well approximated by a monopole, then, at large light-front momentum fraction, the pion valence quark DF is a convex function described by a large-$x$ power law that is practically consistent with expectations based on quantum chromodynamics.

Figures (5)

• Figure 1: Solution of Eq. \ref{['EqMaster']}, which satisfies the requirements imposed by Eq. \ref{['wcons']}.
• Figure 2: Pion valence quark DA, Eq. \ref{['pionDA']}. Legend: solid purple curve -- result obtained herein using ${\mathpzc a}(x)$ from Fig. \ref{['Fig1']} and Eq. \ref{['DFw']}; dashed green curve -- CSM prediction Chang:2013pqCui:2020tdf; dotted grey curve -- asymptotic twist-two pion DA Lepage:1979zbEfremov:1979qkLepage:1980fj.
• Figure 3: Pion valence quark DF. Legend: solid purple curve -- result obtained herein using ${\mathpzc a}(x)$ from Fig. \ref{['Fig1']} and Eq. \ref{['DFw']}; dashed green curve -- CSM prediction Ding:2019lweCui:2020tdf; dotted grey curve -- scale free DF (see text).
• Figure 4: Hadron scale valence quark symmetrised-GPD in impact parameter space, Eqs. \ref{['EqGPD']}, \ref{['HSGPDb']}.
• Figure 5: Pion valence quark DF at the scale, $\zeta_5 = 5.2\,$GeV. Legend: solid purple curve and band -- symmetry-driven result obtained herein, Eq. \ref{['DFw']}; dashed green curve and band -- CSM prediction Ding:2019lweCui:2020tdf; open blue diamonds -- E615 data analysed as described in Refs. Aicher:2010cbChang:2014lva, with soft-gluon resummation; open grey up-triangles -- data inferred via leading-order analysis of the Drell-Yan cross section Conway:1989fs