Abstract
We perform the first global QCD analysis of pion valence, sea quark, and gluon distributions within a Bayesian MonteCarlo framework with threshold resummation on Drell-Yan cross sections at next-to-leading log accuracy. Exploring various treatments of resummation, we find that the large-x asymptotics of the valence quark distribution ∼(1-x)^{β_{v}} can differ significantly, with β_{v} ranging from ≈1 to >2.5 at the input scale. Regardless of the specific implementation, however, the resummation induced redistribution of the momentum between valence quarks and gluons boosts the total momentum carried by gluons to ≈40%, increasing the gluon contribution to the pion mass to ≈40 MeV.
Highlights
Introduction.—As the lightest known hadron, the pion presents itself as a dichotomy of nature
An ongoing debate has pitted arguments based on perturbative QCD models, which predict an asymptotic behavior for the valence quark parton distribution function (PDF) ∼ ð1 − xÞβv with βv 1⁄4 2, against various nonperturbative models which favor smaller values βv ≲ 1 [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]
Significant progress has been made in resumming large logarithmic corrections in perturbative QCD from partonic threshold effects in high-energy reactions through various methods and approximations [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]
Summary
We perform the first global QCD analysis of pion valence, sea quark, and gluon distributions within a Bayesian Monte Carlo framework with threshold resummation on Drell-Yan cross sections at next-toleading log accuracy. Significant progress has been made in resumming large logarithmic corrections in perturbative QCD from partonic threshold effects in high-energy reactions through various methods and approximations [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]. The Jefferson Lab Angular Momentum (JAM) Collaboration recently explored [49] the inclusion of leading neutron (LN) electroproduction data from HERA [50,51], in addition to the DY data, to constrain the valence, sea quark and gluon distributions at low and high x values, using Bayesian Monte Carlo methods. Other phenomenological analyses have utilized DY and prompt photon data to constrain pion PDFs [48,53,54,55,56,57,58], and the growing number of recent lattice calculations [59,60,61,62,63,64,65], some including threshold resummation [66], is a testament to the importance of better understanding the pion’s PDFs
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