Moments of the heavy-quark parton distribution function from QCD sum rules

TL;DR

This paper calculates the moments of heavy-quark distribution functions in mesons using QCD sum rules, analyzing the validity of heavy-mass expansions for charm and bottom quarks.

Contribution

It provides a detailed comparison of finite mass results with heavy-mass limits, highlighting the importance of higher-order terms for charm quarks.

Findings

Heavy-mass expansion is accurate for bottom quarks.

Higher than $(1/m_c)^2$ terms are needed for charm quarks.

Results inform quark fragmentation models based on mass limits.

Abstract

The moments of the heavy quark-parton distribution functions in a heavy pseudoscalar meson are calculated from QCD sum rules. Expanding these sum rules in the inverse heavy quark mass we obtain the heavy-mass limits of the moments. Comparison with the finite mass results reveals that while the heavy mass expansion works reasonably well for the $b$ quark, one has to take into account terms of higher than $(1/m_c)^2$ order for the $c$ quark. This result can provide a quantitative assessment of $c$ and $b$ quark fragmentation models based on the heavy-quark mass limit.