Flavour dependence of the pion and kaon form factors and parton distribution functions

TL;DR

This paper investigates the flavor-dependent structure of pions and kaons, analyzing their form factors and parton distribution functions using a Bethe-Salpeter approach, revealing significant flavor effects and their implications for QCD confinement.

Contribution

It provides a detailed calculation of flavor-separated form factors and distribution functions for pions and kaons within a Bethe-Salpeter framework, highlighting the impact of quark masses.

Findings

The u-quark contribution to the kaon form factor is much smaller than that of the s-quark at high Q^2.

The ratio u_{K^+}(x)/u_{π^+}(x) drops below unity at large x, approximately M_u^2/M_s^2.

Total form factors of K^+ and π^+ differ by only about 10%.

Abstract

The separate quark flavour contributions to the pion and kaon valence quark distribution functions are studied, along with the corresponding electromagnetic form factors in the space-like region. The calculations are made using the solution of the Bethe-Salpeter equation for the model of Nambu and Jona-Lasinio with proper-time regularization. Both the pion and kaon form factors and the valence quark distribution functions reproduce many of the features of the available empirical data. The larger mass if the strange quark naturally explains the empirical fact that the ratio $u_{K^+}(x)/u_{\pi^+}(x)$ drops below unity at large $x$, with a value of approximately $M^2_u/M_s^2$ as $x \to 1$. With regard to the elastic form factors we report a large flavour dependence, with the $u$-quark contribution to the kaon form factor being an order of magnitude smaller than that of the $s$-quark at large $Q^2$, which may be a sensitive measure of confinement effects in QCD. Surprisingly though, the total $K^+$ and $\pi^+$ form factors differ by only 10\%.