Flavour symmetry breaking in the kaon parton distribution amplitude

TL;DR

This paper calculates the kaon's valence-quark distribution amplitude, revealing SU(3) flavor symmetry breaking effects and emphasizing the importance of nonperturbative PDAs for interpreting high-energy experiments.

Contribution

It provides a nonperturbative calculation of the kaon PDA showing flavor symmetry breaking and its impact on experimental observables, advancing understanding of QCD bound states.

Findings

Kaon PDA is broad, concave, and asymmetric at 2 GeV.

The peak of the PDA is shifted 12-16% from the conformal limit.

The ratio of kaon to pion form factors is 1.23, matching experimental data.

Abstract

We compute the kaon's valence-quark (twist-two parton) distribution amplitude (PDA) by projecting its Poincare'-covariant Bethe-Salpeter wave-function onto the light-front. At a scale \zeta=2GeV, the PDA is a broad, concave and asymmetric function, whose peak is shifted 12-16% away from its position in QCD's conformal limit. These features are a clear expression of SU(3)-flavour-symmetry breaking. They show that the heavier quark in the kaon carries more of the bound-state's momentum than the lighter quark and also that emergent phenomena in QCD modulate the magnitude of flavour-symmetry breaking: it is markedly smaller than one might expect based on the difference between light-quark current masses. Our results add to a body of evidence which indicates that at any energy scale accessible with existing or foreseeable facilities, a reliable guide to the interpretation of experiment requires the use of such nonperturbatively broadened PDAs in leading-order, leading-twist formulae for hard exclusive processes instead of the asymptotic PDA associated with QCD's conformal limit. We illustrate this via the ratio of kaon and pion electromagnetic form factors: using our nonperturbative PDAs in the appropriate formulae, $F_K/F_\pi=1.23$ at spacelike-$Q^2=17\,{\rm GeV}^2$, which compares satisfactorily with the value of $0.92(5)$ inferred in $e^+ e^-$ annihilation at $s=17\,{\rm GeV}^2$.