Flavour symmetry breaking in the kaon parton distribution amplitude

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 $s=17\,{\rm GeV}^2$.