Kaon Electromagnetic Form Factor within the $k_T$ Factorization Formalism and It's Light-Cone Wave Function

TL;DR

This paper systematically analyzes the kaon electromagnetic form factors using the $k_T$ factorization formalism, highlighting the importance of transverse momentum effects, helicity components, and twist structures in understanding hard contributions at accessible energy scales.

Contribution

It introduces a detailed analysis of kaon form factors incorporating $k_T$ dependence, helicity, and twist effects, with a model wave function constrained by distribution amplitude moments.

Findings

$k_T$ dependence significantly influences hard and soft contributions.

Higher twist and helicity components are important below a few GeV$^2$.

Uncertainty in form factors is small when varying key distribution amplitude parameters.

Abstract

We present a systematical study on the kaon electromagnetic form factors $F_{K^{\pm},K^0,\bar{K}^0}(Q^2)$ within the $k_T$ factorization formalism, where the transverse momentum effects, the contributions from the different helicity components and different twist structures of the kaon light-cone (LC) wave function are carefully analyzed for giving a well understanding of the hard contributions at the energy region where pQCD is applicable. The right power behavior of the hard contribution from the higher helicity components and from the higher twist structures can be obtained by keeping the $k_T$ dependence in the hard amplitude. Our results show that the $k_T$ dependence in LC wave function affects the hard and soft contributions substantially and the power-suppressed terms (twist-3 and higher helicity components) make an important contribution below $Q^2\sim several GeV^2$ although they drop fast as $Q^2$ increasing. The parameters of the proposed model wave function can be fixed by the first two moments of its distribution amplitude and other conditions. By varying the first two moments $a^K_1(1GeV)$ and $a^K_2(1GeV)$ with the region of $0.05\pm0.02$ and $0.10\pm 0.05$ respectively, we find that the uncertainty of the kaon electromagnetic form factor is rather small.