Kaon T-even transverse-momentum-dependent distributions and form factors in a self-consistent light-front quark model

TL;DR

This paper develops a self-consistent light-front quark model for the kaon, enabling detailed calculations of form factors and TMDs, and compares different definitions and their evolution, providing insights into kaon structure.

Contribution

It introduces a unified light-front quark model for the kaon that consistently incorporates zero-modes and covariance, and computes form factors and TMDs with detailed analysis of definitions and evolution.

Findings

Electromagnetic form factor $F_{K^+}(Q^2)$ is unique across current components.

Twist-2 TMD $f_1^q$ shows Gaussian dependence in transverse momentum.

Higher-twist TMDs exhibit systematic twist and flavor hierarchies.

Abstract

We present a self-consistent light-front quark model (LFQM) for the kaon based on the Bakamjian--Thomas (BT) construction and apply it to the electromagnetic and scalar form factors, as well as the full set of unpolarized T-even transverse-momentum-dependent distributions (TMDs) and their collinear parton distribution functions (PDFs). A uniform implementation of the invariant mass $M_0$ in both the hadronic matrix elements and the associated Lorentz structures enforces four-momentum conservation at the meson--quark vertex and yields current-component--independent observables by consistently incorporating the light-front zero-mode structure required by covariance. The electromagnetic form factor $F_{K^+}(Q^2)$ is demonstrated to be unique by explicit computation from all available current components ($\gamma^+$, $\gamma^\perp$, and $\gamma^-$). In the scalar channel, we compare the direct $f_S(Q^2)$ and mass-factored $F_S(Q^2)$ definitions and show that they are not interchangeable within the BT-based LFQM, since the replacement $M\!\to\!M_0(x,\bm{k}_\perp)$ must be implemented at the integrand level. Using a Gaussian light-front wave function, the twist-2 TMD $f_1^q$ exhibits an exact Gaussian dependence in $\bm{k}_\perp$, while higher-twist TMDs ($f^{\perp q}$, $e^q$, $f_4^q$) display systematic twist and flavor hierarchies. We further analyze the perturbative QCD evolution of the valence PDFs for the pion and kaon and report their Mellin moments at representative scales, enabling direct comparison with phenomenology.