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

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.