Generalized parton distributions of the kaon and pion within the nonlocal chiral quark model

Abstract: In the present study, we explore the properties of generalized parton distributions (GPDs) for the kaon and pion within the framework of the nonlocal chiral quark model (NL$\chi$QM). Valence quark GPDs of the kaon and pion are analyzed with respect to their momentum fraction $x$ and skewness $\xi$ dependencies in the DGLAP and ERBL regions. We observe that the asymmetry of the current quark masses in kaon results in a significant distortion of the quark GPDs in kaon near $\xi=1$, compared to the case of the pion. The quark GPDs of the kaon and pion are evolved to $\mu^2 = 4$ GeV$^2$ and 100 GeV$^2$ by the QCD evolution equation at one-loop order using the \texttt{APFEL++} package. We find that the produced sea quarks and gluons are largely suppressed as $\xi$ becomes nonzero, predominantly confined within the ERBL region. We subsequently examine the polynomiality of the GPDs and numerically obtain the electromagnetic and gravitational form factors of the kaon and pion. For the kaon, gravitational form factor ratios $A_{\bar s/K^+}(0)/A_{s/K^+}(0) = 1.26$ and $D_{\bar s/K^+}(0)/D_{s/K^+}(0) = 1.10$ are reported and compared with results from other effective models.