Ratio of Kaon and Pion valence-quark parton distributions

The $K^+$ and $\pi^+$ are composed of two valence quarks each, $u\bar{s}$ and $u\bar{d}$, respectively. The ratio of momentum fractions carried by the up valence quarks, $u_{K}/u_{\pi}$, has been measured by Badier et al. [1], and found to decrease with increasing Bjorken $x$. I extend the statistical model of Zhang et al. [2] to calculate the parton distribution functions for the $K^+$ meson and the $\pi^+$ meson. I consider the $\pi^+$ and $K^+$ as an infinite series expansion of quark-gluon Fock states. The probabilities of each state were calculated using detailed balance and the three processes $q \rightleftharpoons qg$, $g \rightleftharpoons q\bar{q}$ and $g \rightleftharpoons gg$. I find a sea asymmetry of $\bar{d}-\bar{u}\approx0.265$ in the $K^+$, but no sea asymmetry in the $\pi^+$. I used the RAMBO program to produce a Monte Carlo simulation for the momentum distributions of the n- parton Fock states of both $K^+$ and $\pi^+$, which determine the momentum distribution functions of the mesons. I compare the ratio of momentum fractions carried by the up valence quarks in each meson, $u_{K}/u_{\pi}$, to the experimental results, and to other theoretical calculations. \\[4pt] [1] J. Badier et al., Phys. Lett. B 93 (1980) 354.\\[0pt] [2] Y.-J. Zhang et al., Phys. Lett. B 523 (2001) 260.