Medium modification of pseudoscalar meson structure: Distribution amplitudes and parton distribution functions

Abstract

In this work, we present a comprehensive investigation of the in-medium properties and internal structure of pseudoscalar mesons within the light-front quark model (LFQM), employing both Gaussian and power-law (PL) wave functions. We incorporate in-medium quark properties obtained from the quark-meson coupling (QMC) model into the LFQM, thereby providing a unified description in terms of quark degrees of freedom. We investigate the distribution amplitudes (DAs) and parton distribution functions (PDFs) of $\pi^{\pm}$, $K^{\pm}$, $D^{\pm}$, and $B^{\pm}$ mesons in symmetric nuclear matter. We find that the evolved in-medium pion DA and PDF are strongly suppressed at intermediate $x$, indicating substantial medium-induced modifications to the meson structure. The signs and magnitudes of the modified Gegenbauer coefficients $a_n'$, the parameter $\xi$, and the Mellin moments of the DAs and PDFs in nuclear matter are found to be consistent with other theoretical predictions. In particular, the second Gegenbauer coefficient of the pion DA, $a_2^\pi$, increases substantially with nuclear density, from $0.096$ ($0.057$) in vacuum to $0.232$ ($0.202$) at normal nuclear density for the Gaussian (PL) wave function, respectively. This increase indicates a broader pion DA and an enhanced second Gegenbauer moment in the nuclear medium. We further calculate the pion PDF ratio $R_{\rho/0}^{\pi}$ and find that its $x$ dependence exhibits a behavior qualitatively similar to the observed European Muon Collaboration (EMC) effect, highlighting the important role of QCD evolution in shaping the medium-modified partonic structure. Finally, we compare the calculated free-space $\pi^{\pm}$ and $K^{\pm}$ DAs with available free-space lattice QCD results and find reasonable agreement.