Probing gluon dynamics by charm and bottom mesons in nuclear medium from heavy meson effective theory with 1/M-corrections

We consider heavy mesons with charm and bottom in nuclear medium. We construct the effective Lagrangian with axial-vector coupling including 1/M-corrections for the heavy meson mass $M$ by following the velocity-rearrangement invariance. As an application, we consider heavy mesons, $\bar{\mathrm{D}}$ and $\bar{\mathrm{D}}^{\ast}$ mesons for charm and $\mathrm{B}$ and $\mathrm{B}^{\ast}$ mesons for bottom, bound in nuclear matter, and we discuss their in-medium masses modified by the interaction with nucleons via pion exchanges including the 1/M-corrections. The mass modifications are affected by the gluon dynamics in nuclear medium. By comparison with the heavy quark effective theory, we find that the effects of scale anomaly become suppressed in nuclear medium. We also find that the contributions from the chromoelectric gluon are enhanced in nuclear medium, while those from the chromomagnetic gluon are reduced. We propose to use heavy mesons as probes to research the gluon fields in nuclear medium in experimental studies.