The meson with finite momentum in a dense medium

Kim, H.-J.*; Gubler, P. 

The dispersion relation of the meson in nuclear matter is studied in a QCD sum rule approach. In a dense medium, longitudinal and transverse modes of vector particles can have independently modified dispersion relations due to broken Lorentz invariance. Employing the full set of independent operators and corresponding Wilson coefficients up to operator dimension-6, the meson QCD sum rules are analyzed with changing densities and momenta. The non-trivial momentum dependence of the meson mass is found to have opposite signs for the longitudinal and transverse modes. Specifically, the mass is reduced by 5 MeV for the longitudinal mode, while its increase amounts to 7 MeV for the transverse mode, both at a momentum scale of 1 GeV. In an experiment which does not distinguish between longitudinal and transverse polarizations, this could in principle be seen as two separated peaks at large momenta.