The $\phi$ meson with finite momentum in a dense medium

TL;DR

This paper investigates how the $$ meson's dispersion relation varies with momentum in dense nuclear matter using QCD sum rules, revealing opposite mass shifts for different polarization modes and potential experimental signatures.

Contribution

It provides a detailed analysis of the momentum-dependent dispersion relations of the $$ meson in dense medium, including both longitudinal and transverse modes, up to operator dimension 6.

Findings

Longitudinal mode mass decreases by 5 MeV at 1 GeV momentum.

Transverse mode mass increases by 7 MeV at 1 GeV momentum.

Momentum dependence could lead to observable polarization-dependent peaks.

Abstract

The dispersion relation of the $\phi$ 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 $\phi$ meson QCD sum rules are analyzed with changing densities and momenta. The non-trivial momentum dependence of the $\phi$ 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. Taking however broadening effects into account, the momentum dependence will most likely be seen as a small but positive effective mass shift and an increased effective width for non-zero momenta.