$\phi$ meson properties in nuclear matter from QCD sum rules with chirally separated four-quark condensates

TL;DR

This paper uses an improved QCD sum rule approach to analyze how the $$ meson properties, such as mass and width, are modified in nuclear matter, emphasizing the role of four-quark condensates and the strange sigma term.

Contribution

It introduces a refined method for treating chiral invariant and breaking four-quark condensates in QCD sum rules, providing a detailed analysis of $$ meson modifications in nuclear matter.

Findings

The $$ meson mass decreases in nuclear matter.

The width of the $$ meson increases with density.

The mass shift is highly sensitive to the strange sigma term $sN$.

Abstract

The modification of the $\phi$ meson spectrum in nuclear matter is studied in an updated QCD sum rule analysis, taking into account recent improvements in properly treating the chiral invariant and breaking components of four-quark condensates. Allowing both mass and decay width to change at finite density, the QCD sum rule analysis determines certain combinations of changes for these parameters that satisfy the sum rules equally well. A comprehensive error analysis, including uncertainties related to the behavior of various condensates at linear order in density, the employed renormalization scale and perturbative corrections of the Wilson coefficients, is used to compute the allowed ranges of these parameter combinations. We find that the $\phi$ meson mass shift in nuclear matter is especially sensitive to the strange sigma term $\sigma_{sN}$, which determines the decrease of the strange quark condensate in nuclear matter. Specifically, we obtain a linear relation between the width $\Gamma_{\phi}$ and mass shift $\Delta m_{\phi}$ given as $ \Gamma_{\phi} = a\Delta m_{\phi} + b\sigma_{sN}+c$ with $a = (3.947^{+0.139}_{-0.130})$, $b = (0.936^{+0.180}_{-0.177} )$ and $c = -(7.707^{+4.791}_{-5.679}) \mathrm{MeV}$.