Constraining the strangeness content of the nucleon by measuring the $\phi$ meson mass shift in nuclear matter

TL;DR

This study investigates how the mass of the $\, ext{ extphi}\, ext{'}$ meson shifts in nuclear matter and how this shift relates to the strangeness content of the nucleon, using QCD sum rules and the maximum entropy method.

Contribution

It provides the first detailed analysis linking the $ extphi$ meson mass shift to the strangeness content of the nucleon, incorporating higher order corrections and stability checks.

Findings

The $ extphi$ meson can experience positive or negative mass shifts depending on $\sigma_{sN}$.

The results are weakly affected by changes in the meson width and four-quark condensate assumptions.

Higher order corrections confirm the robustness of the mass shift predictions.

Abstract

The behavior of the $\phi$ meson at finite density is studied, making use of a QCD sum rule approach in combination with the maximum entropy method. It is demonstrated that a possible mass shift of the $\phi$ in nuclear matter is strongly correlated to the strangeness content of the nucleon, which is proportional to the strange sigma term, $\sigma_{sN} = m_s \langle N | \overline{s}s | N \rangle$. Our results furthermore show that, depending on the value of $\sigma_{sN}$, the $\phi$ meson could receive both a positive or negative mass shift at nuclear matter density. We find that these results depend only weakly on potential modifications of the width of the $\phi$ meson peak and on assumptions made on the behavior of four-quark condensates at finite density. To check the stability of our findings, we take into account several higher order corrections to the operator product expansion, including $\alpha_s$-corrections, terms of higher order in the strange quark mass and terms of higher twist that have not been considered in earlier works.