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

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.