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

Abstract

The behavior of the $\varphi$ 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 $\varphi$ in nuclear matter is strongly correlated to the strangeness content of the nucleon, which is proportional to the strange sigma term, ${\sigma }_{sN}=m_s⟨N|\overline{s}s|N⟩$. Our results furthermore show that, depending on the value of ${\sigma }_{sN}$, the $\varphi$ 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 $\varphi$ 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.

arXiv comment8 pages, 4 figures; minor changes, version published in PRD

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