Evidence for In-Medium Modification of the $\varphi$ Meson at Normal Nuclear Density

Invariant mass spectra of $e^{+}{e}^{-}$ pairs have been measured in 12 GeV $p+A$ reactions to detect possible in-medium modification of vector mesons. Copper and carbon targets are used to study the nuclear-size dependence of $e^{+}{e}^{-}$ invariant mass distributions. A significant excess on the low-mass side of the $\varphi$ meson peak is observed in the low $\beta \gamma (=\beta /\sqrt{1-{\beta }^2})$ region of $\varphi$ mesons ($\beta \gamma <1.25$) with copper targets. However, in the high $\beta \gamma$ region ($\beta \gamma >1.25$), spectral shapes of $\varphi$ mesons are well described by the Breit-Wigner shape when experimental effects are considered. Thus, in addition to our earlier publications on $\rho /\omega$ modification, this study has experimentally verified vector meson mass modification at normal nuclear density.

Figure 1

Obtained $e^{+}{e}^{-}$ distributions with the fit results. The target and $\beta \gamma$ region are shown in each panel. The points with error bars represent the data. The solid lines represent the fit results with an expected $\varphi \to e^{+}{e}^{-}$ shape and a quadratic background. The dashed lines represent the background.

Figure 2

Kinematical distributions of $e^{+}{e}^{-}$ pairs in the mass region $0.95<M_{ee}<1.05\mathrm{GeV}/c^2$. Acceptance was not corrected. Distributions of (a) $\beta \gamma$ and (b) contours in transverse momentum and rapidity. In the plot (a), points represent data and the line represents simulation result using the nuclear cascade code, JAM [19].

Figure 3

The best-fit results in cases (i) (solid line) and (ii) (dotted line). The shift parameter $k_1$, and broadening parameters $k_2^{\mathrm{tot}}$ and $k_2^{ee}$, are common to the six spectra. The values of ${\chi }^2$s are the sum of the squares of the deviations over 54 data points in each panel.

Figure 4

Confidence ellipsoids for the modification parameters $k_1$ and $k_2^{\mathrm{tot}}$ in cases (i) in (a) and (ii) in (b). The values of $\Delta {\chi }^2$’s in both panels are the differences from the ${\chi }_{\min }^2(=316.4)$ at the best-fit point in case (i) which is shown by the cross in the panel (a). The best-fit point in case (ii) is shown by the closed circle in the panel (b), and also in (a) since the ordinates are common to the both cases in the parameter space.