Potential of the reaction $e^{+}{e}^{-}\to p\bar{p}{\pi }^0$ for constructing higher $\rho$-meson spectroscopy above 2.4 GeV

Abstract

The spectrum of light unflavored vector mesons above 2.4 GeV has not yet been firmly established experimentally. In this work, we demonstrate that the process $e^{+}{e}^{-}\to p\bar{p}\pi$ serves as a particularly promising channel as a probe for higher isovector $\rho$ excitations. In contrast to typical electron-positron annihilation processes into purely light-meson final states, the reaction $e^{+}{e}^{-}\to p\bar{p}\pi$ benefits from a relatively low continuum background, on the order of $(50\sim 100)\text{pb}$ around 2.4 GeV, which enhances the visibility of even modest resonance contributions. In addition, the comparatively high production threshold further suppresses potential contamination from lower $\rho$-meson excitations. Our analysis based on effective Lagrangian approach indicates that the observed lineshape of the $e^{+}{e}^{-}\to p\bar{p}\pi$ cross section measured by BESIII can be naturally interpreted by including the $\rho (5S)$ and $\rho (6S)$ contributions, namely the fourth and fifth radial excitations of $\rho (770)$. In particular, the pronounced rise of the cross section near 2.4 GeV provides strong evidence for the contribution of $\rho (5S)$ signal. Their branching ratios to the $p\bar{p}\pi$ final state are found to be below 4\%, which do not contradict with usual expectations. In addition, we evaluate pion-induced production of these two $\rho$-meson states as a complementary probe, offering useful guidance for the relevant experiments such as COMPASS.

Comments: 9 pages, 5 figures