Measurement of $e^{+}{e}^{-}\to \ddot{I}•\hat{I}{\cdot }^{\prime }$ cross sections at center-of-mass energies from 3.508 to 4.951 GeV and search for the decay $\ddot{I}ˆ(3770)\to \ddot{I}•\hat{I}{\cdot }^{\prime }$

Abstract

The cross sections of the $e^{+}{e}^{-}\to \ddot{I}•\hat{I}{\cdot }^{\prime }$ process at center-of-mass energies from 3.508 to 4.951 GeV are measured with high precision using 26.1 fb${}^{-1}$ data collected with the BESIII detector operating at the BEPCII storage ring. The cross sections are of the order of a few picobarn, and decrease as the center-of-mass energy increases as $s^{-n/2}$ with $n=4.35\pm 0.14$. This result is in agreement with the Nambu-Jona-Lasinio model prediction of $n=3.5\pm 0.9$. In addition, the charmless decay $\ddot{I}ˆ(3770)\to \ddot{I}•\hat{I}{\cdot }^{\prime }$ is searched for by fitting the measured cross sections, yet no significant signal is observed. The upper limit of $\mathcal{B}(\ddot{I}ˆ(3770)\to \ddot{I}•\hat{I}{\cdot }^{\prime })$ at the 90\% confidence level is determined to be $2.3\times 10^{-5}$.