Measurement of energy-level splitting from Charge-Symmetry Breaking in $A$ = 4 mirror hypernuclei

Abstract

Breaking of fundamental symmetries is a ubiquitous phenomenon in physics, underlying the origin of mass and the emerging structure in the universe. The charge symmetry of $\Lambda$ hyperon-nucleon interactions can be probed through the difference in the $\Lambda$ binding energy ($B_{\Lambda}$) between mirror hypernuclei. In this paper, the $B_{\Lambda}$ of mirror hypernuclei with atomic mass number $A$ = 4, $\rm ^4_{\Lambda}H$ and $\rm ^4_{\Lambda}He$, are measured in Au+Au collisions at the center-of-mass energy of $\sqrt{s_{\rm NN}}$ = 3 GeV with the STAR experiment at RHIC. For the ground states, we obtain $B_{\Lambda}$($\rm ^4_{\Lambda}H$) = 2.24 $\pm$ 0.02 (stat.) $\pm$ 0.04 (syst.) MeV and $B_{\Lambda}$($\rm ^4_{\Lambda}He$) = 2.39 $\pm$ 0.05 (stat.) $\pm$ 0.05 (syst.) MeV, yielding a charge-symmetry breaking (CSB) effect at the level of 0.15 $\pm$ 0.05 (stat.) $\pm$ 0.04 (syst.) MeV. In combination with previous measurements of $\gamma$-ray transitions from their $1^+$ excited states, the CSB in excited states is determined to be $-$0.17 $\pm$ 0.05 (stat.) $\pm$ 0.04 (syst.) MeV. These measurements provide a precise determination of CSB in the hypernuclear system, and establish that the $\Lambda$ binding energy differences in ground and excited states are comparable in magnitude but opposite in sign, offering new insight to the CSB effect in $\Lambda$-nucleon interactions.