Measurement of ${}_{\mathrm{\Lambda }}^4\mathrm{H}$ and ${}_{\mathrm{\Lambda }}^4\mathrm{H}\mathrm{e}$ binding energy in Au+Au collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}$ = 3 GeV

Measurements of mass and $\mathrm{\Lambda }$ binding energy of ${}_{\mathrm{\Lambda }}^4\mathrm{H}$ and ${}_{\mathrm{\Lambda }}^4\mathrm{H}\mathrm{e}$ in Au+Au collisions at $\sqrt{s_{{}_{\mathrm{N}\mathrm{N}}}}=3$ GeV are presented, with an aim to address the charge symmetry breaking (CSB) problem in hypernuclei systems with atomic number A = 4. The $\mathrm{\Lambda }$ binding energies are measured to be $2.22\pm 0.06(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.14(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$ MeV and $2.38\pm 0.13(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.12(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$ MeV for ${}_{\mathrm{\Lambda }}^4\mathrm{H}$ and ${}_{\mathrm{\Lambda }}^4\mathrm{H}\mathrm{e}$, respectively. The measured $\mathrm{\Lambda }$ binding-energy difference is $0.16\pm 0.14(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.10(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$ MeV for ground states. Combined with the $\gamma$-ray transition energies, the binding-energy difference for excited states is $-0.16\pm 0.14(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.10(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$ MeV, which is negative and comparable to the value of the ground states within uncertainties. These new measurements on the $\mathrm{\Lambda }$ binding-energy difference in A = 4 hypernuclei systems are consistent with the theoretical calculations that result in $\mathrm{\Delta }{\mathrm{B}}_{\mathrm{\Lambda }}^4(1_{\mathrm{e}\mathrm{x}\mathrm{c}}^{+})\approx -\mathrm{\Delta }{\mathrm{B}}_{\mathrm{\Lambda }}^4(0_{\mathrm{g}\mathrm{.}\mathrm{s}\mathrm{.}}^{+})<0$ and present a new method for the study of CSB effect using relativistic heavy-ion collisions.