  Measurements of mass and $\Lambda$ binding energy of $\rm ^4_{\Lambda}H$ and
$\rm ^4_{\Lambda}He$ in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=3$ GeV are
presented, with an aim to address the charge symmetry breaking (CSB) problem in
hypernuclei systems with atomic number A = 4. The $\Lambda$ binding energies
are measured to be $\rm 2.22\pm0.06(stat.) \pm0.14(syst.)$ MeV and $\rm
2.38\pm0.13(stat.) \pm0.12(syst.)$ MeV for $\rm ^4_{\Lambda}H$ and $\rm
^4_{\Lambda}He$, respectively. The measured $\Lambda$ binding-energy difference
is $\rm 0.16\pm0.14(stat.)\pm0.10(syst.)$ MeV for ground states. Combined with
the $\gamma$-ray transition energies, the binding-energy difference for excited
states is $\rm -0.16\pm0.14(stat.)\pm0.10(syst.)$ MeV, which is negative and
comparable to the value of the ground states within uncertainties. These new
measurements on the $\Lambda$ binding-energy difference in A = 4 hypernuclei
systems are consistent with the theoretical calculations that result in $\rm
\Delta B_{\Lambda}^4(1_{exc}^{+})\approx -\Delta B_{\Lambda}^4(0_{g.s.}^{+})<0$
and present a new method for the study of CSB effect using relativistic
heavy-ion collisions.
