Violation of NCQ scaling in hadron elliptic flow in Au+Au collisions at $\sqrt{s_{NN}}=3.0-7.7 \,\mathrm{GeV}$

We investigate the number-of-constituent-quark (NCQ) scaling of elliptic flow for various hadrons in non-central Au+Au collisions at $\sqrt{s_{NN}} = 3.0\text{--}7.7\,\mathrm{GeV}$ using the AMPT model with string melting (SM) and pure hadron cascade (HC) modes. For the SM case, NCQ scaling is absent at $\sqrt{s_{NN}} =3.0\,\mathrm{GeV}$ but is largely restored by $\sqrt{s_{NN}} =3.9\,\mathrm{GeV}$. Although quark coalescence occurs at $\sqrt{s_{NN}} =3.0\,\mathrm{GeV}$, the lack of NCQ scaling is attributed to the insufficient development of quark elliptic flow and the limited production of strange quarks and antiquarks. This finding suggests that NCQ scaling could not be considered a definitive signature of quark-gluon plasma (QGP) formation in the RHIC fixed-target energy region. For the HC case, as expected, no NCQ scaling is observed. However, a mass ordering in the elliptic flow emerges at $\sqrt{s_{NN}} =4.5\,\mathrm{GeV}$, indicating that full thermalization may not be a prerequisite for mass ordering.