Mean-$p_T$ fluctuations in Au+Au collisions at $\sqrt{s_{\rm NN}}=3.0$--$19.6$ GeV within JAM2
Event-by-event mean-$p_T$ fluctuations probe initial-state fluctuations and their evolution through the dynamics of heavy-ion collisions. We study second-order mean-$p_T$ fluctuations in Au+Au collisions at $\sqrt{s_{\rm NN}}=3.0$--$19.6$ GeV using JAM2 in the RQMDv mean-field mode with the MH2 parameterization. The model qualitatively reproduces the measured identified-particle $p_T$ spectra, providing a single-particle baseline for the fluctuation analysis. The scaled fluctuation $k_2$ decreases with increasing $\langle N_{\rm part}\rangle$ and shows broad agreement with the available measurements at 7.7--19.6 GeV, whereas its calculated centrality dependence is stronger than that in the data at 3.0--4.5 GeV. For the combined proton-plus-antiproton sample, the unnormalized correlator $\langle c_2\rangle$ is positive and larger than that for charged pions. The charged-pion correlator $\langle c_2\rangle$ is negative or consistent with zero over most centrality intervals at 3.0 and 3.5 GeV, becomes weakly positive at 4.5 GeV, and remains positive at higher energies. Its energy evolution resembles the change in the reaction-plane elliptic flow, but this comparison does not establish a common microscopic origin. These calculations provide species-dependent predictions within a transport model without an explicit partonic stage. Isolating the contributions of mean fields, rescattering, and spectator interactions requires controlled variations of the transport dynamics.