Hot and Dense Medium Effects on the $B_s^*$ and $B^*$ Multiplets

We present an extensive analysis of the in-medium masses and decay constants of the $B_s^*(5415)$ and $B^*(5325)$ multiplets, including both particles and antiparticles, using QCD sum rules at finite temperature and density. The OPE incorporates the full temperature- and density-dependent contributions from the quark, gluon, and mixed condensates. Computing the strange ($B_s^{*0}$, $\bar{B}_s^{*0}$), charged ($B^{*\pm}$), and neutral ($B^{*0}$, $\bar{B}^{*0}$) doublet properties allows us to study the effects of flavor symmetry breaking, strangeness, and heavy-quark decoupling on the beauty vector mesons in the medium. Our results indicate that the mass is remarkably resistant to the medium across the entire multiplet: no state loses more than $\sim 13\%$ of its vacuum value, even at $T = T_c$ and $n = 5n_0$, the extreme conditions explored here. The decay constant is far more sensitive, losing up to $\sim 78\%$ at the same point. Baryon density clearly dominates the medium response, while temperature plays a secondary role until the system approaches the deconfinement crossover. At zero density, every state loses almost the same fraction of its mass and decay constant: mass shifts lie between $-(0.5$-$1.1)\%$ and decay-constant shifts between $-(3.9$-$5.3)\%$, regardless of charge or flavor, so temperature alone does not distinguish a particle from its antiparticle. At finite baryon density, a clear particle-antiparticle asymmetry emerges: at $T = 0$ and $n = 5n_0$, the $\bar{B}^{*0}$ mass decreases by $12.9\%$, whereas the $B^{*0}$ mass shifts by only $6.1\%$, a gap of nearly seven percentage points driven entirely by the vector self-energy. This provides a theoretical basis for the future heavy-ion collision program at RHIC, LHC, FAIR, and NICA.