First-order Electroweak phase transition at finite density

We study the Electroweak phase transition with the Standard Model effective field theory at finite temperature and finite density. Utilizing the dimensional reduction approach, we construct the tree dimensional thermal effective field theory at finite density and investigate the phase transition dynamics. We evaluate how the results depend on the renormalization scale and the chemical potential. Our results show that, with the tree dimensional thermal effective potential at 2-loop level, we can effectively reduce the theoretical uncertainty in the calculations of the phase transition parameters due to the renormalization scale dependence, and the new physics scale is restricted to be $\Lambda\lesssim (770-800)$ GeV by the baryon number washout avoidance condition. Meanwhile, the presence of the chemical potential would affect the phase transition parameter and make the constraints from the baryon number washout avoidance condition more strict, especially for weaker first-order phase transition scenarios at higher new physics scales.