Droplets in the cold and dense linear sigma model with quarks

The linear sigma model with quarks at very low temperatures provides an effective framework for the thermodynamics of the strong interaction in cold and dense matter. It is especially useful in the description of the chiral transition at densities that are still not probed in accelerators but expected to be found in compact stars and protoneutron star matter. Using the MS̄ one-loop effective potential, we compute quantities that are relevant in the process of nucleation of droplets of quark matter in this scenario. In particular, we show that the model predicts a surface tension of Σ~5--15 MeV/fm². Including temperature effects and vacuum logarithmic corrections, we find a clear competition between these features in characterizing the dynamics of the chiral phase conversion, so that if the temperature is low enough the consistent inclusion of vacuum corrections could help preventing the nucleation of quark matter at high densities. We also discuss the first interaction corrections that come about at two-loop order. Low values of the surface tension, as the ones we find in this simplified chiral description, could render nucleation of quark matter possible during the early postbounce stage of core-collapse supernovae.