Renormalization group improvement for thermally resummed effective potential

We propose a novel method for renormalization group improvement of thermally resummed effective potential. In our method, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>β</a:mi></a:mrow></a:math>-functions are temperature dependent as a consequence of the divergence structure in resummed perturbation theory. In contrast to the ordinary <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mover accent="true"><c:mi>MS</c:mi><c:mo stretchy="true">¯</c:mo></c:mover></c:math> scheme, the renormalization group invariance of the resummed finite-temperature effective potential holds order by order, which significantly mitigates a notorious renormalization scale dependence of phase transition quantities such as a critical temperature even at the one-loop order. We also devise a tractable method that enables one to incorporate temperature-dependent higher-order corrections by fully exploiting the renormalization group invariance.