Gauge-independent Thermal $β$ Function In Yang-Mills Theory via the Pinch Technique

It is proposed to use the pinch technique (PT) to obtain the gauge-independent thermal $\beta$ function $\beta_T$ in a hot Yang-Mills gas. Calculations of the thermal $\beta$ function are performed at one-loop level in four different gauges, (i) the background field method with an arbitrary gauge parameter, (ii) the Feynman gauge, (iii) the Coulomb gauge, and (iv) the temporal axial gauge. When the pinch contributions to the gluon self-energy are included, the same result is derived for $\beta_T$ in all four cases.