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It is challenging to build a model that can correctly and unifiedly accountfor the deconfinement phase transition and thermodynamics of the hot $SU(N)$pure Yang-Mills (PYM) system, for any $N$. In this article, we slightlygeneralize the massive PYM model to the situation with a quasigluon mass$M_g(T)$ varying with temperature, inspired by the quasigluon model. In such aframework, we can acquire an effective potential for the temporal gauge fieldbackground by perturbative calculation, rather than adding by hand. Theresulting potential works well to describe the behavior of the hot PYM systemfor all $N$, via the single parameter $M_g(T)$. Moreover, under the assumptionof unified eigenvalue distribution, the $M_g(T)$ fitted by machine learning isfound to follow $N$-universality.

Massive Gauge Theory with Quasigluon for Hot $SU(N)$ Part I: Phase Transition and Thermodynamics