Massive fluctuations in deconfining SU(2) Yang-Mills thermodynamics

TL;DR

This paper investigates the behavior of loop corrections in SU(2) Yang-Mills thermodynamics, demonstrating that higher-loop contributions dominate at high temperatures and that the loop expansion does not terminate at finite order, requiring resummation techniques.

Contribution

It provides a detailed analysis of loop corrections, disproves the finite termination conjecture, and introduces an all-loop resummation method for bubble diagrams in deconfining SU(2) Yang-Mills theory.

Findings

Higher-loop contributions dominate at high temperatures.

Loop expansion does not terminate at finite order.

Resummation yields an analytic continuation across temperatures.

Abstract

We review how vertex constraints inherited from the thermal ground state strongly reduce the integration support of loop four-momenta associated with massive quasi-particles in bubble diagrams constituting corrections to the free thermal quasi-particle pressure. In spite of the observed increasingly suppressing effect when increasing 2-particle-irreducible (2PI) loop order, a quantitative analysis enables us to disprove the conjecture voiced in hep-th/0609033 that the loop expansion would terminate at a finite order. This reveals the necessity to investigate exact expressions of (at least some) higher-loop order diagrams. Explicit calculation shows that although the behaviour of the 2PI three-loop contribution at low temperatures displays hierarchical suppression compared to lower loop-orders, its high-temperature expression instead dominates all lower orders. However, an all-loop-order resummation of a class of 2PI bubble diagrams is shown to yield an analytic continuation of the low-temperature hierarchy to all temperatures in the deconfining phase.