# Massive loops in thermal SU(2) Yang-Mills theory: Radiative corrections to the pressure beyond two loops

## TL;DR

This paper investigates higher-order radiative corrections to the pressure in thermal SU(2) Yang-Mills theory, revealing that certain diagrams dominate at high temperatures and necessitate all-loop resummation for accurate results.

## Contribution

It introduces an efficient method for bookkeeping in loop calculations and demonstrates the need for all-loop resummation due to dominant high-temperature contributions.

## Key findings

- Vertex constraints suppress the number of valid loop combinations.
- The 3-loop diagram dominates at high temperatures with a power of thirteen.
- Loop expansion likely does not terminate at finite order, requiring resummation.

## Abstract

We device an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasi-particles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. The according radiative corrections modify the free thermal-quasiparticle pressure at one loop. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behaviour, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen such that this diagram dominates all lower loop orders for sufficiently high temperatures. An all-loop-order resummation of 2PI diagrams with dihedral symmetry is thus required, defining an extremely well-bounded analytical continuation of the low-temperatures result.