Comments on compositeness in the SU(2) linear sigma model

Abstract

First we summarize the quark-level linear $σ$ model compositeness conditions and verify that indeed $m_σ= 2 m_q$ when $m_π= 0$ and $N_c=3$, rather than in the $N_c\to\infty$ limit, as is sometimes suggested. Later we show that this compositeness picture also predicts a chiral symmetry restoration temperature $T_c = 2f_π$, where $f_π$ is the pion decay constant. We contrast this self-consistent Z=0 compositeness analysis with prior studies of the compositeness problem.