Isospin Breaking and chiral symmetry restoration

Abstract

We analyze quark condensates and chiral (scalar) susceptibilities including isospin breaking effects at finite temperature $T$. These include $m_u\ne m_d$ contributions as well as electromagnetic ($e\ne 0$) corrections, both treated in a consistent chiral lagrangian framework to leading order in SU(2) and SU(3) Chiral Perturbation Theory, so that our predictions are model independent. The chiral restoration temperature extracted from $<\bar{q}q>=<\bar{u}u+\bar{d}d>$ is almost unaffected, while the isospin breaking order parameter $<\bar{u}u-\bar{d}d>$ grows with $T$ for the three-flavour case SU(3). We derive a sum rule relating the condensate ratio $<\bar{q}q>(e\ne 0)/<\bar{q}q>(e=0)$ with the scalar susceptibility difference $\chi (T)-\chi (0)$, directly measurable on the lattice. This sum rule is useful also for estimating condensate errors in staggered lattice analysis. Keeping $m_u\ne m_d$ allows to obtain the connected and disconnected contributions to the susceptibility, even in the isospin limit, whose temperature, mass and isospin breaking dependence we analyze in detail. The disconnected part grows linearly, diverging in the chiral (infrared) limit as $T/M_{\pi }$, while the connected part shows a quadratic behaviour, infrared regular as $T^2/M_{\eta }^2$ and coming from ${\pi }^0\eta$ mixing terms. This smooth connected behaviour suggests that isospin breaking correlations are weaker than critical chiral ones near the transition temperature. We explore some consequences in connection with lattice data and their scaling properties, for which our present analysis for physical masses, i.e. beyond the chiral limit, provides a useful model-independent description for low and moderate temperatures.

18 pages, 5 figures. Comments and references added. Version accepted in Phys.Rev.D

References in corpus (5)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The QCD transition temperature: results with physical masses in the continuum limit II.
• QCD Thermodynamics from the Lattice
• Scalar Meson Spectroscopy with Lattice Staggered Fermions
• Quark disconnected diagrams in chiral perturbation theory

Cited by in corpus (4)

• Scalar susceptibilities and four-quark condensates in the meson gas within Chiral Perturbation Theory
• Electromagnetic effects in the pion dispersion relation at finite temperature
• Quantum Chromodynamics, Antiferromagnets and XY Models from a Unified Point of View
• Thermodynamics and quark condensates of three-flavor QCD at low temperature