hadron2011

Chiral and isospin symmetry breaking: order parameters and susceptibilities

Jun 14, 2011, 6:20 PM

1h 10m

Millerzimmer (Künstlerhaus)

poster Poster Session Poster Session

Speaker

Mr Ricardo Torres-Andres (Universidad Complutense de Madrid)

Description

We analyze the order parameters of chiral and $SU_V(N_f)$ symmetry breaking, as well as their isoscalar and isovector susceptibilities. For that purpose, we include $m_u\neq m_d$ and electromagnetic corrections in a consistent leading order Chiral Perturbation Theory framework for $N_f=2,3$, providing model-independent predictions. At zero temperature and assuming the QCD vacuum to have a ferromagnetic-like behaviour, we show that the increasing of the quark condensate under explicit chiral symmetry breaking induced by electromagnetic corrections leads to constraints for the electromagnetic low-energy constants (LEC) which are checked with different LEC determinations in the literature. We also analyze matching conditions between $SU(2)$ and $SU(3)$ as well as corrections to the sum rule relating quark condensate ratios \cite{Nicola:2010xt}. At finite temperature, the isospin breaking order parameter $\langle\bar uu-\bardd\rangle$ grows with $T$ for $SU(3)$, $T_c$ being almost unaffected. We obtain a sum rule relating EM corrections to the quark condensate with isoscalar susceptibility differences $\chi(T)-\chi(0)$, which can be also useful for estimating errors in staggered lattice analysis. Keeping $m_u\neq m_d$ allows us to separate neatly the quark connected and disconnected susceptibilities, whose mass and temperature behaviour we analyze in detail. Near chiral restoration, the disconnected part grows linearly, diverging in the infrared chiral limit as $T/M_\pi$, while the connected part has an infrared regular behaviour $T^2/M_\eta^2$ coming from $\pi^0-\eta$ mixing. 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 description for the hadron gas at low and moderate temperatures \cite{Nicola:2011gq}. \begin{thebibliography}{99} \bibitem{Nicola:2010xt} A.~G.~Nicola and R.~T.~Andres, %``Isospin-Breaking quark condensates in Chiral Perturbation Theory,'' arXiv:1009.2170 [hep-ph]. %%CITATION = ARXIV:1009.2170;%% \bibitem{Nicola:2011gq} A.~G.~Nicola and R.~T.~Andres, %``Isospin Breaking and chiral symmetry restoration,'' Phys.\ Rev.\ D {\bf 83}, 076005 (2011). arXiv:1101.5362 [hep-ph]. %%CITATION = ARXIV:1101.5362;%% \end{thebibliography}