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Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility
Bernard V., Descotes-Genon S., Toucas G.
JHEP 12 (2012) 080 - http://hal.archives-ouvertes.fr/hal-00737982
Physics/High Energy Physics - Lattice
Physics/High Energy Physics - Phenomenology
Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility
V. Bernard1, S. Descotes-Genon2, G. Toucas2
1:  IPNO - Institut de Physique Nucléaire d'Orsay
http://ipnweb.in2p3.fr
CNRS : UMR8608 – IN2P3 – Université Paris XI - Paris Sud
IPN - 15, rue Georges Clemenceau - 91406 ORSAY CEDEX
France
2:  LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
CNRS : UMR8627 – Université Paris XI - Paris Sud
Bâtiment 210 Université Paris XI 91405 Orsay Cedex
France
The first two non-trivial moments of the distribution of the topological charge (or gluonic winding number), i.e., the topological susceptibility and the fourth cumulant, can be computed in lattice QCD simulations and exploited to constrain the pattern of chiral symmetry breaking. We compute these two topological observables at next-to-leading order in three-flavour Chiral Perturbation Theory, and we discuss the role played by the eta propagation in these expressions. For hierarchies of light-quark masses close to the physical situation, we show that the fourth cumulant has a much better sensitivity than the topological susceptibility to the three-flavour quark condensate, and thus constitutes a relevant tool to determine the pattern of chiral symmetry breaking in the limit of three massless flavours. We provide the complete formulae for the two topological observables in the isospin limit, and predict their values in the particular setting of the recent analysis of the RBC/UKQCD collaboration. We show that a combination of the topological susceptibility and the fourth cumulant is able to pin down the three flavour condensate in a particularly clean way in the case of three degenerate quarks.
English
2012-09-19

JHEP
international
Article in peer-reviewed journal
2012
12
080

29 pages, 7 figures
LPT-ORSAY 12-98

Fulltext link: 
http://fr.arXiv.org/abs/1209.4367