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Title:  Individual eigenvalue distributions of chiral random twomatrix theory and the determination of F_pi 
Authors:  Akemann, G Damgaard, PH 
Keywords:  Matrix Models Lattice QCD Chiral Lagrangians 
Publication Date:  2008 
Abstract:  Dirac operator eigenvalues split into two when subjected to two different external vector sources. In a specific finitevolume scaling regime of gauge theories with fermions, this problem can be mapped to a chiral Random TwoMatrix Theory. We derive analytical expressions to leading order in the associated finitevolume expansion, showing how
individual Dirac eigenvalue distributions and their correlations equivalently can be computed directly from the effective chiral Lagrangian in the epsilonregime. Because of its equivalence to chiral Random TwoMatrix Theory, we use the latter for all explicit computations. On the mathematical side, we define and determine gap probabilities and individual eigenvalue distributions in that theory at finite N, and also derive the relevant scaling limit as N is taken to infinity. In particular, the gap probability for one Dirac eigenvalue is given in terms of a new kernel that depends on the external vector source. This expression may give a new and simple way of determining the pion decay
constant F_pi from lattice gauge theory simulations. 
URI:  http://bura.brunel.ac.uk/handle/2438/1850 
DOI:  http://dx.doi.org/10.1088/11266708/2008/03/073 
Appears in Collections:  School of Information Systems, Computing and Mathematics Research Papers Mathematical Physics

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