The quark mass dependence of the pion mass at infinite N

Details The quark mass dependence of the pion mass at infinite N The quark mass dependence of the pion mass at infinite N

2005-03-23

arxiv.org/abs/hep-lat/0503033v1

Phys.Lett. B616 (2005) 76-84

Physics

High Energy Physics

High Energy Physics - Lattice

14 pages, 1 figure

Scientific paper

10.1016/j.physletb.2005.04.047

In planar QCD, in two space time dimensions, the meson eigenvalue equation has a nonlocal structure interpretable as resulting from hidden degrees of freedom. The nonlocality can be reconstructed from the functional form of the pion mass dependence on quark mass within an expansion starting from a special one dimensional Schroedinger problem. The one dimensional problem makes the pion mass depend on the quark mass through a simple quadratic relation which is shown to be compatible also with numerical data obtained in four dimensions.

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