Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-09-09
Phys.Rev. D70 (2004) 094020
Physics
High Energy Physics
High Energy Physics - Phenomenology
RevTeX4, 37 pages, 5 Postscript figures, uses epsfig.sty, to appear in Phys.Rev.D
Scientific paper
10.1103/PhysRevD.70.094020
In this paper, we study generic non-local NJL models for four-dimensional QCD in the limit of a large number of colours. We diagonalise, through a Bogoliubov-type transformation, the Hamiltonian of the model completely in terms of the compound operators creating/annihilating mesons - bound states of dressed quarks and antiquarks - and demonstrate a one-to-one correspondence between the Bogoliubov diagonalisation condition and the Bethe-Salpeter equation for bound states. We conclude that, in the leading order in N_C, the nontrivial contents of the theory is entirely encoded in the chiral angle - the solution to the mass-gap equation for dressed quarks. As a consequence, we extend the statement of existence of excited solutions to the mass-gap equation, called vacuum replicas, beyond the BCS level and prescribe a new index to the mesonic operators - the label of the vacuum state in which the corresponding meson is created.
Nefediev A. V.
Ribeiro Emilio F. J. T.
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