Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: pi- and K-meson Bethe-Salpeter Amplitudes   Independent of assumptions about the form of the quark-quark scattering
kernel, K, we derive the explicit relation between the flavour-nonsinglet
pseudoscalar meson Bethe-Salpeter amplitude, Gamma_H, and the dressed-quark
propagator in the chiral limit. In addition to a term proportional to gamma_5,
Gamma_H necessarily contains qualitatively and quantitatively important terms
proportional to gamma_5 gamma.P and gamma_5 gamma.k k.P, where P is the total
momentum of the bound state. The axial-vector vertex contains a bound state
pole described by Gamma_H, whose residue is the leptonic decay constant for the
bound state. The pseudoscalar vertex also contains such a bound state pole and,
in the chiral limit, the residue of this pole is related to the vacuum quark
condensate. The axial-vector Ward-Takahashi identity relates these pole
residues; with the Gell-Mann--Oakes-Renner relation a corollary of this
identity. The dominant ultraviolet asymptotic behaviour of the scalar functions
in the meson Bethe-Salpeter amplitude is fully determined by the behaviour of
the chiral limit quark mass function, and is characteristic of the QCD
renormalisation group. The rainbow-ladder Ansatz for K, with a simple model for
the dressed-quark-quark interaction, is used to illustrate and elucidate these
general results. The model preserves the one-loop renormalisation group
structure of QCD. The numerical studies also provide a means of exploring
procedures for solving the Bethe-Salpeter equation without a three-dimensional
reduction.

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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex