Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Pion Mass Formula   The often used Gell-Mann-Oakes-Renner mass formula for Nambu-Goldstone (NG)
bosons in QCD, such as the pions, involves the condensate $<\overline{q}q>$,
$f_{\pi}$ and the quark current masses. Within the context of the Global Colour
Model (GCM) for QCD a manifestly different formula was recently found by Cahill
and Gunner. Remarkably Langfeld and Kettner have shown the two formula to be
equivalent. Here we note that the above recent analyses refer to the
constituent pion and not the exact pion, even within the GCM. Further we
generalise the Langfeld-Kettner identity to include the full response of the
constituent quark propagators to the presence of a non-zero (and running) quark
current mass.

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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas