Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transition rates for q q bar -> pi pi pi in a chiral model   We investigate the nature of transition rates for the hadronization process
of q q bar -> Pi Pi Pi as opposed to the transition rates for q q bar -> Pi Pi,
within the Nambu--Jona-Lasinio model that has manifest chiral symmetry. Feynman
diagrams appropriate to this process can be classified according to the
expansion in the inverse number of colors 1/N_c. Two of these types of graphs
are seen to be either 's-like' or 't-like' in nature. A further graph that
contains both s-like and t-like elements, and which is denoted as st-like, is
also present. To describe such a process with two incoming and three outgoing
particles, it is necessary to extend the number of Mandelstam invariants. It is
convenient to introduce seven such variables, of which only five are
independent. The cross section for two incoming particles to three outgoing
particles is then reexpressed in integral form in terms of these invariants. As
a function of sqrt s, the final expression is reduced to an integral over the
four remaining invariants. The limits of integration, which are now
non-trivial, are also discussed. The transition rate for the explicit case of u
u bar -> Pi^+ Pi^- Pi^0, is evaluated numerically, assuming non-chiral pions,
m_Pi = 135MeV. The rate for three pion production is found to be of the same
order of magnitude as for two pion production, making this a non-negligible
contribution to hadronization.

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The categories of this paper are: cs
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The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex