Transition rates for q q bar -> pi pi pi in a chiral model

Details Transition rates for q q bar -> pi pi pi in a chiral model Transition rates for q q bar -> pi pi pi in a chiral model

1998-10-13

arxiv.org/abs/hep-ph/9810348v1

Nucl.Phys.A643:275-302,1998

Physics

High Energy Physics

High Energy Physics - Phenomenology

33 LaTex pages plus 1 postscript file containing 12 figures. To be published in Nuclear Physics A

Scientific paper

10.1016/S0375-9474(98)00479-5

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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