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Asymptotic behaviour of pion-pion total cross-sections

Autor Greynat, David ; Rafael, Eduardo de; Vulvert, Grégory
Fecha de publicación 24-mar-2014
Citación Journal of High Energy Physics 2014: 107 (2014)
ResumenWe derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the ππ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log2 s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for π + π −, π ± π 0 and π 0 π 0 scattering within the framework of the constituent chiral quark model (CχQM) in the limit of a large number of colours N c and discuss their asymptotic behaviours. The same ππ cross sections are also discussed within the general framework of Large-N c QCD and we show that it is possible to make an Ansatz for the isospin I = 1 and I = 0 spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-N c counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the σtotalπ±π0(s) cross section predicted by the CχQM with the high energy behaviour predicted by the Large-N c Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the pp and pp¯ scattering total cross sections.
Versión del editorhttp://dx.doi.org/10.1007/JHEP04(2014)191
URI http://hdl.handle.net/10261/96485
DOIdoi: 10.1007/JHEP04(2014)191
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