@Article{Greynat_etal2014,
author="Greynat, D.
and de Rafael, E.
and Vulvert, G.",
title="Asymptotic behaviour of pion-pion total cross-sections",
journal="Journal of High Energy Physics",
year="2014",
publisher="Springer",
volume="03",
number="3",
pages="107--21pp",
optkeywords="QCD Phenomenology; Phenomenological Models",
abstract="We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the pi pi total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log(2)s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for pi(+)pi(-), pi(+/-)pi(0) and pi(0)pi(0) scattering within the framework of the constituent chiral quark model (C chi QM) in the limit of a large number of colours N-c and discuss their asymptotic behaviours. The same pi pi 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 sigma(total)(pi +/-pi 0)(s) cross section predicted by the CxQM 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.",
optnote="WOS:000333803000003",
optnote="exported from refbase (https://references.ific.uv.es/refbase/show.php?record=1747), last updated on Thu, 08 May 2014 10:00:40 +0000",
issn="1029-8479",
doi="10.1007/JHEP03(2014)107",
opturl="http://arxiv.org/abs/arXiv:1312.2881",
opturl="https://doi.org/10.1007/JHEP03(2014)107",
archivePrefix="arXiv",
eprint="arXiv:1312.2881",
language="English"
}