TY  - JOUR
AU  - Greynat, D.
AU  - de Rafael, E.
AU  - Vulvert, G.
PY  - 2014
DA  - 2014//
TI  - Asymptotic behaviour of pion-pion total cross-sections
T2  - J. High Energy Phys.
JO  - Journal of High Energy Physics
SP  - 107
EP  - 21pp
VL  - 03
IS  - 3
PB  - Springer
KW  - QCD Phenomenology
KW  - Phenomenological Models
AB  - 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.
SN  - 1029-8479
UR  - http://arxiv.org/abs/arXiv:1312.2881
UR  - https://doi.org/10.1007/JHEP03(2014)107
DO  - 10.1007/JHEP03(2014)107
LA  - English
N1  - WOS:000333803000003
ID  - Greynat_etal2014
ER  -