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Author  |
Greynat, D.; de Rafael, E.; Vulvert, G. |
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Title |
Asymptotic behaviour of pion-pion total cross-sections |
Type |
Journal Article |
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Year |
2014 |
Publication |
Journal of High Energy Physics |
Abbreviated Journal |
J. High Energy Phys. |
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Volume |
03 |
Issue |
3 |
Pages |
107 - 21pp |
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Keywords |
QCD Phenomenology; Phenomenological Models |
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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. |
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Address |
[Greynat, David] Univ Naples Federico II, Dipartimento Sci Fis, I-80126 Naples, Italy, Email: david.greynat@gmail.com; |
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Publisher |
Springer |
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Language |
English |
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Original Title |
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Series Volume |
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Edition |
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ISSN |
1029-8479 |
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Notes |
WOS:000333803000003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1747 |
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