Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2010-09-30
Phys.Rev.D84:096006,2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
22 pages, 8 figures. Version to be published in Physical Review D
Scientific paper
10.1103/PhysRevD.84.096006
The leading $1/N_c$ behaviour of Unitarised Chiral Perturbation Theory distinguishes the nature of the $\rho$ and the $\sigma$. At one loop order the $\rho$ is a ${\bar q}q$ meson, while the $\sigma$ is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger $N_c$, if such a distinction holds. While the $\sigma$ at $N_c=3$ is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as $N_c$ increases above 6-8, the $\sigma$ has a sub-dominant ${\bar q}q$ fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of $N_c \lesssim 15$, where the unitarisation procedure adopted applies.
de Elvira Jacobo Ruiz
Pelaez Jose Ramon
Pennington M. R.
Wilson Dalziel J.
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