Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-03-26
JHEP 0806:039,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
29 pages, 11 figures. Two references added
Scientific paper
10.1088/1126-6708/2008/06/039
We obtain the corrections in $1/n$ and in $1/\ln n$ ($n$ is the principal quantum number of the bound state) of the decay constants of scalar and pseudoscalar currents in two and four dimensions in the large $N_c$. We obtain them from the operator product expansion provided a model for the large $n$ mass spectrum is given. In the two-dimensional case the spectrum is known and the corrections obtained in this paper are model independent. We confirm these results by confronting them with the numerical solution of the 't Hooft model. We also consider a model at finite $N_c$ and obtain the associated decay constants that are consistent with perturbation theory. This example shows that that the inclusion of perturbative corrections, or finite $N_c$ effects, to the OPE does not constrain the slope of the Regge trajectories, which remain a free parameter for each different channel.
Mondejar Jorge
Pineda Antonio
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