The width of Θ+ for large Nc in chiral quark soliton model

Michał Praszałowicz

doi:10.1016/j.physletb.2003.12.056

Abstract

In the chiral quark soliton model the smallness of Θ+ width is due to the cancellation of the coupling constants which are of different order in Nc. We show that taking properly into account the flavor structure of relevant SU(3) representations for arbitrary number of colors enhances the nonleading term by an additional factor of Nc, making the cancellation consistent with the Nc counting. Moreover, we show that, for the same reason, Θ+ width is suppressed by a group-theoretical factor O(1/Nc) with respect to Δ and discuss the Nc dependence of the phase space factors for these two decays.

Highlights

Five experiments announced discovery of a narrow, exotic baryonic state called Θ+ [1]
At first sight to some extent unnatural that the cancellation occurs between the constants which are of different order in the number of colors, Nc
For arbitrary number of colors, baryons do not fall into ordinary flavor octet, decuplet and antidecuplet, but are members of large SU(3) representations [9, 10, 11], which reduce to the standard ones only for Nc = 3

Summary

INTRODUCTION

Five experiments announced discovery of a narrow, exotic baryonic state called Θ+ [1]. For arbitrary number of colors, baryons do not fall into ordinary flavor octet, decuplet and antidecuplet, but are members of large SU(3) representations [9, 10, 11], which reduce to the standard ones only for Nc = 3. Taking this extra Nc dependence into account makes the SU(3) Clebsch-Gordan coefficients depend on Nc. We find that group-theoretical factors suppress ΓΘ+ with respect to Γ∆. This suppression is, ”undone” by the phase space factor, which scales differently with Nc in the chiral limit

LARGE Nc LIMIT

DECAY WIDTH

NONRELATIVISTIC LIMIT

SUMMARY