Large-N_c Relations Among Isgur–Wise Functions

Abstract

We investigate the relations that must hold among baryonic Isgur–Wise functions ηi in the large-Nc limit from unitarity constraints, and compare to those found by Chow using the Skyrme model [or SU(4)]. Given the exponential dropoff of the ηi away from threshold, unitarity requires only that the usual normalization conditions hold at w=1, and that η=η1 near threshold. Our results are consistent with, but less powerful than, the Skyrme model relations. This shows that large-Nc analyses comprise more than just unitarity constraints.

LargeNcuniversality of the baryon Isgur-Wise form factor: The group theoretical approach

“…Ref. [7] found that the relations obtained by this method are "consistent with, but not as powerful as" those obtained in Ref. [1] through the chiral soliton model.…”

“…It must be emphasized that this study does not question the computational correctness of Ref. [7]. While the authors of Ref.…”

“…Naturally it raises the question whether the same universality of baryon Isgur-Wise form factor in the large N c limit can be obtained without reference to the chiral soliton model. In a recent paper [7] it was attempted to get constraints on the Isgur-Wise form factors from unitarity in 1-pion loop renormalization of the Λ b → Λ c decay and weak decays with 1 or 2 pion emission. Since pion-baryon Yukawa couplings are of order N 1/2 c , many individual weak decay graphs involving pion lines diverge in the large N c limit.…”

“…In particular, no constraint can be placed on ζ 2 (w) in Ref. [7]. It is not surprising by noting that ζ 2 (w) contributes only away from the point of zero recoil, where the Isgur-Wise form factors vanish like exp(−N 3/2 c ) in the large N c limit [8], faster than N −n c for any finite positive n.…”

1/Ncexpansion of the heavy baryon Isgur-Wise functions

“…It is pointed out that there is a contracted SU(2N f ) light quark spin-flavor symmetry in the baryon sector in the large N c limit. The observation of this light quark spin-flavor symmetry results in many quantitative applications [8][9][10][11][12][13][14]. In the large N c limit, the relations among the baryon Isgur-Wise functions have been studied [11][12][13].…”