Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0

Details Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0 Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0

2009-04-13

arxiv.org/abs/0904.1942v2

Phys.Rev.D80:054006,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

70 pages

Scientific paper

10.1103/PhysRevD.80.054006

We propose a group theoretical method to study Isgur-Wise functions. A current matrix element splits into a heavy quark matrix element and an overlap of the initial and final clouds, related to the IW functions, that contain the long distance physics. The light cloud belongs to the Hilbert space of a unitary representation of the Lorentz group. Decomposing into irreducible representations one obtains the IW function as an integral formula, superposition of irreducible IW functions with positive measures, providing positivity bounds on its derivatives. Our method is equivalent to the sum rule approach, but sheds another light on the physics and summarizes and gives all its possible constraints. We expose the general formalism, thoroughly applying it to the case j = 0 for the light cloud, relevant to the semileptonic decay Lambda_b -> Lambda_c + l + nu. In this case, the principal series of the representations contribute, and also the supplementary series. We recover the bound for the curvature of the j = 0 IW function xi_Lambda (w) that we did obtain from the sum rule method, and we get new bounds for higher derivatives. We demonstrate also that if the lower bound for the curvature is saturated, then xi_Lambda (w) is completely determined, given by an explicit elementary function. We give criteria to decide if any ansatz for the Isgur-Wise function is compatible or not with the sum rules. We apply the method to some simple model forms proposed in the literature. Dealing with a Hilbert space, the sum rules are convergent, but this feature does not survive hard gluon radiative corrections.

Affiliated with

Also associated with

No associations

Rating

Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-324371