Isgur-Wise functions and unitary representations of the Lorentz group: The baryon case j=0
- Laboratoire de Physique Theorique Universite de Paris XI, Batiment 210, 91405 Orsay Cedex (France)
We propose a group theoretical method to study Isgur-Wise (IW) 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}{sub b}{yields}{lambda}{sub c}l{nu}{sub l}. 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}{sub {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}{sub {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.
- OSTI ID:
- 21322582
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 5; Other Information: DOI: 10.1103/PhysRevD.80.054006; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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