2024/12/10 by V. Morénas, Morénas, V., A. Le Yaouanc +3
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2412.07756
openalex publication_date 2024/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study the transitions Λb → Λc(1 \over 2^± ) in the Bakamjian-Thomas (BT) relativistic quark model formalism, which describes hadrons with a fixed number of constituents. In the heavy quark limit, the BT model yields covariant form factors and Isgur-Wise (IW) scaling, regardless of the spectroscopic model used to describe the bound states. It has been extensively applied to heavy mesons where subtle properties of the IW limit of QCD, including the Bjorken-Uraltsev sum rules, have been shown to be satisfied. The present paper, where the BT construction is applied to baryons, is unavoidably technical because one is dealing with a three-body problem. The complications originate from the natural choice of the Jacobi coordinates ρ (relative space coordinate between the two light spectator quarks) and λ (relative space coordinate between the center-of-mass of the two light quarks and the heavy quark). The corresponding orbital angular momenta are denoted by ℓρ and ℓλ, with ℓρ+ ℓλ= L. For the transitions Λb → Λc(1 \over 2^±), i.e. L = 0 → L = 0 or L = 0 → L = 1, one can see that the moduli ℓρ and ℓλ can take an infinite number of values. For L = 0 → L = 0 one has the constraint ℓλ= ℓρ and for L = 0 → L = 1 the constraint is ℓλ= ℓρ± 1. We compute explicitly the IW function ξΛ(w) in the elastic case Λb (1 \over 2+ ) → Λc (1 \over 2+ ) and the much more involved IW function σΛ(w) in the inelastic case Λb (1 \over 2+ ) → Λc (1 \over 2- ). These functions exhibit the expected properties of covariance and IW scaling.