Heavy baryon wave functions, Bakamjian-Thomas approach to form factors, and observables in ${Λ_b \to Λ_c\left({1 \over 2}^\pm \right) \ell \overlineν}$ transitions

Abstract

Motivated by the calculation of observables in the decays $Λ_b \to Λ_c\left({1 \over 2}^\pm \right) \ell \overlineν$, as tests of Lepton Flavor Universality, we present a calculation of form factors in the quark model. Our scheme combines a spectroscopic model, providing the internal wave functions, and the Bakamjian-Thomas relativistic formalism to deduce the wave functions in motion and current matrix elements, that amount in the heavy quark limit to the Isgur-Wise (IW) function. For baryons we meet difficulties using standard spectroscopic models, leading us to propose a simple phenomenological model : a Q-pointlike-diquark model, non-relativistic with harmonic oscillator forces, with a reasonable low-lying spectrum and good slope of the IW function. We extract this slope from Lattice data and find $ρ_Λ^2 \sim 2$. We are not able to reproduce the right $ρ_Λ^2$ when using standard linear + Coulomb potential models, both with three quarks $Qqq$ or in a Q-pointlike-diquark picture. These difficulties seem to derive from the high sensitivity of $ρ_Λ^2$ to the structure of the light quark subsystem. After fixing the parameters of our interim model to yield correct spectrum and $ρ_Λ^2$, we compute observables. Bjorken sum rule shows that the inelastic IW function is large, and therefore $Λ_b \to Λ_c \left({1 \over 2}^-, {3 \over 2}^- \right) \ell \overlineν$ could be studied at LHCb. Some observables in the $τ$ case present zeroes for specific values of $q^2$ that could be tests of the Standard Model.