Heavy baryon wave functions, Bakamjian-Thomas approach to form factors, and observables in ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c\left({\frac{1}{2}}^{\pm }\right)\mathrm{\ell }\bar{\nu }$ transitions

Motivated by the calculation of observables in the decays $\Lambda_b \to \Lambda_c\left({1 \over 2}^\pm \right) \ell \overline{\nu}$, 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 ${\rho }_{\mathrm{\Lambda }}^2\sim 2$. We are not able to reproduce the right ${\rho }_{\mathrm{\Lambda }}^2$ 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 ${\rho }_{\mathrm{\Lambda }}^2$ to the structure of the light quark subsystem. After fixing the parameters of our interim model to yield correct spectrum and ${\rho }_{\mathrm{\Lambda }}^2$, we compute observables. Bjorken sum rule shows that the inelastic IW function is large, and therefore $\Lambda_b \to \Lambda_c \left({1 \over 2}^-, {3 \over 2}^- \right) \ell \overline{\nu}$ could be studied at LHCb. Some observables in the $\tau$ case present zeroes for specific values of $q^2$ that could be tests of the Standard Model.