Heavy baryon wave functions, Bakamjian-Thomas approach to form factors, and observables in Λ b → Λ c ( 1 2 ± ) ℓ ν ¯ transitions

Motivated by the calculation of observables in the decays ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}({\frac{1}{2}}^{\ifmmode\pm\else\textpm\fi{}})\ensuremath{\ell}\overline{\ensuremath{\nu}}$, we present a calculation of form factors in the quark model. Our scheme combines a spectroscopic model with the internal wave functions and the Bakamjian-Thomas (BT) relativistic formalism to get the wave functions in motion. In the heavy quark limit, the current matrix elements provide the Isgur-Wise (IW) function. This limit is covariant, satisfies a large set of sum rules, and has been successfully applied to mesons. On the other hand, for baryons, we meet difficulties using standard spectroscopic models. This leads us to propose a phenomenological model, a Q-pointlike-diquark model, nonrelativistic, with harmonic oscillator forces, giving both a reasonable low-lying spectrum and the expected slope of the IW function. To begin, we extract this slope from lattice QCD data and find it to be around ${\ensuremath{\rho}}_{\mathrm{\ensuremath{\Lambda}}}^{2}\ensuremath{\sim}2$, that we use as a guideline. We are not able to reproduce the right ${\ensuremath{\rho}}_{\mathrm{\ensuremath{\Lambda}}}^{2}$ using certain typical standard $\text{linear}+\text{Coulomb}$ potential models, both with three quarks $Qqq$ or in a Q-pointlike-diquark picture. These difficulties seem to derive from the high sensitivity of ${\ensuremath{\rho}}_{\mathrm{\ensuremath{\Lambda}}}^{2}$ to the structure of the light quark subsystem in a relativistic scheme. Finally, we present our model, and fixing its parameters to yield the correct spectrum and ${\ensuremath{\rho}}_{\mathrm{\ensuremath{\Lambda}}}^{2}\ensuremath{\sim}2$, we apply it to the calculation of observables. By studying Bjorken sum rule, we show that the inelastic IW function is large, and therefore, the transitions ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}({\frac{1}{2}}^{\ensuremath{-}},{\frac{3}{2}}^{\ensuremath{-}})\ensuremath{\ell}\overline{\ensuremath{\nu}}$ could be studied at LHCb. Interestingly, some observables in the $\ensuremath{\tau}$ case present zeroes for specific values of ${q}^{2}$ that could be tests of the Standard Model.