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

Abstract

Motivated by the calculation of observables in the decays ${\Lambda }_b\to {\Lambda }_c\left({\frac{1}{2}}^{\pm }\right)\ell \overline{\nu }$, 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 ${\rho }_{\Lambda }^2\sim 2$. We are not able to reproduce the right ${\rho }_{\Lambda }^2$ 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 ${\rho }_{\Lambda }^2$ to the structure of the light quark subsystem. After fixing the parameters of our interim model to yield correct spectrum and ${\rho }_{\Lambda }^2$, we compute observables. Bjorken sum rule shows that the inelastic IW function is large, and therefore ${\Lambda }_b\to {\Lambda }_c\left({\frac{1}{2}}^{-},{\frac{3}{2}}^{-}\right)\ell \overline{\nu }$ 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.

arXiv comment62 pages, 30 figures

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• Light-cone Sum Rule Analysis of Semileptonic Decays ${\Lambda }_b^0\to {\Lambda }_c^{+}{\ell }^{-}{\overline{\nu }}_{\ell }$
• Form Factor Counting and HQET Matching for New Physics in ${\Lambda }_b\to {\Lambda }_c^{\ast }l\nu$
• Scrutinizing New Physics in Semi-leptonic $B_c\to J/\psi \tau \nu$ Decay
• b-baryon semi-tauonic decays in the Standard Model
• Is the ${\Lambda }_c(2625{)}^{+}$ the heavy quark spin symmetry partner of the ${\Lambda }_c(2595{)}^{+}$?
• Electromagnetic and weak decay of singly Heavy Baryons (Qqq)
• Form factors of ${\Lambda }_b^0\to {\Lambda }_c(2595{)}^{+}$ within light-cone QCD sum rules