Abstract
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 $\rho_\Lambda^2 \sim 2$. 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 $\Lambda_b \to \Lambda_c \left({1 \over 2}^-, {3 \over 2}^- \right) \ell \overline{\nu}$ 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.
Highlights
Possible physics beyond the Standard Model (SM), suggesting lepton flavor universality violation (LFUV), has been pointed out by data of different experiments on B → DðÃÞlν [1,2,3], summarized in [4]
By studying Bjorken sum rule, we show that the inelastic IW function is large, and the transitions
[20], we have found a slope ρ2Λ ≃ 4. This is much larger than the estimate by LHCb, ρ2Λ ≃ 1.8 [21], and the value that follows from lattice QCD calculations by Detmold et al [13], that gives ρ2Λ ≃ 2, as we show below
Summary
Possible physics beyond the Standard Model (SM), suggesting lepton flavor universality violation (LFUV), has been pointed out by data of different experiments on B → DðÃÞlν [1,2,3], summarized in [4]. Coordinates, it depends strongly on the ratio Rρ=Rλ and may acquire much too large values Another important feature of the BT approach is that it implements automatically the heavy quark effective theory (HQET) sum rules like Bjorken’s or the curvature sum rules, which help to constrain the contributions of higher states. We turn to the quark-diquark model in Sec. IV, we compute the IW functions for the elastic and inelastic cases in the BT scheme from the wave functions of the Bing Chen et al. Hamiltonian [27], and we find a too small slope compared to the lattice result. It has been established [30] that the “dipole” form (2), that depends on a single parameter, satisfies these constraints provided that ρ2Λ ≥ 14
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