Is the $Λ_c(2625)^+$ the heavy quark spin symmetry partner of the $Λ_c(2595)^+$?

Abstract

We use a $\mathcal{O}(Λ_\text{QCD}/m_c)$ heavy quark effective theory scheme, where only $\mathcal{O}(Λ_\text{QCD}/m_b)$ and perturbative QCD short distance corrections are neglected, to study the matrix elements of the scalar, pseudoscalar, vector, axial-vector and tensor currents between the $Λ_b$ ground state and the odd parity charm $Λ_c(2595)^+$ and $Λ_c(2625)^+$ resonances. We show that in the near-zero recoil regime, the scheme describes reasonably well, taking into account uncertainties, the results for the 24 form-factors obtained in lattice QCD (LQCD) just in terms of only 4 Isgur-Wise (IW) functions. We also find some support for the possibility that the $Λ_c(2595)^+$ and $Λ_c(2625)^+$ resonances might form a heavy-quark spin symmetry (HQSS) doublet. However, we argue that the available LQCD description of these two resonances is not accurate enough to disentangle the possible effects of the $Σ_c π$ and $Σ_c^*π$ thresholds, located only a few MeV above their position, and that it cannot be ruled out that these states are not HQSS partners. Finally, we study the ratio $\frac{dΓ[Λ_b\to Λ_{c,1/2^-}^* \ell \barν_\ell]/dq^2}{dΓ[Λ_b\to Λ_{c,3/2^-}^*\ell \barν_\ell]/dq^2}$ of the Standard Model differential semileptonic decay widths, with $q^μ$ the momentum transferred between the initial and final hadrons. We provide a natural explanation for the existence of large deviations, near the zero recoil, of this ratio from 1/2 (value predicted in the infinite heavy quark mass limit, assuming that the $Λ_{c,1/2^-}^*$ and $Λ_{c,3/2^-}^*$ are the two members of a HQSS doublet) based on S-wave contributions to the $Λ_b\to Λ_{c,1/2^-}^*$ decay amplitude driven by a sub-leading IW function.