Is the ${\Lambda }_c(2625{)}^{+}$ the heavy quark spin symmetry partner of the ${\Lambda }_c(2595{)}^{+}$?

Abstract

We use a $\mathcal{O}({\Lambda }_{\text{QCD}}/m_c)$ heavy quark effective theory scheme, where only $\mathcal{O}({\Lambda }_{\text{QCD}}/m_b)$ 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 ${\Lambda }_b$ ground state and the odd parity charm ${\Lambda }_c(2595{)}^{+}$ and ${\Lambda }_c(2625{)}^{+}$ 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 ${\Lambda }_c(2595{)}^{+}$ and ${\Lambda }_c(2625{)}^{+}$ 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 ${\Sigma }_c\pi$ and ${\Sigma }_c^{\ast }\pi$ 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 $\frac{d\Gamma [{\Lambda }_b\to {\Lambda }_{c,1/2^{-}}^{\ast }\ell {\bar{\nu }}_{\ell }]/d{q}^2}{d\Gamma [{\Lambda }_b\to {\Lambda }_{c,3/2^{-}}^{\ast }\ell {\bar{\nu }}_{\ell }]/d{q}^2}$ of the Standard Model differential semileptonic decay widths, with $q^{\mu }$ 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 ${\Lambda }_{c,1/2^{-}}^{\ast }$ and ${\Lambda }_{c,3/2^{-}}^{\ast }$ are the two members of a HQSS doublet) based on S-wave contributions to the ${\Lambda }_b\to {\Lambda }_{c,1/2^{-}}^{\ast }$ decay amplitude driven by a sub-leading IW function.

arXiv comment26 pages, 8 figures

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