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

TL;DR

This paper investigates whether the $\\Lambda_c(2625)^+$ and $\\\Lambda_c(2595)^+$ are heavy quark spin symmetry partners, using effective theory and lattice QCD, and analyzes decay width ratios to understand their possible HQSS doublet nature.

Contribution

It applies an $\\mathcal{O}(\\Lambda_{QCD}/m_c)$ heavy quark effective theory to analyze form factors and explores the potential HQSS doublet relationship between the two resonances.

Findings

The scheme describes lattice QCD form factors reasonably well within uncertainties.

There is some support for the two resonances forming an HQSS doublet.

Large deviations in decay width ratios are explained by S-wave contributions and sub-leading IW functions.

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 $\Sigma_c^*\pi$ 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 $\frac{d\Gamma[\Lambda_b\to \Lambda_{c,1/2^-}^* \ell \bar\nu_\ell]/dq^2}{d\Gamma[\Lambda_b\to \Lambda_{c,3/2^-}^*\ell \bar\nu_\ell]/dq^2}$ 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 $\Lambda_{c,1/2^-}^*$ and $\Lambda_{c,3/2^-}^*$ are the two members of a HQSS doublet) based on S-wave contributions to the $\Lambda_b\to \Lambda_{c,1/2^-}^*$ decay amplitude driven by a sub-leading IW function.