Pseudoscalar and vector [formula omitted] spectra and couplings from LSR at NLO

Abstract

We present systematic and improved estimates of the masses and couplings of the Pseudoscalar (0−) and Vector (1−)TQQq¯q¯′ states (Q≡c,b;q,q′≡u,d,s) using (inverse) QCD Laplace sum rules (LSR) and their ratios R within τ and tc-stabilities criteria complemented by the (rigorous) condition: RP/C≡ Pole (Resonance) over the QCD continuum contributions ≥1. Next-to-leading order (NLO) factorized perturbative (PT) QCD corrections are included for giving a meaning on the choice of the used running MS‾ heavy quark mass, while the operator product expansion (OPE) is truncated at the under-controlled d=6 dimension condensates. Our results are compiled in Tables and compared with some LO existing ones. We observe that the interpolating currents lead to two classes: Class H (Heavy) states with masses around 6 (resp. 13) GeV for charm (resp. bottom) channels. Class L (Light) states Tccq¯q¯′(3.8∼4.4) where the pseudoscalar (resp. all vector states) are below the open charm thresholds and Tbbq¯q¯′(≃10.4) where all of them are below the open beauty thresholds. Mass-splittings due to SU3 breakings are tiny (≤ 50 MeV). Though more accessible experimentally, Class L states have weaker couplings to the currents than the Class H ones and may be difficult to observe. The mass-splittings between the 1st radial excitation and the ground state of TQQq¯d¯ (q≡,u,d) are about 2 GeV which are (almost) heavy flavor and current-type independent while their couplings are large signaling new dynamics of these exotic states. Quark masses behaviors of the masses and couplings based on empirical observation are discussed. The eventual findings of the Tccu¯d¯(6.3) pseudoscalar ground state which may not be obscured by the Class L 1st radial excitations can be an alternative way to test the vacuum saturation violation of the four-quark d=6 condensates.