Pseudoscalar and Vector $T_{QQ\bar q\bar q'}$ Spectra and Couplings from LSR at NLO

TL;DR

This paper uses QCD Laplace sum rules at NLO to estimate the masses and couplings of exotic tetraquark states with heavy quarks, revealing two classes of states with distinct properties and potential experimental signatures.

Contribution

It provides improved NLO estimates of $T_{QQ\bar q\bar q'}$ tetraquark masses and couplings, classifies states into heavy and light groups, and discusses their experimental accessibility and underlying dynamics.

Findings

Heavy class states have masses around 6 GeV (charm) and 13 GeV (bottom).

Light class states are below open charm/beauty thresholds with weaker couplings.

Mass splittings between radial excitations and ground states are about 2 GeV.

Abstract

We present systematic and improved estimates of the masses and couplings of the $(0^-)$ and $(1^-)$ $T_{QQ\bar q\bar q'}$ states ($Q= c,b;q,q'= u,d,s$) using QCD Laplace sum rules (LSR) and their ratios R within $\tau$ and $t_c$-stabilities criteria complemented by the (rigorous) condition: $R_{P/C} \equiv$ { Pole (Resonance) over the QCD continuum contributions} $ \geq 1$. 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 OPE is truncated at the under-controlled $d=6$ dimension condensates. Our results are compiled in Tables 4,7,10,12 and compared with some LO existing ones. We observe that the icurrents lead to two classes : Class H (Heavy) states with masses around 6 (resp. 13) GeV for charm (resp. bottom) channels. Class L (Light) states $T_{cc\bar q\bar q'}(3.8\sim 4.4)$ where the pseudoscalar (resp. all vector states) are below the open charm thresholds and $T_{bb\bar q\bar q'}(\simeq 10.4)$ 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 are about 2 GeV which are (almost) heavy flavour and current-type independent while their couplings are large signaling new dynamics of these exotic states. Quark masses behaviours of the masses and couplings based on empirical observation are discussed. The eventual findings of the $T_{cc\bar u\bar d}$(6.3) $0^-$ 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.