1-- and 0++ Four-Quarks and Molecules from QCD Spectral Sum Rules

TL;DR

This paper estimates the masses of 1-- and 0++ heavy four-quark and molecule states using QCD spectral sum rules, providing predictions that relate to experimental candidates and exploring their possible mixing.

Contribution

It introduces a combined sum rule approach to predict heavy four-quark and molecule state masses, including SU(3) breaking effects and decay constants, extending previous analyses.

Findings

Mass splittings are almost heavy-flavour independent.

Predicted masses for 1-- states align with some experimental candidates.

0++ states are 0.5-1.0 GeV heavier than 1-- states.

Abstract

We estimate the masses of the 1-- heavy four-quark and molecule states by combining exponential Laplace (LSR) and finite energy (FESR) sum rules known perturbatively to lowest order (LO) in \alpha_s but including non perturbative terms up to the complete dimension-six condensate contributions. We use double ratio of sum rules (DRSR) for determining the SU(3) breakings terms. The SU(3) mass-splittings of about (50 - 110) MeV and the ones of about (250 - 300) MeV between the lowest ground states and their 1st radial excitations are (almost) heavy-flavour independent. The mass predictions summarized in Table 2 are compared with the ones in the literature (when available) and with the three Yc(4260, 4360, 4660) and Yb(10890) 1-- experimental candidates. We conclude that the lowest observed state cannot be a pure 1-- four-quark nor a pure molecule but may result from their mixings. We extend the above analyzes to the 0++ four-quark and molecule states which are about (0.5-1.0) GeV heavier than the corresponding 1-- states, while the splittings between the 0++ lowest ground state and the 1st radial excitation is about (300-500) MeV. We complete the analysis by estimating the decay constants of the 1-- and 0++ four-quark states. Our predictions can be tested using some alternative non-perturbative approaches or/and at LHCb or some other hadron factories.