Relation between $T_{cc,bb}$ and $X_{c,b}$ from QCD

TL;DR

This paper uses QCD sum rules to compare the masses of $T_{cc,bb}$ and $X_{c,b}$, suggesting they are nearly degenerate and proposing the existence of similar molecular states, supported by analysis of SU(3) breaking and recent experimental data.

Contribution

It introduces a novel QCD sum rule approach to relate $T_{cc,bb}$ and $X_{c,b}$ masses, predicting new molecular states and analyzing SU(3) breaking effects.

Findings

$T_{cc}$ and $X(3872)$ are nearly degenerate in mass.

If $X(3872)$ is a $Dar{D}^*$ molecule, then $DD^*$ should also exist with similar mass.

Extension to $b$-quark states supports the same conclusion.

Abstract

We have studied, using double ratio of QCD (spectral) sum rules, the ratio between the masses of $T_{cc}$ and X(3872) assuming that they are respectively described by the $D-{D}^*$ and $D-\bar{D}^*$ molecular currents. We found (within our approximation) that the masses of these two states are almost degenerate. Since the pion exchange interaction between these mesons is exactly the same, we conclude that if the observed X(3872) meson is a $D\bar{D}^*+c.c.$ molecule, then the $DD^*$ molecule should also exist with approximately the same mass. An extension of the analysis to the $b$-quark case leads to the same conclusion. We also study the SU(3) breakings for the $T^s_{QQ}/T_{QQ}$ mass ratios. Motivated by the recent Belle observation of two $Z_b$ states, we revise our determination of $X_b$ by combining results from exponential and FESR sum rules.