Heavy-light diquark masses from QCD sum rules and constituent diquark models of tetraquarks

Abstract

Diquarks with ${J}^{P}={0}^{\ifmmode\pm\else\textpm\fi{}}$, ${1}^{\ifmmode\pm\else\textpm\fi{}}$ containing a heavy (charm or bottom) quark and a light quark are investigated using QCD Laplace sum rules. Masses are determined using appropriately constructed gauge invariant correlation functions, including for the first time next-to-leading order perturbative contributions. The ${J}^{P}={0}^{+}$ and ${1}^{+}$ charm-light diquark masses are, respectively, found to be $1.86\ifmmode\pm\else\textpm\fi{}0.05$ and $1.87\ifmmode\pm\else\textpm\fi{}0.10\text{ }\text{ }\mathrm{GeV}$, while those of the ${0}^{+}$ and ${1}^{+}$ bottom-light diquarks are both determined to be $5.08\ifmmode\pm\else\textpm\fi{}0.04\text{ }\text{ }\mathrm{GeV}$. The sum rules derived for heavy-light diquarks with negative parity are poorly behaved and do not permit unambiguous mass predictions, in agreement with previous results for negative parity light diquarks. The scalar and axial vector heavy-light diquark masses are degenerate within uncertainty, as expected by heavy quark symmetry considerations. Furthermore, these mass predictions are in good agreement with masses extracted in constituent diquark models of the tetraquark candidates $X(3872)$ and ${Y}_{b}(10890)$. Thus these results provide QCD support for the interpretation of the $X(3872)$ and ${Y}_{b}(10890)$ as ${J}^{\mathrm{PC}}={1}^{++}$ tetraquark states composed of diquark clusters. Further implications for tetraquarks among the heavy quarkoniumlike XYZ states are discussed.