# Tetraquark-adequate formulation of QCD sum rules

Lucha, Wolfgang (Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna, Austria) ; Melikhov, Dmitri (Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna, Austria) (D. V. Skobeltsyn Institute of Nuclear Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia) (Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria) ; Sazdjian, Hagop (Institut de Physique Nucléaire, CNRS-IN2P3, Université Paris-Sud, Université Paris-Saclay, 91406 Orsay, France)

10 July 2019

Abstract: We study details of QCD sum rules à la Shifman-Vainshtein-Zakharov for exotic tetraquark states. We point out that duality relations for correlators involving exotic currents have fundamental differences compared with the duality relations for the correlators of bilinear quark currents: namely, the $O\left(1\right)$ and $O\left({\alpha }_{s}\right)$ (${\alpha }_{s}$ the strong coupling constant) terms in the operator product expansion for the exotic correlators exactly cancel against the contributions of the two-meson states on the hadron side of QCD sum rules. As a result, the tetraquark properties turn out to be related to the specific nonfactorizable parts of the exotic Green functions; the relevant nonfactorizable diagrams start at order $O\left({\alpha }_{s}^{2}\right)$.

Published in: Physical Review D 100 (2019)