$ \bar D^*D$ and $\bar B^*B~(1^{++})$ molecules at N2LO from QSSR

Abstract

We use QCD spectral sum rules (QSSR) and the factorization properties of molecule currents to estimate the masses and couplings of the $\bar D^*D$ and $\bar B^*B~(1^{++})$ molecules at N2LO of PT QCD. We include in the OPE the contributions of non-perturbative condensates up to dimension-eight. With the Laplace sum rules approach (LSR) and in the $\overline{MS}$-scheme, we obtain $M_{D^*D}=3738(152)$ MeV, which agrees within the errors with the newly discovered $Z_c$(3900). For the bottom channel, we find $M_{B^*B}=10687(232)$ MeV in good agreement with the observed $Z_b$(10610). Couplings of these states to the currents are also extracted. Our results are improvements of the LO ones in the existing literature.