Tests of the -like Laplace sum rule results using finite energy sum rule at NLO
R. M. Albuquerque (Faculty of Technology, Rio de Janeiro State University (FAT, UERJ), 27537-000 Resende, Brazil); S. Narison (Laboratoire Univers et Particules de Montpellier (LUPM), CNRS-IN2P3 and University of Montpellier Case 070, Place Eugène Bataillon, Montpellier 34095, France and Institute of High-Energy Physics of Madagascar (iHEPMAD), University of Ankatso, Antananarivo 101, Madagascar); D. Rabetiarivony (Institute of High-Energy Physics of Madagascar (iHEPMAD), University of Ankatso, Antananarivo 101, Madagascar)
In this note, we use local duality finite energy sum rule to test the validity of the Laplace sum rules results truncated at the dimension-six condensates for the estimates of the masses and couplings of the -like ground states in Albuquerque et al. [Phys. Rev. D 103, 074015 (2021)] by taking the example of the molecule configuration. We confirm the existence of an eventual radial excitation with a mass around 5700 MeV and coupling of 197(25) keV to the current which may mask the eventual radial excitation candidate [named in Albuquerque et al.] having a relatively small coupling . We add more explanations on the estimates in Albuquerque et al. from Laplace sum rules and comment on the results in Wang [arXiv:2202.06058; Commun. Theor. Phys. 63, 325 (2015)].