Shedding light on the X(3930) and X(3960) states with the B^- K^- J/צ reaction

We have studied the contribution of the state X(3930), coming from the interaction of the D ($) over bar and D-s(+) D ($) over bar (s) channels, to the B- -> K- J/psi omega decay. The purpose of this work is to offer a complementary tool to see if the X(3930) state observed in the D+ D- channel is the same or not as the X(3960) resonance claimed by the LHCb Collaboration from a peak in the D-s(+) D s mass distribution around threshold. We present results for what we expect in the J/psi omega mass distribution in the B- -> K- J/psi omega decay and conclude that a clear signal should be seen around 3930 MeV. At the same time, finding no extra resonance signal at 3960 MeV would be a clear indication that there is not a new state at 3960 MeV, supporting the hypothesis that the near-threshold peaking structure peak in the D-s(+) D-s(-) mass distribution is only a manifestation of a resonance below threshold.