The problem of exotic states: view from complex angular momenta

Having in mind present uncertainty of the experimental situation in respect to exotic hadrons, it is important to discuss any possible theoretical arguments, pro and contra. Up to now, there are no theoretical ideas which could forbid existence of the exotic states. Theoretical proofs for their existence are also absent. However, there are some indirect arguments for the latter case. It will be shown here, by using the complex angular momenta approach, that the standard assumptions of analyticity and unitarity for hadronic amplitudes lead to a non-trivial conclusion: the S-matrix has infinitely many poles in the energy plane (accounting for all its Riemann sheets). This is true for any arbitrary quantum numbers of the poles, exotic or non-exotic. Whether some of the poles may provide physical (stable or resonance) states, should be determined by some more detailed dynamics.Comment: 6 pages, Latex; based on talks at HSQCD2005 (St.Petersburg, Russia, September 20 - 24, 2005), NSTAR2005 (Tallahassee, FA, USA, October 12 - 15. 2005), Scientific session of the Nuclear Physics Section of RAS (Moscow, Russia, December 5 - 9, 2005

Complex Angular Momenta and the Problem of Exotic States

After some brief personal recollections about V.N.Gribov, I demonstrate that his results and ideas on complex angular momenta may be applied in unfamiliar directions. As an example, it is shown, that any strong interaction amplitude, satisfying dispersion relation (in momentum transfer), has infinite number of energy-plane poles, both for exotic and non-exotic quantum numbers. This result ensures the necessary condition for existence of exotic hadrons. However, without more detailed knowledge of dynamics one cannot secure sufficient conditions for the exotics existence.Comment: To appear in the Gribov Memorial Volume (Proceedings of the Gribov-75 Memorial Workshop on Quarks, Hadrons, and Strong Interactions, May 22-24, 2005, Budapest, Hungar