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A fresh look at generalized Veneziano amplitudes
Institution:1. University of Durham, South Road, Durham, DHI 3LE, UK;2. University of Mons-Hainaut, 7000 Mons, Belgium;1. Department of Physics, Sophia University, Tokyo 102-8554, Japan;2. Department of Physics, the University of Tokyo 113-0033, Japan;3. Theoretical Research Division, Nishina Center, Riken, Wako 351-0198, Japan;1. Department of Physics, University of Jyväskylä, P.O. Box 35 (YFL), 40014 Jyväskylä, Finland;2. INFN, Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy;1. AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, 30-059 Kraków, Poland;2. RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA;3. Department of Physics, Western Michigan University, Kalamazoo, MI 49008, USA;1. Faculty of Physics, Baku State University, AZ-1148, Baku, Azerbaijan;2. Physics Department, Middle East Technical University, 06531 Ankara, Turkey
Abstract:The dual resonance model, which was a precursor of string theory was based upon the idea that two-particle scattering amplitudes should be expressible equivalently as a sum of contributions of an infinite number of s channel poles each corresponding to a finite number of particles with definite spin, or as a similar sum of t channel poles. The famous example of Veneziano Nuovo Cimento A 57 (1968) 190] satisfies all these requirements, and is additionally ghost free. We recall other trajectories which provide solutions to the duality constraints, e.g. the general Mobiüs trajectories and the logarithmic trajectories, which were thought to be lacking this last feature. We however demonstrate, partly empirically, the existence of a regime within a particular deformation of the Veneziano amplitude for logarithmic trajectories for which the 4-point amplitude remains ghost free.
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