The scattering amplitude of stringy hadrons: strings with opposite charges on their endpoints

In this note we describe hadrons: mesons and baryons as strings with electric charges on their endpoints. We consider here only the neutral system with opposite charges, coupled to an external constant electromagnetic field. We derive certain classical solutions including rotating folded open strings. We write down the mode expansion and canonically quantize the system. The OPEs associated with such strings are determined. We rederive the non-commutativity of the zero modes and the fact that the charges modify the spacetime metric. We show that the quantum worldsheet energy momentum tensor on the boundary is affected by the endpoint charges and differs from the corresponding Noether current. We determine the generalization of the Veneziano scattering amplitude for such strings in the critical dimension. Phenomenological implications are addressed and in particular we show that the external magnetic field can be tuned so that the amplitude vanishes for particular kinematic setups. We discuss the generalization of such strings to non-critical four dimensional spacetime. In particular we renormalize the divergence of the Polchinski-Strominger effective action associated with the rotating folded string.