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Next: 1.1 Elastic Form Factors Up: Chapter 9 Section 1 Previous: Chapter 9 Section 1

1 Elastic and transition form factors

Low-energy -machines are the ideal tool to investigate the time-like region of the electromagnetic form factors (F.F.) of low-mass hadrons, i.e., of the lowest spin mesonic and baryonic states constructed only with u-, d- and s-quarks. The initial pair converts into an exclusive final state containing two particles (A and , with four-momenta p and ) through the exchange of a virtual single-photon of squared four-momentum as shown in Fig.(1). The amplitude associated to this process is

 

where the first factors contain the QED point-like vertex and the photon propagator, whereas the final one, written in terms of the hadronic electromagnetic (e.m.) current and represented by the blob in Fig.(1), incorporates the effects of strong interactions and hadronic structure in one or a few form factors, .

From the well-known conservation rules in both strong and e.m. interactions, and the fact that we are exclusively considering processes mediated by a single photon, the two-particle final state is forced to have the photonic quantum numbers too, i.e., J = 1, P = C = -1 and isospin I = 1 or 0. These quantum numbers can be achieved either with A = B or with , thus allowing to distinguish between ``elastic (or static)" form factors and ``transition (or dynamical)" ones, as we now proceed to discuss.





Carlos E.Piedrafita