SPECTRAL FUNCTION OF PHOTON PROPAGATOR - MASS SPECTRUM AND TIMELIKE FORM FACTORS OF PARTICLES

We consider contributions to the spectral function of the photon propagator from the states which contain a particle (charge e and mass mJ) of arbitrary spin J, and its antiparticle. We express the contributions in terms of timelike form factors FJ(a) (where a=-P2>0, and P is the momentum of the photon) with the normalization FJ(0)=(2J+1)e2. The unitarity limit of the spectral function can be transformed into the asymptotically bounded condition FJ(a)O(a). The experimental information about the anomalous magnetic moment of the muon gives a restriction on the sum of all the contributions. Using the restriction, we examine various mass spectra of charged particles and obtain simple results. For example: If there is an infinitely rising mass spectrum mJ=f(J), then the asymptotic form of the mass formula must be bounded by condition mJ>O(J) (case I or II) or mJ>O(J1(2l+1)) (case III), where l is a parameter in the form factors, assumed to be FJ(a)=(2J+1)e2(a4mJ2-1)|1-aμ2|-2l for J=0,1,2, and FJ(a)=(2J+1)e2|1-aμ2|-2l for J=12,32, For the purpose of experimental observations of the timelike form factors and the spectral function of the photon, the colliding-beam experiments e++e-μ++μ-)→λ+λ̄ (where λ is a particle of arbitrary spin) are discussed in some detail. © 1969 The American Physical Society.