Electroweak Synchrotron Radiation*

We calculate the emission rate and spectrum for radiation of neutral electroweak bosons (Z”) f rom an electron in a weak external homogeneous electromagnetic field satisfying 1 f Fcly Fp”/1/2 < Fc 3 mzc3/eti. The calculational method is based on the source theory formulation of quantum field theory introduced by Schwinger. In particular for ultra-relativistic electrons, we find that the 2’ emission rate is exponentially suppressed relative to photon emission for values of the radiation parameter T = III, Fp” II’ Fx,11/2/mecFc << (Mz/m,)2 lOlo, where II, is the electron mechanical momentum. This implies that the decay rate for e+ W+ ve is also exponentially small under similar conditions. An application of these results to accelerator physics is discussed. Submitted to Physical Review Letters * Work supported by the Department of Energy, contract DE AC03 76SF00515. The quantum mechanical problem of calculating the synchrotron radiation of photons from relativistic electrons in a homogeneous external magnetic field has been addressed by various authors. ‘-’ Sokolov et al.’ utilized the Dirac wave functions of an electron in a constant magnetic field to calculate synchrotron radiation. The transition amplitude for e-+ e+r was computed by perturbation theory (i.e. to first order in the fine structure constant cr.) and the power spectrum obtained by squaring the amplitude and summing over final states. Recently Tsai and Yildiz’ have presented a more efficient method for calculating radiation in external fields based on Schwinger’s source theory formulation of quantum field theory.4 This latter approach, which we use in this paper, eliminates the need for using wave functions by replacing the sum over final states by expectation values obtained directly from the Dirac equation. The previous results for radiation in external magnetic fields are of course applicable in all Lorentz frames where H2 E2 = i F,, Fp” > 0 and E . B = $ FPy FpV = 0.’ The corresponding problem of radiation in a homogeneous electric field has received far less attention, possibly because of the well-known difficulty of the “Klein catastrophe,” that is, spontaneous pair creation by an electric field.6 In the weak field limit If F,, Fp”j1j2 < Fc = mz/e (sz 4.4 x 1013 G = 1.3 x 101’j V/cm) that we consider, pair creation effects are negligible,’ and we may treat fields with both positive and negative values of H2 E2 and ,!?s B = 0 in the same manner. In the standard unified electroweak theory,’ the electron couples to the massive neutral weak boson, Z”, as well as the photon. In this paper, the concept of synchrotron radiation is generalized to include the decay e+ e+ 2’ in an external electromagnetic field using the source theory method of Tsai and