Notes

(1) We assume the values given above for the electromagnetic components.

(2) We assume universality for NWI, although this is not yet well-established from other data.

(3) If is a scalar, rather than pseudoscalar state, then this process measures , rather than , if invariance holds.

(4) It cannot be scalar/pseudoscalar, since such particles cannot decay to in the Weinberg-Salam model.

(5) A scalar Z would give no contribution to this decay.

(6) We take account of the vector mesons by a factor 0.17 in the matrix element deduced from . There is a slight ambiguity in the factor by which must be multiplied to render it dimensionless. We use the vector meson rather than the mass here.

(7) For example, in , [9].

(8) mesons cannot decay to in this model.

(9) We note that this should be the only use made of ; it cannot be in (1), for example, since decay is a final-state interaction, and our conclusions only hold in their absence.

(10) invariance forbids a contribution.

(11) Formally, this is because the assumption that a Lorentz transformation may be made to the Z rest frame, fails.

(12) Alternatively all the photons might come from a virtual quark loop with a or inside, but this again gives .

(13) It is difficult to estimate the PVM coupling required here; we have used for this purpose.

(14) The electromagnetic contribution is an effective scalar.

(15) We transform to the rest frame of the decaying particle, which has polarization , and decays to two photons . We satisfy gauge invariance by setting . Then Bose statistics demands that any possible amplitude constructed be zero (it must also be linear in in correspondence with the annihilation and creation operators).

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