Contradiction of the Electroweak W±, Z Bosons Home Contact Me

Consider the quite simple case of an elastic neutrino-electron scattering (see fig. 3 on p. 4 here ). This figure shows the electroweak explanation of the following scattering event: an electron and a neutrino collide and exchange energy-momentum, and a W± bosons or a Z boson mediate the process. Let us calculate the 4-momentum transfer qμ of the process in the center of energy frame. This quantity is the difference between the 4-momentum of the incoming electron and that of the outgoing electron qμ = (E,p,0,0,) - (E,px,py,pz) = (0,p - px,-py,-pz). (1) (Note that an elastic collision conserves particle's energy in the center of energy frame.) The right-hand side of eq. (1) is a space-like 4-vector. By contrast, the W± boson and the Z are massive particles (see here ) whose 4-momentum is time-like. Conclusion: The electroweak theory violates relativistic covariance. Remarks: Standard Model supporters are aware of the above-mentioned contradiction. Thus, they call particles like W±, Z virtual particles and state that "a virtual particle does not carry the same mass as the corresponding free particle. In fact, a virtual particle can have any mass. In the business, we say that virtual particles do not lie on their mass shell" (see [1], p. 65). The following points are relevant to an evaluation of the virtue of this argument. Evidently, there is no doubt that the theory would have a better structure if relativistic properties of interaction mediating particles, like the W±, Z bosons would have a relativistically consistent energy-momentum 4-vector. In the present case one wonders whether the argument has a physically solid basis or it is just an excuse. The situation would have been much better if the problem presented above is the only contradiction of the electoweak theory. It turns out that this is not the case. As a matter of fact, the electroweak theory is plagued with many inherent contradictions (see section 2 here ). Obviously, there is no justification for adding a doubtful excuse in order to justify a theory that suffers many other contradictions. It turns out that a different argument proves another kind of noncovariant property of the electroweak theory (see here ). Evidently, this argument provides a very strong support for the above-mentioned conclusion. References: [1] D. Griffiths, Introduction to Elementary Particles, 2nd edition (Wiley-VCH, Weinheim, 2008).