How does the mass ratio M_W/M_Z evolve with energy?

[heinz]

The masses of the elementary particles are renormalized somewhat, when the energy (the momentum) increases. Assuming that the standard model of particle physics is correct to all energies, is there any data on how the ratio M_W/M_Z between the two vector boson masses changes with energy? Does it increase or does it decrease? Or does the question make no sense at all?

Heinz

 

[Avodyne]

First of all, which (if any) parameters run depends on the choice of renormalization scheme. For processes involving direct observation of W and/or Z bosons, it's common to use an "on shell" scheme in which the particle masses do not run; see http://arxiv.org/abs/0709.1075 for a review. For processes at energies well above the W and Z masses, it's easier to use modified minimal subtraction, and define the W/Z mass ratio via [itex]M_W/M_Z \equiv g_2/(g_2^2+g_1^2)^{1/2}[/itex]. Then, since [itex]g_2[/itex] decreases with energy while [itex]g_1[/itex] increases, we see that [itex]M_W/M_Z[/itex] decreases with energy.

 

[heinz]

First of all, which (if any) parameters run depends on the choice of renormalization scheme. For processes involving direct observation of W and/or Z bosons, it's common to use an "on shell" scheme in which the particle masses do not run; see http://arxiv.org/abs/0709.1075 for a review. For processes at energies well above the W and Z masses, it's easier to use modified minimal subtraction, and define the W/Z mass ratio via [itex]M_W/M_Z \equiv g_2/(g_2^2+g_1^2)^{1/2}[/itex]. Then, since [itex]g_2[/itex] decreases with energy while [itex]g_1[/itex] increases, we see that [itex]M_W/M_Z[/itex] decreases with energy.

Thank you for the clarification, which helps me a lot. Is there a number estimate possible, say for 10^19 GeV, about how much the ratio decreases compared to low energy?

Heinz

 

[Avodyne]

Look up reviews on grand unification; these often contains plots of the running couplings at high energies. Of course, one needs to assume the particle content above the electroweak scale (eg, just the Standard Model, or additional supersymmetric particles, or ...)