Abstract
We show how the infra-red divergences associated to Goldstone bosons in the minimum condition of the two-loop Landau-gauge effective potential can be avoided in general field theories. This extends the resummation formalism recently developed for the Standard Model and the MSSM, and we give compact, infra-red finite expressions in closed form for the tadpole equations. We also show that the results at this loop order are equivalent to (and are most easily obtained by) imposing an "on-shell" condition for the Goldstone bosons. Moreover, we extend the approach to show how the infra-red divergences in the calculation of the masses of neutral scalars (such as the Higgs boson) can be eliminated. For the mass computation, we specialise to the gaugeless limit and extend the effective potential computation to allow the masses to be determined without needing to solve differential equations for the loop functions -- opening the door to fast, infra-red safe determinations of the Higgs mass in general theories.
Highlights
The discovery of the Higgs boson has added a wealth of electroweak precision observables, chief among them being its mass, which is remarkably known to within a few hundred MeV
We have shown how to avoid the Goldstone Boson Catastrophe in general renormalisable field theories, and how this can be applied to calculating neutral scalar masses in the gaugeless limit in a generalised effective potential approximation
We have presented a solution to the Goldstone Boson Catastrophe in general renormalisable theories to two-loop order
Summary
The discovery of the Higgs boson has added a wealth of electroweak precision observables, chief among them being its mass, which is remarkably known to within a few hundred MeV. In appendix B we give a complete set of analytic expressions for expansions of the necessary functions including all divergent and constant terms in an expansion of the four-momentum-squared s around zero (neglecting those of O(s)) This allows fast evaluation of a generalised effective potential approximation for the neutral scalar masses — for this part we shall be restricted to the gaugeless limit (setting the couplings of all broken gauge groups to zero) since the mass diagrams are known only up to second order in the gauge couplings. We have endeavoured to keep the paper as self-contained as possible, and for that purpose we provide in appendix A a set of all of the loop functions used throughout
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