Abstract
We consider the application of a Fleischer–Jegerlehner-like treatment of tadpoles to the calculation of neutral scalar masses (including the Higgs) in general theories beyond the Standard Model. This is especially useful when the theory contains new scalars associated with a small expectation value, but comes with its own disadvantages. We show that these can be overcome by combining with effective field theory matching. We provide the formalism in this modified approach for matching the quartic coupling of the Higgs via pole masses at one loop, and apply it to both a toy model and to the mu NMSSM as prototypes where the standard treatment can break down.
Highlights
The mass of the SM-like Higgs boson, discovered by ATLAS and CMS [1,2,3], is an electroweak precision observable, thanks to its outstandingly accurate determination at the LHC [4,5,6], and it plays an important role in constraining the allowed parameter space of Beyond-the-StandardModel (BSM) theories
What we want to illustrate is the difficulty in even defining our theory: in the standard approach, since we are required to choose a vacuum-expectation value for the heavy singlet fields, the phenomenologist will often use a guess or a tree-levelapproximate solution for this, rather than iteratively solve the tadpole equations
The best way to do this is to expand the expressions on both sides of the matching relation in terms of the same parameters; the most efficient way to do this is to use those of the high-energy theory (HET) even though this adds a layer of complication because it is the SM parameters that we know from the bottom-up observations
Summary
The mass of the SM-like Higgs boson, discovered by ATLAS and CMS [1,2,3], is an electroweak precision observable, thanks to its outstandingly accurate determination at the LHC [4,5,6], and it plays an important role in constraining the allowed parameter space of Beyond-the-StandardModel (BSM) theories. The relevant observables for the electroweak sector are typically, as in calculations in the SM, either MZ , MW , α(0) or MZ , G F , α(0) where MZ,W are the Z and W boson masses, α(0) is the fine-structure constant extracted in the Thompson limit, and G F is the Fermi constant This latter quantity is extracted from muon three-body decays, whereas the others are related essentially to self-energies. When considering a BSM theory with additional scalars that may have an expectation value, it is typical to take the same approach as for the scalar field in the SM and fix their expectation values, solving the additional tadpole equations for other dimensionful parameters – for example, their mass-squared parameters, or sometimes a cubic scalar coupling. The archetypal example of this problem is the case where the neutral scalar obtaining an expectation value comes from an SU (2) triplet T with expectation value vT and mass-squared m
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