Abstract
We discuss different choices that can be made when matching a general high-energy theory – with the restriction that it should not contain heavy gauge bosons – onto a general renormalisable effective field theory at one loop, with particular attention to the quartic scalar couplings and Yukawa couplings. This includes a generalisation of the counterterm scheme that was found to be useful in the case of high-scale/split supersymmetry, but we show the important differences when there are new heavy scalar fields in singlet or triplet representations of SU(2). We also analytically compare our methods and choices with the approach of matching pole masses, proving the equivalence with one of our choices. We outline how to make the extraction of quartic couplings using pole masses more efficient, an approach that we hope will generalise beyond one loop. We give examples of the impact of different scheme choices in a toy model; we also discuss the MSSM and give the threshold corrections to the Higgs quartic coupling in Dirac gaugino models.
Highlights
In the absence of clear collider signals of new particles, there has been much recent interest in constraining deviations from the Standard Model (SM) in terms of effective operators
It is the only approach to constraining the Higgs mass in split supersymmetry [12,13,14] where new physics could be around 100–105 TeV [15,16]; high-scale supersymmetry [15,17,18,19,20] where it could be around 107–109 TeV; the FSSM [21,22] where it could be as high as the GUT/Planck scale, etc
The presence of trilinear couplings with two light Higgs scalars leads to infra-red divergences in the amplitudes which cancel in the threshold corrections: we explicitly show how these cancel and how they can be dealt with
Summary
In the absence of clear collider signals of new particles, there has been much recent interest in constraining deviations from the Standard Model (SM) in terms of effective operators. Given that there are different possible choices for parameter definitions when we perform a “conventional” matching calculation, it is not immediately obvious how to compare the definitions in the two approaches (i.e. to know what we obtain from the pole-matching calculation!) This has been seen in the case of high scale/split SUSY in [20,27,60], where the pole mass calculation gives a result equivalent to the “counterterm” approach to the angle β, which we define in Sect. The appendices contain our notation, the general results for threshold corrections, and specific results for Dirac gaugino models
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