Pole mass determination in presence of heavy particles

Abstract

We investigate the determination of the Higgs-boson propagator poles in the MSSM. Based upon earlier works, we point out that in case of a large hierarchy between the electroweak scale and one or more SUSY masses a numerical determination with DR Higgs field renormalization induces higher order terms which would cancel in a more complete calculation. The origin of these terms is the momentum dependence of contributions involving at least one of the heavy particles. We present two different methods to avoid their appearance. In the first approach, the poles are determined by expanding around the one-loop solutions. In the second approach, a "heavy-OS" Higgs field renormalization is employed in order to absorb the momentum dependence of heavy contributions. We will find that the first approach leads to an unwanted behavior of the Higgs boson mass predictions close to crossing points where two Higgs bosons that mix with each other are almost mass degenerate. These problems are avoided in the second approach, which became the default approach used in the public code FeynHiggs. Despite the discussion being very specific to the MSSM, the argumentation and the methods presented in this work are straightforwardly applicable to the determination of propagator poles in other models involving a large mass hierarchy. *

Theoretical uncertainties in the MSSM Higgs boson mass calculation

“…Therefore at low SUSY scales, the EFT approach is less precise than the fixed-order approach, which includes all suppressed terms up to the order of the calculation. In order to obtain a precise prediction also for intermediary scales, where both a resummation of large logarithms as well as suppressed terms might be relevant, hybrid approaches combining fixed-order and EFT calculations have been developed [20,26,[30][31][32][33][34][35][36].…”

Precise prediction for the Higgs-Boson masses in the $${\varvec{\mu }}{\varvec{\nu }}$$SSM with three right-handed neutrino superfields

“…These corrections, together with a resummation of leading and subleading logarithms from the top/stop sector [48] (see also [49,50] for more details on this type of approach), a resummation of leading contributions from the bottom/sbottom sector [46,47,[51][52][53][54] (see also [55,56]) and momentum-dependent two-loop contributions [57,58] (see also [59]) are included in the public code FeynHiggs [40,48,[60][61][62][63][64][65][66][67]. The most recent version of FeynHiggs contains an improved effective field theory calculation relevant for large SUSY scales [64,66,68]. The complete two-loop QCD contributions in the CP-violating MSSM were calculated in Ref.…”

Full two-loop QCD corrections to the Higgs mass in the MSSM with heavy superpartners

“…The EFT approach to the computation of the MSSM Higgs mass dates back to the early 1990s [53][54][55], and it has also been exploited in the past [56][57][58][59][60][61][62] to determine analytically the coefficients of the logarithmic terms in the Higgs-mass corrections, by solving perturbatively the appropriate systems of boundary conditions and RGEs. In recent years, after the LHC results pushed the expectations for the SUSY scale into the TeV range, the realization that an accurate prediction for the Higgs mass in the MSSM cannot prescind from the resummation of the large logarithmic corrections brought the EFT computation under renewed focus [63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78]. In the simplest scenario in which all of the SUSY particles as well as the heavy Higgs doublet of the MSSM are clustered around a single scale M S , so that the EFT valid below that scale is just the SM, the state of the art now includes: full one-loop and partial two-loop matching conditions for the quartic Higgs coupling at the SUSY scale, computed for arbitrary values of the relevant SUSY parameters [65,72]; full three-loop RGEs for all of the parameters of the SM Lagrangian [79][80][81][82][83][84]; full two-loop relations at the EW scale between the running SM parameters and a set of physical observables which include the pole Higgs mass [85][86][87].…”

“…In the EFT calculation, those terms can be mapped to the effect of non-renormalizable, higher-dimensional operators, and they are neglected when the theory valid below the matching scale is taken to be the plain SM in the unbroken phase of the EW symmetry. To avoid double counting, the hybrid approaches require a careful subtraction of the terms that are accounted for by both the diagrammatic and the EFT calculations, and indeed a few successive adjustments [73,74,78] were necessary to obtain predictions for m h that, in the limit of very heavy SUSY masses in which the O(v 2 /M 2 S ) terms are certainly negligible, show the expected agreement with the pure EFT calculation. The comparison between the predictions of the hybrid and pure EFT calculations, as well as a direct study [72] of the effects of non-renormalizable operators in the EFT, also show that the O(v 2 /M 2 S ) corrections are significantly suppressed for the values of M S that are 2 A partial N 3 LL resummation of the corrections involving only the highest powers of the strong gauge coupling is also available, combining the three-loop matching condition of ref.…”