Precise estimates of the Higgs mass in heavy supersymmetry

Abstract

In supersymmetric models, very heavy stop squarks introduce large logarithms into the computation of the Higgs boson mass. Although it has long been known that in simple cases these logs can be resummed using effective field theory techniques, it is technically easier to use fixedorder formulas, and many public codes implement the latter. We calculate three-and four-loop next-to-next-to-leading-log corrections to the Higgs mass and compare the fixed order formulas numerically to the resummation results in order to estimate the range of supersymmetry scales where the fixed-order results are reliable. We find that the four-loop result may be accurate up to a few tens of TeV. We confirm an accidental cancellation between different three-loop terms, first observed in [19], and show that it persists to higher scales and becomes more effective with the inclusion of higher radiative corrections. Existing partial three-loop calculations that include only one of the two cancelling terms may overestimate the Higgs mass. We give analytic expressions for the three-and four-loop corrections in terms of Standard Model parameters and provide a complete dictionary for translating parameters between the SM and the MSSM and the MS and DR renormalization schemes.2

Higgs mass determination in supersymmetry

“…Our computation follows very closely the ones in [7,8,10,[23][24][25][26], providing independent checks of such computations. We improved them in various ways.…”

“…The effort in the Higgs mass calculation has been remarkable, reaching the two-loop and in some cases the three-loop level, with different techniques and schemes, see e.g. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Some of the computations, however, are only valid for small SUSY breaking scales, where log-corrections do not need resummations; in fact currently available computer codes have a very limited range of applicability compared to the allowed parameter space.…”

“…The latter coefficients take into account the tan β enhanced corrections discussed in section 3.3 which require resummation, the explicit expressions can be found e.g. in [25,27]. The loop functions F n are defined in appendix A of [26].…”

“…We start summarizing our conventions. For the numerical part we used the values m t = 173.34 GeV [31], α s (m Z ) = 0.1185 [89], y b (m t ) = 0.0156 and y τ (m t ) = 0.0100 [25]. The MSSM Lagrangian is written with all the parameters in the DR scheme (or the "OS" scheme described below), and is matched with the SM Lagrangian with all couplings and masses in the MS scheme.…”

Higgs bosons in heavy supersymmetry with an intermediatemA

“…In a previous work [26], we used EFT calculations to compute the mass of the lightest CP-even Higgs boson in the MSSM, in the case of heavy stops and non-standard Higgs bosons. A similar approach was also taken recently in Refs.…”