Table of Contents
HSSUSY (high scale supersymmetry) is an implementation of the Standard Model, matched to the MSSM at the SUSY scale, MSUSY. The setup of HSSUSY is shown in the following figure.
In HSSUSY, the HighScale variable is set to the SUSY scale, MSUSY. At this scale the quartic Higgs coupling, λ(MSUSY), is predicted from the matching to the MSSM using the full 1-loop and dominant 2- and 3-loop threshold corrections of O((αt + αb)αs + (αt + αb)2 + αbατ + ατ2 + αtαs2) from [1407.4081], [1504.05200], [1703.08166], [1807.03509].
The 3- and partial 4- and 5-loop renormalization group equations of [1303.4364], [1307.3536], [1508.00912], [1508.02680], [1604.00853], [1606.08659] are used to run λ(MSUSY) down to the electroweak scale MZ or MEWSB.
If MSUSY is set to zero,
The LowScale is set to MZ. At this scale, the
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See the documentation of the SLHA input parameters for a description of the individual flags to enable/disable higher-order threshold corrections in FlexibleSUSY.
The Higgs and W boson pole masses, Mh and MW are calculated at the scale MEWSB, which is an input parameter. We recommend to set MEWSB = Mt.
Furthermore, the electroweak symmetry breaking condition is imposed at the scale MEWSB to fix the value of the bililear Higgs coupling μ2(MEWSB).
The Higgs and W boson pole masses, Mh and MW, are calculated at the full 1-loop level in the Standard Model, including potential flavour mixing and momentum dependence. Depending on the given configuration flags, additional 2-, 3- and 4-loop corrections to the Higgs pole mass of O(αtαs + αbαs) [1407.4336] O((αt + αb)2) [1205.6497] and O(ατ2), as well as 3-loop corrections O(αt3 + αt2αs + αtαs2) [1407.4336] and 4-loop corrections O(αtαs3) [1508.00912] can be taken into account.
HSSUSY takes the following physics parameters as input:
| Parameter | Description | SLHA block/field | Mathematica symbol |
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| MSUSY |
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| M1(MSUSY) |
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| M2(MSUSY) |
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| M3(MSUSY) |
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| μ(MSUSY) |
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| mA(MSUSY) |
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| MEWSB |
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| At(MSUSY) |
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| Ab(MSUSY) |
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| Aτ(MSUSY) |
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| tan β(MSUSY) |
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| (mq̃2)ij(MSUSY) |
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| (mũ2)ij(MSUSY) |
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| (md̃2)ij(MSUSY) |
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| (ml̃2)ij(MSUSY) |
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| (mẽ2)ij(MSUSY) |
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The MSSM parameters are defined in the
In addition, HSSUSY defines further input parameters / flags to enable/disable higher order threshold corrections to the quartic Higgs coupling λ(MSUSY) and to estimate the EFT and SUSY uncertainty:
| Parameter | Description | Possible values | Recommended value | SLHA block/field | Mathematica symbol |
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We recommend to run HSSUSY with the following configuration flags: In an SLHA input file we recommend to use:
Block FlexibleSUSY
0 1.0e-05 # precision goal
1 0 # max. iterations (0 = automatic)
2 0 # algorithm (0 = all, 1 = two_scale, 2 = semi_analytic)
3 1 # calculate SM pole masses
4 4 # pole mass loop order
5 4 # EWSB loop order
6 4 # beta-functions loop order
7 4 # threshold corrections loop order
8 1 # Higgs 2-loop corrections O(alpha_t alpha_s)
9 1 # Higgs 2-loop corrections O(alpha_b alpha_s)
10 1 # Higgs 2-loop corrections O((alpha_t + alpha_b)^2)
11 1 # Higgs 2-loop corrections O(alpha_tau^2)
12 0 # force output
13 3 # Top pole mass QCD corrections (0 = 1L, 1 = 2L, 2 = 3L)
14 1.0e-11 # beta-function zero threshold
15 0 # calculate all observables
16 0 # force positive majorana masses
17 0 # pole mass renormalization scale (0 = SUSY scale)
18 0 # pole mass renormalization scale in the EFT (0 = min(SUSY scale, Mt))
19 0 # EFT matching scale (0 = SUSY scale)
20 2 # EFT loop order for upwards matching
21 1 # EFT loop order for downwards matching
22 0 # EFT index of SM-like Higgs in the BSM model
23 1 # calculate BSM pole masses
24 124111421 # individual threshold correction loop orders
25 0 # ren. scheme for Higgs 3L corrections (0 = DR, 1 = MDR)
26 1 # Higgs 3-loop corrections O(alpha_t alpha_s^2)
27 1 # Higgs 3-loop corrections O(alpha_b alpha_s^2)
28 1 # Higgs 3-loop corrections O(alpha_t^2 alpha_s)
29 1 # Higgs 3-loop corrections O(alpha_t^3)
30 1 # Higgs 4-loop corrections O(alpha_t alpha_s^3)In the Mathematica interface we recommend to use:
handle = FSHSSUSYOpenHandle[
fsSettings -> {
precisionGoal -> 1.*^-5, (* FlexibleSUSY[0] *)
maxIterations -> 0, (* FlexibleSUSY[1] *)
solver -> 0, (* FlexibleSUSY[2] *)
calculateStandardModelMasses -> 1, (* FlexibleSUSY[3] *)
poleMassLoopOrder -> 4, (* FlexibleSUSY[4] *)
ewsbLoopOrder -> 4, (* FlexibleSUSY[5] *)
betaFunctionLoopOrder -> 4, (* FlexibleSUSY[6] *)
thresholdCorrectionsLoopOrder -> 4,(* FlexibleSUSY[7] *)
higgs2loopCorrectionAtAs -> 1, (* FlexibleSUSY[8] *)
higgs2loopCorrectionAbAs -> 1, (* FlexibleSUSY[9] *)
higgs2loopCorrectionAtAt -> 1, (* FlexibleSUSY[10] *)
higgs2loopCorrectionAtauAtau -> 1, (* FlexibleSUSY[11] *)
forceOutput -> 0, (* FlexibleSUSY[12] *)
topPoleQCDCorrections -> 3, (* FlexibleSUSY[13] *)
betaZeroThreshold -> 1.*^-11, (* FlexibleSUSY[14] *)
forcePositiveMasses -> 0, (* FlexibleSUSY[16] *)
poleMassScale -> 0, (* FlexibleSUSY[17] *)
eftPoleMassScale -> 0, (* FlexibleSUSY[18] *)
eftMatchingScale -> 0, (* FlexibleSUSY[19] *)
eftMatchingLoopOrderUp -> 2, (* FlexibleSUSY[20] *)
eftMatchingLoopOrderDown -> 1, (* FlexibleSUSY[21] *)
eftHiggsIndex -> 0, (* FlexibleSUSY[22] *)
calculateBSMMasses -> 1, (* FlexibleSUSY[23] *)
thresholdCorrections -> 124111421, (* FlexibleSUSY[24] *)
higgs3loopCorrectionRenScheme -> 0,(* FlexibleSUSY[25] *)
higgs3loopCorrectionAtAsAs -> 1, (* FlexibleSUSY[26] *)
higgs3loopCorrectionAbAsAs -> 1, (* FlexibleSUSY[27] *)
higgs3loopCorrectionAtAtAs -> 1, (* FlexibleSUSY[28] *)
higgs3loopCorrectionAtAtAt -> 1, (* FlexibleSUSY[29] *)
higgs4loopCorrectionAtAsAsAs -> 1, (* FlexibleSUSY[30] *)
parameterOutputScale -> 0 (* MODSEL[12] *)
},
...
];In the Section LibraryLink documentation an example Mathematica script can be found, which illustrates how to perform a parameter scan using the HSSUSY model.
In the file model_files/HSSUSY/HSSUSY_uncertainty_estimate.m FlexibleSUSY provides the Mathematica function CalcHSSUSYDMh[], which calculates the Higgs pole mass at the 3-loop level with HSSUSY and performs an uncertainty estimate of missing higher order corrections. Three main sources of the theory uncertainty are taken into account:
- SM uncertainty: Missing higher order corrections in the calculation of the running Standard Model top Yukawa coupling and in the calculation of the Higgs pole mass. The uncertainty from this source is estimated by (i) switching on/off the 3-loop QCD contributions in the calculation of the running top Yukawa coupling ytSM(MZ) from the top pole mass and by (ii) varying the renormalization scale at which the Higgs pole mass is calculated within the interval [MEWSB/2, 2MEWSB].
- EFT uncertainty: Missing terms of O(v2/MSUSY2). These missing terms are estimated by adding 1-loop terms of the form v2/MSUSY2 to the quartic Higgs coupling λ(MSUSY).
- SUSY uncertainty: Missing higher order corrections in the calculation of the quartic Higgs coupling λ(MSUSY). This uncertainty is estimated by (i) varying the matching scale within the interval [MSUSY/2, 2MSUSY] and by (ii) re-parametrization of λ(MSUSY) in terms of ytMSSM(MSUSY) and g3MSSM(MSUSY).
The following code snippet illustrates the calculation of the Higgs pole mass calculated at the 3-loop level with HSSUSY as a function of the SUSY scale (red solid line), together with the estimated uncertainty (grey band).
When this script is executed, the following figure is produced:
- 0707.0650
- 0810.5101
- 0901.2065
- 1009.5455
- 1205.6497
- 1303.4364
- 1307.3536
- 1407.4081
- 1407.4336
- 1504.05200
- 1508.00912
- 1508.02680
- 1604.00853
- 1604.01134
- 1606.08659
- 1703.08166
- 1807.03509
- hep-ph:0004189
- hep-ph:0105096
- hep-ph:0210258
- hep-ph:0308231
- hep-ph:0507139
- hep-ph:0509048
- hep-ph:0512060
- hep-ph:9305305
- hep-ph:9707474
- hep-ph:9708255
- hep-ph:9803493
- hep-ph:9911434
- hep-ph:9912391