NUHMSSMNoFVHimalaya

Table of Contents

NUHMSSMNoFVHimalaya
Building the NUHMSSMNoFVHimalaya
Input parameters
Running the NUHMSSMNoFVHimalaya
Uncertainty estimate of the predicted Higgs pole mass
References

NUHMSSMNoFVHimalaya

NUHMSSMNoFVHimalaya (non-universal Higgs MSSM without flavour violation + Himalaya) is an implementation of the MSSM without flavour violation. The Himalaya library [1708.05720] is linked to this model to include 3-loop corrections of O(\alpha_t\alpha_s^2) [0803.0672], [1005.5709] to the light CP-even Higgs pole mass. The setup of NUHMSSMNoFVHimalaya is shown in the following figure.

Building the NUHMSSMNoFVHimalaya

In order to use the 3-loop contributions to the light CP-even Higgs mass from the Himalaya library, the NUHMSSMNoFVHimalaya must be configured with the --enable-himalaya flag:

./createmodel --name=NUHMSSMNoFVHimalaya
./configure --with-models=NUHMSSMNoFVHimalaya \
    --enable-himalaya \
    --with-himalaya-incdir=${HIMALAYA_DIR}/source/include \
    --with-himalaya-libdir=${HIMALAYA_DIR}/build
make

In the above example HIMALAYA_DIR is the path to the Himalaya directory.

Input parameters

NUHMSSMNoFVHimalaya takes the following physics parameters as input:

Parameter	Description	SLHA block/field	Mathematica symbol
`Q_{\text{in}}`	input scale	`EXTPAR[0]`	`Qin`
`M_1(M_\text{SUSY})`	Bino mass	`EXTPAR[1]`	`M1`
`M_2(M_\text{SUSY})`	Wino mass	`EXTPAR[2]`	`M2`
`M_3(M_\text{SUSY})`	Gluino mass	`EXTPAR[3]`	`M3`
`A_t(M_\text{SUSY})`	trililear stop coupling	`EXTPAR[11]`	`AtIN`
`A_b(M_\text{SUSY})`	trililear sbottom coupling	`EXTPAR[12]`	`AbIN`
`A_\tau(M_\text{SUSY})`	trililear stau coupling	`EXTPAR[13]`	`AtauIN`
`A_c(M_\text{SUSY})`	trililear scharm coupling	`EXTPAR[14]`	`AcIN`
`A_s(M_\text{SUSY})`	trililear sstrange coupling	`EXTPAR[15]`	`AsIN`
`A_\mu(M_\text{SUSY})`	trililear smuon coupling	`EXTPAR[16]`	`AmuonIN`
`A_u(M_\text{SUSY})`	trililear sup coupling	`EXTPAR[17]`	`AuIN`
`A_d(M_\text{SUSY})`	trililear sdown coupling	`EXTPAR[18]`	`AdIN`
`A_e(M_\text{SUSY})`	trililear selectron coupling	`EXTPAR[19]`	`AeIN`
`\mu(M_\text{SUSY})`	`\mu`-parameter	`EXTPAR[23]`	`MuIN`
`m_A^2(M_\text{SUSY})`	running CP-odd Higgs mass	`EXTPAR[24]`	`mA2IN`
`(m_{\tilde{l}}^2)_{11}(M_\text{SUSY})`	soft-breaking 1st generation left-handed slepton mass parameters	`EXTPAR[31]`	`ml11IN`
`(m_{\tilde{l}}^2)_{22}(M_\text{SUSY})`	soft-breaking 2nd generation left-handed slepton mass parameters	`EXTPAR[32]`	`ml22IN`
`(m_{\tilde{l}}^2)_{33}(M_\text{SUSY})`	soft-breaking 3rd generation left-handed slepton mass parameters	`EXTPAR[33]`	`ml33IN`
`(m_{\tilde{e}}^2)_{11}(M_\text{SUSY})`	soft-breaking 1st generation right-handed slepton mass parameters	`EXTPAR[34]`	`me11IN`
`(m_{\tilde{e}}^2)_{22}(M_\text{SUSY})`	soft-breaking 2nd generation right-handed slepton mass parameters	`EXTPAR[35]`	`me22IN`
`(m_{\tilde{e}}^2)_{33}(M_\text{SUSY})`	soft-breaking 3rd generation right-handed slepton mass parameters	`EXTPAR[36]`	`me33IN`
`(m_{\tilde{q}}^2)_{11}(M_\text{SUSY})`	soft-breaking 1st generation left-handed squark mass parameters	`EXTPAR[41]`	`mq11IN`
`(m_{\tilde{q}}^2)_{22}(M_\text{SUSY})`	soft-breaking 2nd generation left-handed squark mass parameters	`EXTPAR[42]`	`mq22IN`
`(m_{\tilde{q}}^2)_{33}(M_\text{SUSY})`	soft-breaking 3rd generation left-handed squark mass parameters	`EXTPAR[43]`	`mq33IN`
`(m_{\tilde{u}}^2)_{11}(M_\text{SUSY})`	soft-breaking 1st generation right-handed up-type squark mass parameters	`EXTPAR[44]`	`mu11IN`
`(m_{\tilde{u}}^2)_{22}(M_\text{SUSY})`	soft-breaking 2nd generation right-handed up-type squark mass parameters	`EXTPAR[45]`	`mu22IN`
`(m_{\tilde{u}}^2)_{33}(M_\text{SUSY})`	soft-breaking 3rd generation right-handed up-type squark mass parameters	`EXTPAR[46]`	`mu33IN`
`(m_{\tilde{d}}^2)_{11}(M_\text{SUSY})`	soft-breaking 1st generation right-handed down-type squark mass parameters	`EXTPAR[47]`	`md11IN`
`(m_{\tilde{d}}^2)_{22}(M_\text{SUSY})`	soft-breaking 2nd generation right-handed down-type squark mass parameters	`EXTPAR[48]`	`md22IN`
`(m_{\tilde{d}}^2)_{33}(M_\text{SUSY})`	soft-breaking 3rd generation right-handed down-type squark mass parameters	`EXTPAR[49]`	`md33IN`
`M_\text{low}`	scale where the SM(5) is matched to the MSSM	`EXTPAR[100]`	`Mlow`
`\tan\beta(M_Z)`	`\tan\beta(M_Z)=v_u(M_Z)/v_d(M_Z)`	`MINPAR[3]`	`TanBeta`

All MSSM parameters, except for \tan\beta, are defined in the \overline{\text{DR}} scheme at the scale M_{\text{SUSY}}. \tan\beta is defined in the \overline{\text{DR}} scheme at the scale M_Z.

Running the NUHMSSMNoFVHimalaya

We recommend to run NUHMSSMNoFVHimalaya 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   0            # calculate SM pole masses
    4   3            # pole mass loop order
    5   3            # EWSB loop order
    6   3            # beta-functions loop order
    7   2            # 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^2 + alpha_t alpha_b + alpha_b^2)
   11   1            # Higgs 2-loop corrections O(alpha_tau^2)
   12   0            # force output
   13   1            # Top pole mass QCD corrections (0 = 1L, 1 = 2L, 2 = 3L)
   14   1.0e-11      # beta-function zero threshold
   15   0            # calculate observables (a_muon, ...)
   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   122111221    # 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 = FSNUHMSSMNoFVHimalayaOpenHandle[
    fsSettings -> {
        precisionGoal -> 1.*^-5,           (* FlexibleSUSY[0] *)
        maxIterations -> 0,                (* FlexibleSUSY[1] *)
        solver -> 0,                       (* FlexibleSUSY[2] *)
        calculateStandardModelMasses -> 0, (* FlexibleSUSY[3] *)
        poleMassLoopOrder -> 3,            (* FlexibleSUSY[4] *)
        ewsbLoopOrder -> 3,                (* FlexibleSUSY[5] *)
        betaFunctionLoopOrder -> 3,        (* FlexibleSUSY[6] *)
        thresholdCorrectionsLoopOrder -> 2,(* FlexibleSUSY[7] *)
        higgs2loopCorrectionAtAs -> 1,     (* FlexibleSUSY[8] *)
        higgs2loopCorrectionAbAs -> 1,     (* FlexibleSUSY[9] *)
        higgs2loopCorrectionAtAt -> 1,     (* FlexibleSUSY[10] *)
        higgs2loopCorrectionAtauAtau -> 1, (* FlexibleSUSY[11] *)
        forceOutput -> 0,                  (* FlexibleSUSY[12] *)
        topPoleQCDCorrections -> 1,        (* 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 -> 122111221, (* 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] *)
    },
    ...
];

Uncertainty estimate of the predicted Higgs pole mass

In the file model_files/NUHMSSMNoFVHimalaya/NUHMSSMNoFVHimalaya_uncertainty_estimate.m FlexibleSUSY provides the Mathematica function CalcNUHMSSMNoFVHimalayaDMh[], which calculates the Higgs pole mass at the 3-loop level with NUHMSSMNoFVHimalaya and performs an uncertainty estimate of missing higher order corrections. Three sources of the theory uncertainty are taken into account:

missing higher order contributions to the Higgs mass: The Higgs pole mass is calculated at the SUSY scale, M_\text{SUSY}, as a function of the running MSSM \overline{\text{DR}} parameters at full 1-loop level plus 2-loop corrections of O((\alpha_t + \alpha_b)\alpha_s + (\alpha_t + \alpha_b)^2 + \alpha_\tau^2) plus 3-loop corrections of O((\alpha_t + \alpha_b)\alpha_s^2). The missing contributions are estimated by varying the scale within the interval [M_{\text{SUSY}}/2, 2 M_{\text{SUSY}}].

missing higher order contributions to the strong gauge coupling: The running MSSM \overline{\text{DR}} strong gauge coupling g_3(M_Z) is calculated at the full 1-loop level plus 2-loop contributions of O(\alpha_s^2 + (\alpha_t + \alpha_b)\alpha_s).

If the Higgs mass is calculated at the 3-loop level, then missing 4-loop strong corrections to M_h are estimated by switching on/off the 2-loop contributions to g_3(M_Z).

missing higher order contributions to the top Yukawa coupling: The running MSSM \overline{\text{DR}} Yukawa coupling, y_t(M_Z), is calculated at the full 1-loop level plus 2-loop contributions of O(\alpha_s^2).

If the Higgs mass is calculated at the 2-loop level, then missing 3-loop top Yukawa-type corrections to M_h are estimated by switching on/off the 2-loop contributions to y_t(M_Z).

If the Higgs mass is calculated at the 3-loop level, then missing 4-loop top Yukawa-type corrections can currently not be estimated by switching on/off potential 3-loop contributions to y_t(M_Z), because the latter are currently unknown.

The following code snippet illustrates the calculation of the Higgs pole mass at the 3-loop level with NUHMSSMNoFVHimalaya as a function of the SUSY scale (red solid line), together with the estimated uncertainty (grey band).