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HSSUSY

HSSUSY

HSSUSY (high scale supersymmetry) is an implementation of the Standard Model, matched to the MSSM at the SUSY scale, $M_\text{SUSY}$. At the SUSY scale, the quartic Higgs coupling, $\lambda(M_\text{SUSY})$ is predicted from the matching to the MSSM using the 1- and 2-loop threshold corrections of [arXiv:1407.4081, arxiv:1504.05200, arXiv:1703.08166]. The 3-loop renormalization group equations of [arxiv:1504.05200, arxiv:1303.4364] are used to run $\lambda(M_\text{SUSY})$ down to the electroweak scale. At the electroweak scale, the gauge and Yukawa couplings as well as the SM vacuum expectation value (VEV) are calculated at the 1-loop level from the known low-energy couplings $\alpha_{\text{em}}(M_Z)$, $\alpha_s(M_Z)$ and Standard Model masses. The known 2-loop and 3-loop QCD threshold corrections for $\alpha_s(M_Z)$ can also be taken into account [hep-ph/9305305, hep-ph/9708255, hep-ph/9707474, hep-ph/0004189] by setting the threshold corrections flag appropriately. The top Yukawa coupling $y_t(M_Z)$ is calculated at the full 1-loop level from the top pole mass, taking optionally 2-loop [hep-ph/9803493] and 3-loop [arxiv:hep-ph/9911434] corrections into account, see FlexibleSUSY configuration block (FlexibleSUSY) .

In Mathematica interface an example Mathematica script can be found, which illustrates how to perform a parameter scan using the HSSUSY model.

__Input parameters__

Parameter | description | input block/field --------------------------------------------|--------------------------------------------------------------|------------------ $M_{\text{SUSY}}$ | SUSY scale | `EXTPAR[0]` $M_1(M_\text{SUSY})$ | Bino mass | `EXTPAR[1]` $M_2(M_\text{SUSY})$ | Wino mass | `EXTPAR[2]` $M_3(M_\text{SUSY})$ | Gluino mass | `EXTPAR[3]` $\mu(M_\text{SUSY})$ | $\mu$-parameter | `EXTPAR[4]` $m_A(M_\text{SUSY})$ | running CP-odd Higgs mass | `EXTPAR[5]` $M_{\text{EWSB}}$ | scale at which the pole mass spectrum is calculated | `EXTPAR[5]` $A_t(M_\text{SUSY})$ | trililear stop coupling | `EXTPAR[7]` $\tan\beta(M_\text{SUSY})$ | $\tan\beta(M_\text{SUSY})=\frac{v_u}{v_d}$ | `EXTPAR[25]` $(m_{\tilde{q}}^2)_{ij}(M_\text{SUSY})$ | soft-breaking left-handed squark mass parameters | `MSQ2IN` $(m_{\tilde{u}}^2)_{ij}(M_\text{SUSY})$ | soft-breaking right-handed up-type squark mass parameters | `MSU2IN` $(m_{\tilde{d}}^2)_{ij}(M_\text{SUSY})$ | soft-breaking right-handed down-type squark mass parameters | `MSD2IN` $(m_{\tilde{l}}^2)_{ij}(M_\text{SUSY})$ | soft-breaking left-handed slepton mass parameters | `MSL2IN` $(m_{\tilde{e}}^2)_{ij}(M_\text{SUSY})$ | soft-breaking right-handed down-type slepton mass parameters | `MSE2IN`

__EWSB__

The 1-loop electroweak symmetry breaking condition is imposed at the scale $M_{\text{EWSB}}$ and is used to fix the value of the bililear Higgs coupling $\mu^2(M_{\text{EWSB}})$.

__Boundary conditions__

_High scale_

The high scale (`HighScale`) is fixed $M_{\text{SUSY}}$. At $M_{\text{SUSY}}$, the quartic Higgs coupling $\lambda(M_\text{SUSY})$ is fixed using the 1- and leading 2-loop threshold corrections of [arXiv:1407.4081, arxiv:1504.05200, arXiv:1703.08166].

_EWSB scale_

The scale at which the pole mass spectrum (including the Higgs mass) (`SUSYScale`) is calculated is the electroweak symmetry breaking scale, $M_{\text{EWSB}}$.

_Low scale_

At the low scale (`LowScale`) the gauge and Yukawa couplings as well as the VEV are calculated from the input parameters $\alpha_{\text{em}}(M_Z)$, $\alpha_s(M_Z)$, $G_F$, $m_u(2\,\text{GeV})$, $m_d(2\,\text{GeV})$, $m_s(2\,\text{GeV})$, $m_c(m_c)$, $m_b(m_b)$, $M_t$, $M_e$, $M_\mu$, $M_\tau$, $M_Z$ using the approach described in [arxiv:1609.00371].

Depending on the given input flags, the top Yukawa coupling, $y_t(M_Z)$, is calculated at the 1-loop level plus additional 2-loop [hep-ph/9803493] and 3-loop [arxiv:hep-ph/9911434] QCD corrections, see FlexibleSUSY configuration block (FlexibleSUSY) .

Depending on the given input flags, the strong coupling constant, $\alpha_s(M_Z)$, is calculated at the 1-loop level plus additional 2-loop and 3-loop QCD corrections [hep-ph/9305305, hep-ph/9708255, hep-ph/9707474, hep-ph/0004189], see FlexibleSUSY configuration block (FlexibleSUSY) .

__Pole masses__

The Standard Model pole mass spectrum is calculated at the 1-loop level. Depending on the given input flags, 2-loop corrections $O(\alpha_t\alpha_s)$ [arxiv:1407.4336, Eq.(2.47)] and $O(\alpha_t^2)$ [arxiv:1205.6497, Eq.(20)], as well as 3-loop corrections $O(\alpha_t^3 + \alpha_t^2\alpha_s + \alpha_t\alpha_s^2)$ [arxiv:1407.4336] are included.

Note:
Note, that the 3-loop contributions $O(\alpha_t^3 + \alpha_t^2\alpha_s)$ are incomplete, because the corresponding 2-loop threshold corrections $O(\alpha_t^2 + \alpha_t\alpha_s)$ for the running top Yukawa coupling are not implemented yet.