SLHA input parameters

Table of Contents

1 FlexibleSUSY configuration block (FlexibleSUSY)
2 Additional physical input parameters (FlexibleSUSYInput)
3 MODSEL block (MODSEL)
4 Output blocks
5 References

1 FlexibleSUSY configuration block (FlexibleSUSY)

Block name: FlexibleSUSY

Default values:

Block FlexibleSUSY
    0   1.0e-04   # 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   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, 3 = 4L)
   14   1.0e-11   # beta-function zero threshold
   15   0         # calculate observables (a_muon, effective couplings)
   16   0         # force positive majorana masses
   17   0         # pole mass scale
   18   0         # pole mass 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 (SM -> BSM)
   21   1         # EFT loop order for downwards matching (BSM -> SM)
   22   0         # EFT index of SM-like Higgs in the BSM model (0 = lightest Higgs)
   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', 2 = H3m)
   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)

Description:

The FlexibleSUSY block contains fields to configure the spectrum calculation at run-time. For example, in the FlexibleSUSY block the renormalization group running precsision, the beta function loop order or the loop order of the pole mass calculation can be selected.

index	description	possible values	default value
0	precision goal	any positive double	1.0e-4
1	max. number of iterations	any positive double	0 (= automatic)
2	BC solver	0 (all), 1 (two-scale) or 2 (semi-analytic)	0 (= all)
3	calculate SM pole masses	0 (no) or 1 (yes)	0 (= no)
4	pole mass loop order	0, 1, 2, 3, 4	4 (= 4-loop)
5	EWSB loop order	0, 1, 2, 3, 4	4 (= 4-loop)
6	beta function loop order	0, 1, 2, 3, 4, 5	4 (= 4-loop)
7	threshold corrections loop order	0, 1, 2, 3, 4	4 (= 4-loop)
8	higgs 2-loop correction O(at as)	0, 1	1 (= enabled)
9	higgs 2-loop correction O(ab as)	0, 1	1 (= enabled)
10	higgs 2-loop correction O(at at)	0, 1	1 (= enabled)
11	higgs 2-loop correction O(atau atau)	0, 1	1 (= enabled)
12	force output	0 (no) or 1 (yes)	0 (= no)
13	top quark pole QCD corrections	0 (1L), 1 (2L), 2 (3L), 3 (4L)	3 (= 4L QCD)
14	beta function zero threshold	any positive double	1.0e-11
15	calculate observables	0 (no) or 1 (yes)	0 (= no)
16	force positive Majorana masses	0 (no) or 1 (yes)	0 (= no)
17	pole mass scale	any positive double	0 (= SUSY scale)
18	EFT pole mass scale	any positive double	0 (= minimum of {Mt, SUSY scale})
19	EFT matching scale	any positive double	0 (= SUSY scale)
20	EFT loop order for upwards matching	0, 1, 2	2 (= 2-loop)
21	EFT loop order for downwards matching	0, 1	1 (= 1-loop)
22	EFT Higgs index	any integer >= 0	0 (= lightest)
23	calculate pole masses of BSM particles	0 (no) or 1 (yes)	1 (= yes)
24	individual threshold corrections	positive integer	124111421
25	ren. scheme for higgs 3L corrections	0 (DR'), 1 (MDR'), 2 (H3m)	0 (= DR')
26	higgs 3-loop correction O(at as^2)	0, 1	1 (= enabled)
27	higgs 3-loop correction O(ab as^2)	0, 1	1 (= enabled)
28	higgs 3-loop correction O(at^2 as)	0, 1	1 (= enabled)
29	higgs 3-loop correction O(at^3)	0, 1	1 (= enabled)
30	higgs 4-loop correction O(at as^3)	0, 1	1 (= enabled)

1.1 Precision goal (`FlexibleSUSY[0]`)

FlexibleSUSY solves the given boundary value problem (BVP) by running all model parameters to each scale and imposing the corresponding boundary conditions until a convergent solution has been found or the maximum number of iterations has been reached. In FlexibleSUSY[0], precision goal of the BVP solver can be specified. The precision goal determines

the precision of the numerical solution of the RGEs,
the precision of the numerical solution of the EWSB equations and
to test whether the BVP solver has found a convergent solution.

1.2 Maximum number of iterations (`FlexibleSUSY[1]`)

FlexibleSUSY solves the given boundary value problem (BVP) by running to each scale and imposing the corresponding boundary conditions until a convergent solution has been found or the maximum number of iterations, N_{\text{max.it.}}, has been reached. In FlexibleSUSY[1], the maximum number of iterations N_{\text{max.it.}} used to solve the BVP can be specified. If N_{\text{max.it.}} is set to 0, the maximum number of iterations is set to N_{\text{max.it.}} = -10 \log_{10}(p), where p is the precision goal specified in FlexibleSUSY[0].

1.3 BVP solver (`FlexibleSUSY[2]`)

Choses the boundary value problem (BVP) solver: 0 = all that are enabled (starting with the two-scale solver, if present), 1 = two-scale solver (if present), 2 = semi-analytic solver (if present).

1.4 Calculate pole masses of Standard Model particles (`FlexibleSUSY[3]`)

Calculate pole masses of Standard Model particles: 0 = do not calculate Standard Model pole masses, 1 = calculate the Standard Model pole masses.

1.5 Pole mass loop order (`FlexibleSUSY[4]`)

Maximum pole mass loop order. 0 = tree-level, 1 = 1-loop, 2 = 2-loop (if available), 3 = 3-loop (if available).

1.6 EWSB loop order (`FlexibleSUSY[5]`)

Maximum loop order of the electroweak symmetry breaking (EWSB) equations. 0 = tree-level, 1 = 1-loop, 2 = 2-loop (if available), 3 = 3-loop (if available).

Important

The EWSB loop order should always be set to the same value as the pole mass loop order!

1.7 beta-function loop order (`FlexibleSUSY[6]`)

Loop order of the renormalization group running. 0 = no running, 1 = 1-loop running, 2 = 2-loop running, 3 = 3-loop running (if available), etc.

1.8 Threshold correction loop order (`FlexibleSUSY[7]`)

Using the flag FlexibleSUSY[7] the "global" loop order of the threshold corrections of the SM to the full BSM model can be selected. The threshold corrections affect the determination of the running BSM model parameters \alpha_{\text{em}}, \alpha_s, \sin(\theta_W), y_e, y_\mu, y_\tau, y_b, y_t, v at the low-energy scale Q_{\text{low}} in the \overline{\text{MS}} or \overline{\text{DR}} scheme.

Note

The individual loop orders of the threshold corrections can be specified using FlexibleSUSY[24].

\alpha_{\text{em}}(Q_{\text{low}}): If the threshold correction loop order is set to 0, \alpha_{\text{em}}(Q_{\text{low}}) is set to \alpha_{\text{em}}^{\text{SM}(5)}(Q_{\text{low}}) in the Standard Model with 5 active quark flavours. If the threshold correction loop order is set to 1, \alpha_{\text{em}}(Q_{\text{low}}) is calculated from \alpha_{\text{em}}^{\text{SM}(5)}(Q_{\text{low}}) using the full 1-loop threshold correction.
\alpha_s(Q_{\text{low}}): If the threshold correction loop order is set to 0, \alpha_s(Q_{\text{low}}) is set to \alpha_s^{\text{SM}(5)}(Q_{\text{low}}) in the Standard Model with 5 active quark flavours. If the threshold correction loop order is set to 1, \alpha_s(Q_{\text{low}}) is calculated from \alpha_s^{\text{SM}(5)}(Q_{\text{low}}) using the full 1-loop threshold correction.
\sin(\theta_W)(Q_{\text{low}}): If the threshold correction loop order is set to 0, the weak mixing angle is calculated from either (i) \{G_F,M_Z\} or (ii) \{M_W,M_Z\} (depending on the choice of the weak mixing angle calculation in the FlexibleSUSY model file, see FlexibleSUSY model file) using the corresponding tree-level relation.

If the threshold correction loop order is set to 1, the the weak mixing angle is calculated at the 1-loop level, taking into account
- (i): complete 1-loop corrections to the W and Z self-energies \Pi_{ZZ}^T, \Pi_{ZZ}^T as well as 1-loop corrections to \Delta r, which includes vertex and box contributions \delta_{\text{VG}} from neutralinos, charginos, selectrons and smuons.
- (ii): complete 1-loop corrections to the W and Z self-energies \Pi_{ZZ}^T, \Pi_{ZZ}^T.
If the threshold correction loop order is set to 2, the weak mixing angle is calculated at the 1-loop level, as above, and the following 2-loop correction is taken into account:
- (i): 2-loop corrections to \Delta r of the order O(\alpha_{\text{em}} \alpha_s + y_t^4) from [hep-ph:9606211] Eqs. (C.5)-(C.6).
y_e(Q_{\text{low}}), y_\mu(Q_{\text{low}}), y_\tau(Q_{\text{low}}): If the threshold correction loop order is set to 0, the lepton Yukawa couplings y_e(Q_{\text{low}}), y_\mu(Q_{\text{low}}), y_\tau(Q_{\text{low}}) are calculated from the lepton pole masses in the Standard Model with 5 active quark flavours using the tree-level relation.

If the threshold correction loop order is set to 1, y_e(Q_{\text{low}}), y_\mu(Q_{\text{low}}), y_\tau(Q_{\text{low}}) are calculated at the scale Q_{\text{low}} at the 1-loop level from the running lepton masses in Standard Model with 5 active quark flavours.
y_b(Q_{\text{low}}): If the threshold correction loop order is set to 0, the bottom Yukawa couplings y_b(Q_{\text{low}}) is calculated from the running bottom mass in the Standard Model with 5 active quark flavours, m_b^{(5)}(Q_{\text{low}}), using the tree-level relation.

If the threshold correction loop order is set to 1, y_b(Q_{\text{low}}) is calculated at the scale Q_{\text{low}} from m_b^{(5)}(Q_{\text{low}}) taking the complete 1-loop correction into account.

y_t(Q_{\text{low}}): If the threshold correction loop order is set to 0, the running top Yukawa coupling y_t(Q_{\text{low}}) is calculated from the top pole mass, M_t, using the tree-level relation.

If the threshold correction loop order is set to 1, the running y_t(Q_{\text{low}}) is calculated at the scale Q_{\text{low}} from M_t taking the complete 1-loop correction into account.

m_t(Q) &= M_t +
\text{Re\;}\Sigma_{t}^{S}(M_t)
+ M_t
\left[ \text{Re\;}\Sigma_{t}^{L}(M_t) +
  \text{Re\;}\Sigma_{t}^{R}(M_t) + \Delta
  m_t^{(1),\text{QCD}} \right] ,

where \Sigma_{t}^{S}(p), \Sigma_{t}^{L}(p), \Sigma_{t}^{R}(p) denote the scalar, left- and right-handed parts of the top self-energy without the gluon contribution. The 1-loop SM-QCD contribution m_t^{(1),\text{QCD}} reads in the \overline{\text{DR}} scheme

\Delta m_t^{(1),\text{QCD}} &=
   -\frac{g_3^2}{12 \pi^2} \left[5-3 \log\left(\frac{m_t^2}{Q^2}\right)\right],

and in the \overline{\text{MS}} scheme

\Delta m_t^{(1),\text{QCD}} &=
   -\frac{g_3^2}{12 \pi^2} \left[4-3 \log\left(\frac{m_t^2}{Q^2}\right)\right].

If the threshold correction loop order is set to 2, 2-loop SM-QCD corrections are taken into count as

m_t(Q) &= M_t +
\text{Re\;}\Sigma_{t}^{S}(M_t)
+ M_t
\left[ \text{Re\;}\Sigma_{t}^{L}(M_t) +
  \text{Re\;}\Sigma_{t}^{R}(M_t) + \Delta
  m_t^{(1),\text{QCD}} + \Delta m_t^{(2),\text{QCD}} \right] ,

where \Delta m_t^{(2),\text{QCD}} reads in the \overline{\text{DR}} scheme [hep-ph:0210258]

\Delta m_t^{(2),\text{QCD}} &= \left(\Delta
  m_t^{(1),\text{QCD}}\right)^2
- \frac{g_3^4}{4608 \pi^4} \Bigg[396
\log^2\left(\frac{m_t^2}{Q^2}\right)-1476
\log\left(\frac{m_t^2}{Q^2}\right)
-48 \zeta(3)+2011+16 \pi^2 (1+\log 4)\Bigg] \,,

and in the \overline{\text{MS}} scheme [hep-ph:9803493]

\Delta m_t^{(2),\text{QCD}} &= \left(\Delta
  m_t^{(1),\text{QCD}}\right)^2 - \frac{g_3^4}{4608 \pi^4}
\Bigg[396 \log^2\left(\frac{m_t^2}{Q^2}\right)
- 2028 \log\left(\frac{m_t^2}{Q^2}\right)
- 48 \zeta(3) + 2821 + 16 \pi^2 (1+\log 4)\Bigg] \,.

If the threshold correction loop order is set to 3 in non-SUSY models, the 3-loop SM-QCD corrections from Refs. [hep-ph:9912391], [hep-ph:9911434] are taken into count as

m_t(Q) &= M_t +
\text{Re\;}\Sigma_{t}^{S}(M_t)
+ M_t
\left[ \text{Re\;}\Sigma_{t}^{L}(M_t) +
  \text{Re\;}\Sigma_{t}^{R}(M_t) + \Delta
  m_t^{(1),\text{QCD}} + \Delta m_t^{(2),\text{QCD}} + \Delta m_t^{(3),\text{QCD}} \right] ,

where \Delta m_t^{(3),\text{QCD}} reads in the \overline{\text{MS}} scheme

\Delta m_t^{(3),\text{QCD}} =
-\frac{g_3^6 \left\{2700 \left[-312 \zeta (3)+1645+8 \pi ^2
   (1+\log (4))\right] \log \left(\frac{Q^2}{m^2}\right)+48600 \log
   ^3\left(\frac{Q^2}{m^2}\right)+714420 \log
   ^2\left(\frac{Q^2}{m^2}\right)-15 \left[69120
   \text{Li}_4\left(\frac{1}{2}\right)+116496 \zeta(3)-94800 \zeta
   (5)-531197+2880 \log^4(2)\right] - 4 \pi^2 [129510 \zeta
   (3)-393101+240 \log(2) (697+24 \log(2))] + 10500 \pi
   ^4\right\}}{9953280 \pi^6}

Note

The 1-, 2-, and 3-loop QCD corrections can be found in Mathematica form in meta/TwoLoopQCD.m and meta/ThreeLoopQCD.m.

1.9 2-loop Higgs pole mass contributions (`FlexibleSUSY[8-11]`)

Selects (on/off = 1/0) the individual 2-loop Higgs pole mass contributions (if available).

1.10 Force output (`FlexibleSUSY[12]`)

If set to 1, an output is always printed, even if a problem has occurred during the calculation.

Warning

Be careful with this option! Check the problems and warnings that have occurred!

1.11 Top pole mass loop order (`FlexibleSUSY[13]`)

Loop order of contributions to the top pole mass. 0 = full 1-loop, 1 = 2-loop QCD, 2 = 3-loop QCD.

Note

The top pole mass is only calculated if FlexibleSUSY[3] = 1.

1.12 Beta-function zero threshold (`FlexibleSUSY[14]`)

Below this threshold, beta-functions are treated as being exactly zero. Setting this threshold to a non-zero value can avoid numerical problems / non-convergence problems in models with complex parameters.

1.13 Calculate observables (`FlexibleSUSY[15]`)

Enable/disable (1/0) the calculation of the observables specified in the FlexibleSUSY model file. See the section on observables in FlexibleSUSY model file for further details about how to select the calculation of observables in FlexibleSUSY.

1.14 Force positive Majorana masses (`FlexibleSUSY[16]`)

If set to 1, the masses of Majorana fermions will always be positive. In this case, the corresponding mixing matrices may be complex.

Warning

Setting FlexibleSUSY[6] = 1 violates the SLHA standard.

1.15 Pole mass scale (`FlexibleSUSY[17]`)

Using FlexibleSUSY[17], the renormalization scale at which the pole mass spectrum is calculated can be overwritten. By default the renormalization scale is the SUSY scale (SUSYScale variable in the model file). If FlexibleSUSY[17] is set to 0, the value given by the SUSYScale variable is used. If FlexibleSUSY[17] is set to a non-zero value, then this value is used as renormalization scale.