GM2Calc calculates the new physics contributions to the anomalous magnetic moment of the muon a_µ = (g-2)/2 in the real MSSM and in the THDM at the 1- and leading 2-loop level.
- Homepage: https://gm2calc.hepforge.org
- Source code repository: https://github.com/gm2calc
- Source code documentation: https://gm2calc.github.io
- References: Eur.Phys.J. C76 (2016) no.2, 62 [arxiv:1510.08071] and [arxiv:2110.13238]
Build GM2Calc as follows:
mkdir -p build
cd build
cmake ..
make
Run GM2Calc with input files at the command line:
bin/gm2calc.x --gm2calc-input-file=../input/example.gm2
bin/gm2calc.x --slha-input-file=../input/example.slha
bin/gm2calc.x --thdm-input-file=../input/example.thdm
- Requirements
- Building GM2Calc
- Running GM2Calc
- Input parameters
- C/C++ interface
- Mathematica interface
- Python interface
- Source code documentation
- References
- C++14 compatible compiler (g++ >= 5 or clang++ >= 3.4 or icpc >= 14.0.3)
- C11 compatible compiler (gcc >= 4.6 or clang)
- Boost (version 1.37.0 or higher) [http://www.boost.org]
- Eigen 3 (version 3.1 or higher) [http://eigen.tuxfamily.org]
Optional:
- Mathematica (version 9.0 or higher) [https://www.wolfram.com/mathematica/]
- Python (version 2 or 3)
The dependencies listed above can be installed using the package manager of your Linux distribution. On Debian/Ubuntu, for example, one may run:
sudo apt-get install libeigen3-dev libboost-all-dev uuid-dev
Alternatively, the Conan package manager can be used to install the dependencies:
mkdir -p build
cd build
conan install ..
To compile GM2Calc run:
mkdir -p build
cd build
cmake ..
make
The GM2Calc executable can then be found in bin/gm2calc.x and the
GM2Calc library can be found in the lib/ directory. The used
compiler and package paths can be passed as arguments to cmake.
Example:
cmake \
-DCMAKE_CXX_COMPILER=icpc \
-DEIGEN3_INCLUDE_DIR=/opt/eigen3/eigen3 \
-DBOOST_ROOT=/opt/boost \
..
GM2Calc can be run from the command line using an SLHA or SLHA-like
input. For the MSSM the input can be given in the SLHA format or in a
custom GM2Calc input format (similar to SLHA, but different definition
of input parameters in a mixed DR-bar/on-shell scheme). For the THDM
the input can be given in an SLHA-like format (compatible with
2HDMC). See bin/gm2calc.x --help for all options.
Examples: Running GM2Calc with an SLHA input file for the MSSM:
bin/gm2calc.x --slha-input-file=../input/example.slha
or
cat ../input/example.slha | bin/gm2calc.x --slha-input-file=-
Example: Running GM2Calc with a custom GM2Calc input file for the MSSM (mixed DR-bar/on-shell scheme):
bin/gm2calc.x --gm2calc-input-file=../input/example.gm2
or
cat ../input/example.gm2 | bin/gm2calc.x --gm2calc-input-file=-
Example: Running GM2Calc with SLHA input file generated by SOFTSUSY:
./softpoint.x leshouches < inOutFiles/lesHouchesInput | bin/gm2calc.x --slha-input-file=-
Example: Running GM2Calc with SLHA input file generated by SPheno:
bin/SPheno input/LesHouches.in.mSUGRA
bin/gm2calc.x --slha-input-file=SPheno.spc
Example: Running GM2Calc with an input file for the THDM:
bin/gm2calc.x --thdm-input-file=../input/example.thdm
or
cat ../input/example.thdm | bin/gm2calc.x --thdm-input-file=-
When Mathematica is installed, a MathLink executable for GM2Calc is
build, which allows one to run GM2Calc from within Mathematica. The
MathLink executable can be found in bin/gm2calc.mx. This executable
can be installed in Mathematica by calling
Install["bin/gm2calc.mx"]
Afterwards, the GM2Calc Mathematica interface functions can be used.
See examples/example-slha.m (MSSM), examples/example-gm2calc.m
(MSSM) and examples/example-thdm.m (THDM) for examples with
different input parameters.
Example:
math -run "<< ../examples/example-slha.m"
math -run "<< ../examples/example-gm2calc.m"
math -run "<< ../examples/example-thdm.m"
When a valid Python installation is detected, GM2Calc, will attempt to
create example_*.py files in build/bin/. Either Python 2 or 3 can
be used, and the Python package cppyy is required. See the
cppyy installation instructions
for further details. In examples/example_slha.py (MSSM),
examples/example_gm2calc.py (MSSM) and examples/example_thdm.py
(THDM) examples with different input parameters can be found.
Example:
python bin/example_slha.py
python bin/example_gm2calc.py
python bin/example_thdm.py
When GM2Calc is called with an SLHA-1 input file for the MSSM, for example as
bin/gm2calc.x --slha-input-file=../input/example.slha
then the input parameters are read from the following blocks:
-
SMINPUTS: α_s(MZ), Standard Model fermion masses, W and Z pole masses.Example:
Block SMINPUTS 3 0.1184 # alpha_s(MZ) SM MS-bar [2L] 4 9.11876000E+01 # MZ(pole) [1L] 5 4.18000000E+00 # mb(mb) SM MS-bar [2L] 6 1.73340000E+02 # mtop(pole) [2L] 7 1.77700000E+00 # mtau(pole) [2L] 9 8.03850000E+01 # MW(pole) [1L] 13 0.1056583715 # mmuon(pole) [1L] -
MASS: pole masses of SUSY particles, W pole mass. If the W pole mass is given inMASS[24], then this value will be used instead of the W pole mass given inSMINPUTS[9].Example:
Block MASS # pole mass spectrum 24 8.03773317e+01 # W [1L] 36 1.50000000e+03 # A0 [2L] 1000022 2.01611468e+02 # neutralino(1) [1L] 1000023 4.10040273e+02 # neutralino(2) [1L] 1000024 4.09989890e+02 # chargino(1) [1L] 1000025 -5.16529941e+02 # neutralino(3) [1L] 1000035 5.45628749e+02 # neutralino(4) [1L] 1000037 5.46057190e+02 # chargino(2) [1L] 1000013 5.25187016e+02 # smuon(1) [1L] 1000014 5.18860573e+02 # muon sneutrino [1L] 2000013 5.05095249e+02 # smuon(2) [1L] -
HMIX: μ parameter (initial guess), tan(β), renormalization scale QExample:
Block HMIX Q= 1.00000000e+03 # renormalization scale 1 4.89499929e+02 # mu(Q) MSSM DR-bar [initial guess] 2 3.93371545e+01 # tan(beta)(Q) MSSM DR-bar Feynman gauge [1L] -
AU,AD,AE: soft-breaking trilinear couplings at the renormalization scale Q, which has been read from theHMIXblockExample:
Block AU Q= 1.00000000e+03 3 3 1.57871614e-05 # At(Q) [2L] Block AD Q= 1.00000000e+03 3 3 8.99561673e-06 # Ab(Q) [2L] Block AE Q= 1.00000000e+03 2 2 2.84230475e-06 # Amu(Q) MSSM DR-bar [1L] 3 3 3.02719242e-06 # Atau(Q) [2L] -
MSOFT: soft-breaking gaugino masses, soft-breaking sfermion masses at the renormalization scale Q, which has been read from theHMIXblockExample:
Block MSOFT Q= 1.00000000e+03 1 2.00000000e+02 # M_1(Q) [initial guess] 2 4.00000000e+02 # M_2(Q) [initial guess] 3 2.00000000e+03 # M_3(Q) [2L] 31 5.00000000e+02 # meL(Q) [2L] 32 5.00000000e+02 # mmuL(Q) [irrelevant] 33 3.00000000e+03 # mtauL(Q) [2L] 34 4.99999999e+02 # meR(Q) [2L] 35 4.99999999e+02 # mmuR(Q) [initial guess] 36 3.00000000e+03 # mtauR(Q) [2L] 41 7.00000000e+03 # mqL1(Q) [2L] 42 7.00000000e+03 # mqL2(Q) [2L] 43 6.99999999e+03 # mqL3(Q) [2L] 44 7.00000000e+03 # muR(Q) [2L] 45 7.00000000e+03 # mcR(Q) [2L] 46 6.99999999e+03 # mtR(Q) [2L] 47 7.00000000e+03 # mdR(Q) [2L] 48 7.00000000e+03 # msR(Q) [2L] 49 7.00000000e+03 # mbR(Q) [2L] -
GM2CalcInput: α_em(MZ), α_em(0) in the Thomson limitExample:
Block GM2CalcInput 1 0.00775520 # alpha(MZ) [1L] 2 0.00729735 # alpha(0) [2L]
See input/example.slha for an example SLHA input file.
Important note:
We strongly encourage passing SLHA input in
SLHA-1 convention to GM2Calc.
We strongly discourage passing
SLHA-2 input to GM2Calc. The reason
is, that GM2Calc interprets the PDG numbers 1000013, 2000013 and
1000014 in the MASS block as the two smuon and the muon sneutrino
pole masses, respectively. In an SLHA-2-compliant input, however, it
is not ensured, that these PDG numbers correspond to the two smuon and
the muon sneutrino pole masses, because of possibly allowed slepton
flavour violation.
When GM2Calc is called with an input file in the custom GM2Calc format (in a mixed DR-bar/on-shell scheme), for example as
bin/gm2calc.x --gm2calc-input-file=../input/example.gm2
then the input parameters are read from the following blocks:
-
SMINPUTS: α_s(MZ), Standard Model fermion masses, W and Z pole masses.Example:
Block SMINPUTS 3 0.1184 # alpha_s(MZ) SM MS-bar [2L] 4 9.11876000E+01 # MZ(pole) [1L] 5 4.18000000E+00 # mb(mb) SM MS-bar [2L] 6 1.73340000E+02 # mtop(pole) [2L] 7 1.77700000E+00 # mtau(pole) [2L] 9 8.03850000E+01 # MW(pole) [1L] 13 0.1056583715 # mmuon(pole) [1L] -
GM2CalcInput: renormalization scale Q, α_em(MZ), α_em(0) in the Thomson limit, tan(β) (DR-bar scheme), μ parameter (on-shell), soft-breaking gaugino masses (M1 and M2 in on-shell scheme), CP-odd Higgs pole mass MA, soft-breaking sfermion masses (msl(2,2) and mse(2,2) in on-shell scheme), soft-breaking trilinear couplings (Ae(2,2) in DR-bar scheme)Example:
Block GM2CalcInput 0 8.66360379E+02 # ren. scale Q [2L] 1 0.00775531 # alpha(MZ) [1L] 2 0.00729735 # alpha(0) [2L] 3 10 # tan(beta) DR-bar at Q [1L] 4 619.858 # mu parameter on-shell [1L] 5 211.722 # M1 on-shell [1L] 6 401.057 # M2 on-shell [1L] 7 1.10300877E+03 # M3 [2L] 8 707.025 # MA(pole) [2L] 9 3.51653258E+02 # msl(1,1) [2L] 10 356.09 # msl(2,2) on-shell [1L] 11 3.50674223E+02 # msl(3,3) [2L] 12 2.21215037E+02 # mse(1,1) [2L] 13 225.076 # mse(2,2) on-shell [1L] 14 2.18022142E+02 # mse(3,3) [2L] 15 1.00711403E+03 # msq(1,1) [2L] 16 1.00711149E+03 # msq(2,2) [2L] 17 9.29083096E+02 # msq(3,3) [2L] 18 9.69369660E+02 # msu(1,1) [2L] 19 9.69366965E+02 # msu(2,2) [2L] 20 7.99712943E+02 # msu(3,3) [2L] 21 9.64756473E+02 # msd(1,1) [2L] 22 9.64753818E+02 # msd(2,2) [2L] 23 9.60016201E+02 # msd(3,3) [2L] 24 0 # Ae(1,1) [irrelevant] 25 -2.93720212E+02 # Ae(2,2) DR-bar [1L] 26 -2.92154796E+02 # Ae(3,3) [2L] 27 0 # Ad(1,1) [irrelevant] 28 0 # Ad(2,2) [irrelevant] 29 -1.28330100E+03 # Ad(3,3) [2L] 30 0 # Au(1,1) [irrelevant] 31 0 # Au(2,2) [irrelevant] 32 -8.70714986E+02 # Au(3,3) [2L]
See input/example.gm2 for an example input file with custom GM2Calc
input parameters.
When GM2Calc is called with an SLHA-like input file for the THDM, for example as
bin/gm2calc.x --thdm-input-file=../input/example.thdm
then the input parameters are read from different blocks, depending on the input basis.
The THDM-specific input parameters in the gauge basis are read from the following blocks:
-
MINPAR: tan(β), λ_{1,...,7}, m_{12}^2, ζ_{u,d,l} and the Yukawa type (1 = type I, 2 = type II, 3 = type X, 4 = type Y, 5 = aligned THDM, 6 = general)Note: The parameters ζ_{u,d,l} are only used if the Yukawa type is set to the aligned THDM (Yukawa type = 5).
Example:
Block MINPAR # model parameters in gauge basis 3 3 # tan(beta) 11 0.7 # lambda_1 12 0.6 # lambda_2 13 0.5 # lambda_3 14 0.4 # lambda_4 15 0.3 # lambda_5 16 0.2 # lambda_6 17 0.1 # lambda_7 18 40000 # m_{12}^2 21 0 # zeta_u 22 0 # zeta_d 23 0 # zeta_l 24 2 # Yukawa type (1, 2, 3, 4, 5 = aligned, 6 = general) -
GM2CalcTHDMDeltauInput,GM2CalcTHDMDeltadInput,GM2CalcTHDMDeltalInput: The real parts of the matrices Delta_u, Delta_d and Delta_l -
GM2CalcTHDMPiuInput,GM2CalcTHDMPidInput,GM2CalcTHDMPilInput: The real parts of the matrices Pi_u, Pi_d and Pi_l
Note: The parameters Delta_{u,d,l} are only used if the Yukawa type is not set to the general THDM (Yukawa type = 1,...,5).
Note: The parameters Pi_{u,d,l} are only used if the Yukawa type is set to the general THDM (Yukawa type = 6).
The THDM-specific input parameters in the mass basis are read from the following blocks:
-
MINPAR: tan(β), λ_{6,7}, m_{12}^2, sin(β-α), ζ_{u,d,l} and the Yukawa type (1 = type I, 2 = type II, 3 = type X, 4 = type Y, 5 = aligned THDM, 6 = general)Note: The parameters ζ_{u,d,l} are only used if the Yukawa type is set to the aligned THDM (Yukawa type = 5).
Example:
Block MINPAR # model parameters 3 3 # tan(beta) 16 0.2 # lambda_6 17 0.1 # lambda_7 18 40000 # m_{12}^2 20 0.999 # sin(beta - alpha) 21 0 # zeta_u 22 0 # zeta_d 23 0 # zeta_l 24 2 # Yukawa type (1, 2, 3, 4, 5 = aligned, 6 = general) -
MASS: CP-even Higgs boson masses m_h, m_H, the CP-odd Higgs boson mass m_A and the charged Higgs boson mass m_{H^+}Example:
Block MASS # Higgs masses 25 100 # mh, lightest CP-even Higgs 35 400 # mH, heaviest CP-even Higgs 36 420 # mA, CP-odd Higgs 37 440 # mH+, charged Higgs -
GM2CalcTHDMDeltauInput,GM2CalcTHDMDeltadInput,GM2CalcTHDMDeltalInput: The real parts of the matrices Delta_u, Delta_d and Delta_l -
GM2CalcTHDMPiuInput,GM2CalcTHDMPidInput,GM2CalcTHDMPilInput: The real parts of the matrices Pi_u, Pi_d and Pi_l
Note: The parameters Delta_{u,d,l} are only used if the Yukawa type is not set to the general THDM (Yukawa type = 1,...,5).
Note: The parameters Pi_{u,d,l} are only used if the Yukawa type is set to the general THDM (Yukawa type = 6).
See input/example.thdm for an example input file.
When running GM2Calc from the command line with SLHA or SLHA-like
input, the input may contain the GM2CalcConfig configuration block
to customize the calculation and the output. The GM2CalcConfig
block entries are summarized in the following table and are described
below:
| Entry | Description | Possible values | Defaul value |
|---|---|---|---|
| 0 | output format | 0, ..., 4 |
4 for SLHA input, 1 for GM2Calc input |
| 1 | loop order | 0, 1, 2 |
2 |
| 2 | tan(beta) resummation | 0, 1 |
1 |
| 3 | force output | 0, 1 |
0 |
| 4 | verboe output | 0, 1 |
0 |
| 5 | estimate uncertainty | 0, 1 |
0 |
| 6 | running parameters | 0, 1 |
1 |
Description:
-
GM2CalcConfig[0]: defines the output format (0...4)0: minimal output (a single number)
1: detailed (a detailed output of the various contributions)
2: write the value of a_mu intoLOWENblock, entry6
3: write the value of a_mu intoSPhenoLowEnergyblock, entry21
4: write the value of a_mu intoGM2CalcOutputblock, entry0 -
GM2CalcConfig[1]: loop order of the calculation (0,1or2). We recommend to use2. -
GM2CalcConfig[2]: disable/enable tan(beta) resummation (0or1). We recommend to use1. -
GM2CalcConfig[3]: force output even if physical problem has occured (0or1). WARNING: The result might not be trusted if a problem has occured! We recommend to use0. -
GM2CalcConfig[4]: disable/enable verbose output (0or1). We recommend to use0by default, and1only for debugging. -
GM2CalcConfig[5]: disable/enable uncertainty estimation (0or1). Depending on the chosen output format (seeGM2CalcConfig[0]) the uncertainty is written- as a single number to stdout in case of minimal output,
- to the first line in case of detailed output,
- to
GM2CalcOutput[1]otherwise.
-
GM2CalcConfig[6]: disable/enable use of running parameters (0or1) in the fermionic 2-loop contributions in the THDM.
We recommend to use the following configuration block in an SLHA input file:
Block GM2CalcConfig
0 4 # output format (0 = minimal, 1 = detailed,
# 2 = NMSSMTools, 3 = SPheno, 4 = GM2Calc)
1 2 # loop order (0, 1 or 2)
2 1 # disable/enable tan(beta) resummation (0 or 1)
3 0 # force output (0 or 1)
4 0 # verbose output (0 or 1)
5 1 # calculate uncertainty (0 or 1)
6 1 # running parameters (0 or 1)
GM2Calc provides a C and a C++ interface. To use the routines of GM2Calc in a C++ program and perform an MSSM calculation, the following C++ header files have to be included:
include/gm2calc/gm2_1loop.hpp
include/gm2calc/gm2_2loop.hpp
include/gm2calc/gm2_uncertainty.hpp
include/gm2calc/gm2_error.hpp
include/gm2calc/MSSMNoFV_onshell.hpp
For the calculation in the THDM, the following C++ header files have to be included:
include/gm2calc/gm2_1loop.hpp
include/gm2calc/gm2_2loop.hpp
include/gm2calc/gm2_uncertainty.hpp
include/gm2calc/gm2_error.hpp
include/gm2calc/THDM.hpp
To use the routines of GM2Calc in a C program to perform an MSSM calculation, the following C header files have to be included:
include/gm2calc/gm2_1loop.h
include/gm2calc/gm2_2loop.h
include/gm2calc/gm2_uncertainty.h
include/gm2calc/MSSMNoFV_onshell.h
For the calculation in the THDM, the following C header files must be included:
include/gm2calc/gm2_1loop.h
include/gm2calc/gm2_2loop.h
include/gm2calc/gm2_uncertainty.h
include/gm2calc/THDM.h
include/gm2calc/SM.h
Please refer to the content of these header files for a precise
definition of all interface functions. The C/C++ example programs in
the examples/ directory serve as an illustration of the interface
routines.
After the GM2Calc MathLink executable has been loaded by
e.g. Install["bin/gm2calc.mx"], the following functions are
available:
| Function | Description |
|---|---|
| GM2CalcSetFlags | Sets configuration flags for the calculation |
| GM2CalcGetFlags | Returns currently set configuration flags |
| GM2CalcSetSMParameters | Sets Standard Model parameters |
| GM2CalcGetSMParameters | Returns currently set Standard Model parameters |
| GM2CalcAmuSLHAScheme | Calculates a_mu, in the MSSM with SLHA input parameters |
| GM2CalcAmuGM2CalcScheme | Calculates a_mu, in the MSSM with GM2Calc-specific input parameters |
| GM2CalcAmuTHDMGaugeBasis | Calculates a_mu, in the THDM with gauge basis input parameters |
| GM2CalcAmuTHDMMassBasis | Calculates a_mu, in the THDM with mass basis input parameters |
See the example Mathematica scripts examples/example-slha.m,
examples/example-gm2calc.m and examples/example-thdm.m.
After building GM2Calc with shared libraries, it is possible to load GM2Calc functions into Python using the C-Python interface provided by cppyy.
To use the routines of GM2Calc in a Python script, the following folders and C++ header files have to be included:
`Eigen3 include folder` # /usr/include/eigen3/ or similar
include/ # GM2Calc's include folder
include/gm2calc/gm2_1loop.hpp
include/gm2calc/gm2_2loop.hpp
include/gm2calc/gm2_uncertainty.hpp
include/gm2calc/gm2_error.hpp
To perform an MSSM calculation, the following C++ header files have to be included:
include/gm2calc/MSSMNoFV_onshell.hpp
For the calculation in the THDM, the following C++ header files have to be included:
include/gm2calc/THDM.hpp
And finally for any GM2Calc model the following library must be loaded:
cppyy.load_library("libgm2calc")
Then one can import the C++ functions into Python using the command
from cppy.gbl import gm2calc. Then the following functions are
available:
| Function | Description |
|---|---|
| gm2calc.SM | Constructs an SM model |
| gm2calc.MSSMNoFV_onshell | Constructs an MSSMNoFV model |
| gm2calc.THDM | Constructs a THDM model |
| gm2calc.calculate_amu_1loop | Calculates the 1-loop contributions to a_mu |
| gm2calc.calculate_amu_2loop | Calculates the 2-loop contributions to a_mu |
| gm2calc.calculate_uncertainty_amu_0loop | Calculates the uncertainty of a_mu if working at tree-level |
| gm2calc.calculate_uncertainty_amu_1loop | Calculates the uncertainty of a_mu if working at 1 level |
| gm2calc.calculate_uncertainty_amu_2loop | Calculates the uncertainty of a_mu if working at 2 level |
See the example Python scripts examples/example_slha.py,
examples/example_gm2calc.py and examples/example_thdm.py.
The source code documentation of GM2Calc can be found online at https://gm2calc.github.io.
GM2Calc uses Doxygen to document the source code. The complete source code documentation can be generated by running
make doc
Afterwards, the generated HTML pages can be found in doc/html/ and
can be openend with your favourite web browser, e.g.
firefox doc/html/index.html
GM2Calc has been published in [Athron:2015rva, Athron:2021evk]:
-
Peter Athron, Markus Bach, Helvecio G. Fargnoli, Christoph Gnendiger, Robert Greifenhagen, Jae-hyeon Park, Sebastian Paßehr, Dominik Stöckinger, Hyejung Stöckinger-Kim, Alexander Voigt: GM2Calc: Precise MSSM prediction for (g-2) of the muon [Eur.Phys.J. C76 (2016) no.2, 62]
-
Peter Athron, Csaba Balazs, Adriano Cherchiglia, Douglas Jacob, Dominik Stöckinger, Hyejung Stöckinger-Kim, Alexander Voigt: Two-loop Prediction of the Anomalous Magnetic Moment of the Muon in the Two-Higgs Doublet Model with GM2Calc 2 [arxiv:2110.13238]
The expressions implemented in GM2Calc for the MSSM have been taken from [Phys.Rev. D81 (2010) 093004, Phys.Lett. B726 (2013) 717-724, JHEP 1402 (2014) 070, JHEP 1510 (2015) 026]
The expressions implemented in GM2Calc for the THDM have been taken from [JHEP 01 (2017) 007]