H3m Reference Manual (v1.2)
Table of Contents
1 Overview
This document describes the usage of the program H3.m
, a Mathematica
package for evaluating the mass of the light Higgs Boson within the
minimal supersymmetric extension of the Standard Model (MSSM) to
three-loop accuracy.
For details on the calculation and phenomenological applications, see the paper [Kant:2010tf] (which you should also cite in case you use this code for a publication).
The results presented in Ref. [Kant:2010tf] are based on
FeynHiggs
2.6.5 which contains a bug in the SUSY Les Houches
interface. This results in a numerical change of MH of the order of
\,GeV already at one-loop order. The bug has been fixed in version
2.7.x.1.
2 Frontend
The package provides a handful of functions for interaction with the user. These fall into two categories: functions for setting up the parameters, and functions for evaluating the Higgs mass.
2.1 Functions that set up or retrieve parameters
The parameters for the calculation are set using the SUSY Les Houches Accord (SLHA) interface [Skands:2003cj]. One can either prepare a spectrum file and call H3GetSLHA to read it, or use H3SetSLHA, which prepares an SLHA input file, passes it to a spectrum generator to prepare a spectrum file which is then read using H3GetSLHA.
For even more convenience, there are the functions
H3SetSPS1a/2/3(m12)
, H3SetSPS2(m12)
, H3SetSPS3(m12)
, H3SetSPS4/5()
H3SetSPS7/8(lambda)
, H3SetSPS9(m32)
, which call H3SetSLHA
using
parameters according to a benchmark scenario from the Snowmass Points
and Slopes.
In each case, the function H3ChooseHH is called automatically to
decide which mass hierarchy will be chosen for the calculation of Mh
at the three-loop level, and the spectrum file is given to FeynHiggs
for the two-loop calculation. In addition (if not suppressed by
setting the options mt2l
or decSUSY
, resp. to False
), the values
of the top mass and αs in the scheme at
the chosen renormalisation scale are computed using RunDec
[Chetyrkin:2000yt] and its supersymmetric extension, decSUSY.
To speed things up, the generated spectrum files (as well as the values
for the top mass and strong coupling) are cached on disk and re-used,
unless the option recycle
is set to False
.
It is also possible to change the value of particular parameters by
manipulating the list H3`Private`parameters
, although in this case
the changes are not passed to FeynHiggs
, and one would have to call
decSUSY manually, if desired.
2.1.1 H3GetSLHA
Parse an SLHA [Skands:2003cj] spectrum file and set the parameters for the
calculation accordingly. Then, pass the file to FeynHiggs
.
Additionally, the top mass and αs are calculated within
SUSY-QCD
.
- Options:
- mt2l
- If True, compute the
top mass to using two-loop decoupling and four-loop running within SUSY-QCD.
- decSUSY
- If True, use the package decSUSY to compute αs in the full theory to three-loop accuracy.
- recycle
- If True, use the cache for values of the
top mass and αs.
- savepath
- The path to a directory where the cache should be stored
(if
recycle
is set to True).
Additional options control the behaviour of
FeynHiggs
and should not be altered.The spectrum file should contain at least the following data:
Block Required Entries SMINPUTS 2, 3, 4, 5, 6 GAUGE 1, 2, 3 HMIX 1, 2, 3 MSOFT 3, 41 - 49 AU (3, 3) YU (3, 3) MASS 36, 1000021, 1000001 - 1000006, 2000001-2000006 STOPMIX (1, 1)
2.1.2 H3SetSLHA
Prepare an input file for SoftSUSY and call that program to create a spectrum file. This file, in turn, is passed to H3GetSLHA.
- Options: All options that apply to H3GetSLHA are passed to that function. In addition, there are the following options:
- spectGen
- This option governs which spectrum generator to use. Possible choices are "softsusy", "spheno", and "suspect".
- Model
- Select the model of SUSY breaking. So far, "msugra", "mgmsb", and "mamsb" are implemented. In addition, the benchmark scenarios from [Carena:2002qg] are implemented and can be accessed by setting Model to "mhmax", "nomix", "gluophob" and "smallalpha".
- softsusytwoloop
- Either 1 (default) or 0. If 1, SoftSUSY uses full 2-loop running in the RGEs.
- mu
- The renormalisation scale at which the
parameters are evaluated.
- invalpha, GF, asmz, MZ, mb, Mt, mtau
- Standard Model input values.
- Options specific to
msugra
- m0, m12, tanb, signmu, A0
- Specify a point in the
msugra
parameter space. See [AguilarSaavedra:2005pw][Allanach:2002nj] for details.
- Options specific to
mgmsb
- lambda, mmess, tanb, signmu, nmess
- Specify a point in the
mgmsb
parameter space. See [AguilarSaavedra:2005pw][Allanach:2002nj] for details.
- Options specific to
mamsb
- m0, m32, tanb, signmu
- Specify a
point in the
mamsb
parameter space. See [AguilarSaavedra:2005pw][Allanach:2002nj] for details.
- Options specific to the benchmark scenarios from [Carena:2002qg]
- tanb, MA
- Set tan(beta) and the mass of the pseudoscalar Higgs.
2.1.3 H3ChooseHH
Automatically choose a mass hierarchy suitable for the
current parameters. The hierarchies from which to choose are given in
the list H3`Private`H3HHList
. Hierarchies that do not fit the mass
spectrum are discarded. For each of the remaining hierarchies, the Higgs
mass is evaluated at the two-loop level, and the result is compared with
the exact result. The hierarchy with the smallest deviation is chosen.
This function is automatically called when parameters are being set
using the SLHA interface.
2.1.4 H3`Private`H3SetPar
This routine is used internally to give values to specific parameters.
It is possible for the user to use it directly, although care has to
be taken to maintain a consistent spectrum. In particular, it will
not be a good idea to use the routine H3m after modifying individual
parameters, since H3m combines corrections parametrised by
parameters with corrections given in terms on
on-shell parameters, and the conversion between the two schemes will
be spoiled.
The variable H3`Private`parameters
contains a list of all parameters
that are used by H3.m
.
2.1.5 H3GetSpectrum
This function returns the values of the parameters that are relevant
to the calculation of the Higgs mass. Most of the parameters are
given in the scheme. Names containing "OS" indicate that the
corresponding parameter is given in the on-shell scheme. The suffix
"mod" is given to parameters in the modified
scheme as described
in [Kant:2010tf]. All other parameters are given in the
scheme.
2.2 Functions for calculating the Higgs mass
The calculation of the Higgs mass is performed by the function H3m, which can be called after the parameters have been set using the SLHA interface described above. Without giving any options, it just returns the value of mh using the mass hierarchy that has been chosen to minimise the error at two loops.
2.2.1 H3m
This routine performs the calculation of the Higgs mass. FeynHiggs
is
queried for the neutral Higgs mass matrix including corrections up to
two loop order, using on-shell input parameters (masses of the top and
the SUSY particles). Subsequently, the O(αt) and O(αt
αs) contributions are subtracted, to be added again expressed
through parameters in the modified scheme described
in [Kant:2010tf]. This is neccessary in order to treat the corrections
from the top/stop sector consistently, since the three-loop
corrections are handled in the modified
scheme.
The function returns a replacement rule that, when applied, assigns
the Higgs mass to the symbol mh. By setting the option tests
, one
can increase the verbosity.
- Options
- HH
- Governs the choice of the mass hierarchy according to which the three-loop terms are expanded. If set to "auto", the optimal choice as determined by H3ChooseHH is used. Alternatively, one can choose the name of a specific hierarchy to force evaluation according to this hierarchy.
- upcut
- A list of lists of the form {DELTA, NN}. In the evaluation of the three-loop corrections, terms of Order > DELTANN are neglected. This is useful to get a feeling for the convergence in the expansion in the mass hierarchies (as in Figure 9 and Table 3 of [Kant:2010tf]).
- tests
- List of strings, where every string present causes the output to be more verbose.
- Possible strings are
- "FH2l"
- Give the
FeynHiggs
result, without any subtractions or additions. This will be calledmhFL1l
in the output. - "2lCompareWithDSZ"
- Make a comparison at the two-loop level
between the exact calculation of [Degrassi:2001yf] and the expansion in
the ratios of masses. Output will feature
mh2lDSZ
,mh2lHH
andrelerr2l
, the last of which is the relative error (in %) due to the expansion at two loops. - "1lCompareWithDSZ"
- as above, but with every 2 replaced by a 1.
- "expandAll"
- Instead of using the exact 1- and 2-loop results, use
the expansion in 1 through 3 loops. This check returns
mhHH
. - "showSpectrum"
- Give the value of the masses of the superpartners, the top mass, αs, etc. in the output.
- "all"
- Do all of the above checks.
2.2.2 H3mhmt4
Calculates Higgs mass taking into account only the mt4 corrections.
Since FeynHiggs
is not needed for this, this function does not rely on
the conversion of on-shell and corrections. This allows the
user to modify specific parameters in the
scheme (via
H3SetPar) without worrying about the corresponding
values in the on-shell scheme. This feature has been used, for
example, to produce figs. 2, 3 and 11 in [Kant:2010tf].
2.2.3 H3SchemeCompare
This routine compares the predictions for the Higgs mass using
and on-shell input parameters. Since the on-shell result
from [Harlander:2008ju] assumes a degenerate SUSY mass spectrum, in this
function a degenerate spectrum is assumed also in the
calculation.
2.2.4 H3ExpansionError
This function gives an estimate on the stability of the expansion in mass ratios at the three-loop level. It does so by comparing the Higgs mass calculated using all available terms with the value that results if the highest terms in the expansion are dropped. See fig. 9 in [Kant:2010tf] for an example.
3 Setup
3.1 Prerequisites
H3.m
is a Mathematica
package and thus needs Mathematica
. It
has been tested with versions 7 and 8. The one- and two-loop
corrections from other sectors of the MSSM are evaluated using the
Mathematica
version of FeynHiggs
[Heinemeyer:1998yj][Heinemeyer:1998np][Degrassi:2002fi][Frank:2006yh], MFeynHiggs
. Please note that
version 2.8.3 or later of FeynHiggs
is required.
To use the function H3SetSLHA (or any of the H3SetSPS
functions), you will need a spectrum generator. Currently,
softsusy
[Allanach:2001kg], SPheno
[Porod:2003um][Porod:2011nf] ans SuSpect
[Djouadi:2002ze] are supported by
H3SetSLHA. Of course, you do not have to use this
interface and could rely, instead, on H3GetSLHA to
read in spectrum files prepared by any other means.
3.2 Installation procedure
H3m
comes with an autoconf
generated configure
script, which
searches for the required programs and compilers. Make sure that the
executable files
MFeynHiggs (version >= 2.8.3) softpoint.x OR SPheno OR suspect2 math
are in a directory that is in your $PATH
variable. Then, unpack the file
H3.tar.gz
via
tar xzvf H3.tar.gz
which will create a directory H3
. Go to this directory and execute
configure
and make
:
cd H3 ./configure make make install
To install to some custom directory, you might want to use the
--prefix
option of configure
:
./configure --prefix=/path/you/want/to/install/to make && make install
3.2.1 Installation on 32bit architecture
The makefile assumes a 64bit architecture. To install on 32bit machines, you have to modify the file mh2l/makefile. Change the line
$(CC) -o $@ -I$(INCDIR) -L$(INCDIR) -lML64i3 -lm -lpthread -lrt -lstdc++ $(libs) -lm -shared-libgcc $^ -Wl,-rpath,$(INCDIR)
to
$(CC) -o $@ -I$(INCDIR) -L$(INCDIR) -lML32i3 -lm -lpthread -lrt -lstdc++ $(libs) -lm -shared-libgcc $^ -Wl,-rpath,$(INCDIR)
3.3 Changes
- v1.1: adapted to the new FeynHiggs version 2.8.x.
- v1.2: improved the calculation of the top mass in the
scheme to work for scales much higher than the top mass.
3.4 Acknowledgements
We thank Thomas Hahn for support regarding the inner workings of FeynHiggs and Karina Williams for useful comments about our program and this manual.
Footnotes:
1 Thanks to Thomas Hahn for confirmation.
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