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FEYNHIGGS 2.1: HIGH PRECISION CALCULATIONS IN THE

MSSM HIGGS SECTOR

T. Hahn1 , S. Heinemeyer 2 , W. Hollik 1 , G. Weiglein3

1 Max-Planck-Institut für Physik, Föhringer Ring 6, D–80805 Munich, Germany2 CERN, TH Division, CH–1211 Geneva 23, Switzerland3 Institute for Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, UK

Abstract

FeynHiggs 2.1 is a Fortran code for the evaluations within the Higgs-boson sec-

tor of the Minimal Supersymmetric Standard Model (MSSM) including possi-

ble complex phases. Besides the masses and mixing angles, all relevant decay

widths for the neutral and charged Higgs bosons are evaluated. The code can

easily be linked to other Fortran codes, it can be used as a stand-alone code, or

it can be called from Mathematica.

1. INTRODUCTION

The search for the lightest Higgs boson is a crucial test of Supersymmetry (SUSY) which can be per-

formed with the present and the next generation of accelerators. Especially for the Minimal Supersym-metric Standard Model (MSSM) a precise prediction for the masses of the Higgs bosons and their decay

widths to other particles in terms of the relevant SUSY parameters is necessary in order to determine the

discovery and exclusion potential of the upgraded Tevatron, and for physics at the LHC and future linear

colliders.

In the case of the MSSM with complex parameters (cMSSM) the task is even more involved.

Several parameters can have non-vanishing phases. In particular, these are the Higgs mixing parameter,

µ, the trilinear couplings,  Af ,  f   =   t,b ,τ , . . ., and the gaugino masses  M 1,  M 2, and  M 3   ≡  mg̃   (thegluino mass). Furthermore the neutral Higgs bosons are no longer  CP -eignestates, but mix with each

other once loop corrections are taken into account [1].

(h,H,A) → h1, h2, h3   with   mh1  ≤ mh2  ≤mh3 .   (1)

The input parameters within the Higgs sector are then (besides the Standard Model (SM) ones)  tan β ,the ratio of the two vacuum expectation values, and the mass of the charge Higgs boson,  M H ± .

2. THE CODE FeynHiggs 2.1

FeynHiggs 2.1  [2] is a Fortran code for the evaluation of masses and mixing angles in the MSSM with

real or complex parameters. The calculation of the higher-order corrections is based on the Feynman-

diagrammatic (FD) approach [3]. At the one-loop level, it consists a complete evalutaion, including

the full momentum dependence. The renormalization has been performed in a hybrid MS   /on-shellscheme [4]. At the two-loop level all existing corrections from the real MSSM have been included

(see Ref. [5] for a review). They are supplemented by the resummation of the leading effects from the(scalar) b  sector including the full complex phase dependence.

Besides the evaluation of the Higgs-boson masses and mixing angles, the program also includes

the evaluation of all relevant Higgs-boson decay widths. These are in particular:

•   the total width for the three neutral and the charged Higgs boson,

•   the BR’s of the Higgs bosons to SM fermions (see also Ref. [6]), BR(hi  → f  f̄ ), BR(H + → f  f̄ ′),

•  the to SM gauge bosons (possibly off-shell),  BR(hi  → γγ,ZZ ∗,WW ∗, gg),

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•   the decay into gauge and Higgs bosons,  BR(hi  → Zh j), BR(hi  → h jhk), BR(H + → hiW 

+),

•   the decay to scalar fermions, BR(hi  →  f̃ ̄f̃ ), BR(H + →  f̃ 

 ¯̃f ′),

•   the decay of the Higgs bosons to gauginos, BR(hi  → χ±k χ∓ j ), BR(hi  → χ

0l χ

0m),

BR(H + → χ+k χ0l ).

For comparisons with the SM the following quantities are also evaluated for SM Higgs bosons with the

same mass as the three neutral MSSM Higgs bosons:

•   the total decay widths,

•   the BR’s of a SM Higgs boson to SM fermions,

•   the BR’s of a SM Higgs boson to SM gauge bosons (possibly off-shell).

In addition, the following couplings and cross sections are evaluated

•   the coupling of Higgs and gauge bosons,  gV V hi , gV hihj ,

•   the Higgs-boson self couplings,  ghihjhk ,

•   the Higgs-boson production cross section at a  γγ   collider, σ(γγ  → hi).Finally as external constraints are evaluated

•   the ρ-parameter up to the two-loop level [7] that indicates disfavored scalar top and bottom masses

•   the anomalous magnetic moment of the muon, including a full one-loop calculation as well as

leading and subleading two-loop corrections [8].

Comparing our results to existing codes like Hdecay [9] (for the real case) or CPsuperH [10] (for

the cMSSM), we find differences in the mass evaluations for the lightest Higgs boson of  O(4 GeV).These are due to the inclusion of higher-order corrections in  FeynHiggs 2.1 that shift the lightest Higgs-

boson mass upwards. Concerning the BR evaluation (and compensating for the effects from the different

Higgs-boson masses) we find quantitative and qualitative agreement. For more details see Ref. [2].

FeynHiggs 2.1 possesses some further features that can be summarizes as,

•   transformation of the input parameters from the DR  to the on-shell scheme (for the scalar top andbottom parameters), including the full O(αs) and O(αt,b) corrections.

•   processing of Les Houches Accord (LHA) data [11]. FeynHiggs 2.1 reads the output of a spectrum

generator file and evaluates the Higgs boson masses, brachning ratios etc. The results are written

in the LHA format to a new output file.

•   the SPS benchmark scenarios [12] and the Les Houches benchmarks for Higgs boson searches at

hadron colliders [13] are given as a possibly predefined input

•   detailed information about all the features of  FeynHiggs 2.1 (see also the next section) are provided

in man pages.

3. HOW TO INSTALL AND USE FeynHiggs 2.1

To take advantage of all features of  FeynHiggs 2.1, the LoopTools library [14] needs to be installed,

which can be obtained from www.feynarts.de/looptools. Without this library,  FeynHiggs 2.1  will still

compile, but not all branching ratios will be available.

•  Download the package from www.feynhiggs.de.

•   Say ./configure and make. This creates libFH.a and the command-line frontend.

• To build also the Mathematica frontend, say  make all.There are three different ways to use  FeynHiggs 2.1.

3.1 The Fortran library

The libFH.a library can be linked directly to other Fortran programs. To avoid naming conflicts, all

externally visible symbols have been prefixed with “fh.” No include files are needed since the user calls

only subroutines (no functions). Detailed descriptions of the invocations of the subroutines are given in

the respective man pages.

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3.2 The command-line frontend

The FeynHiggs executable is a command-line frontend to the libFH.a library. It reads the parameters

from an ASCII input file and writes the output in a human-readable form to the screen. Alternatively,

this output can be piped through a filter to yield a machine-readable version appropriate for plotting

etc. The parameter file is fairly flexible and allows to define also loops over parameters. Also the Les-

Houches-Accord file format can be read and written.

3.3 The Mathematica frontend

The MFeynHiggs executable provides access to the libFH.a functions from Mathematica via the Math-

Link protocol. This is particularly convenient both because FeynHiggs 2.1  be be used interactively this

way and because Mathematica’s sophisticated numerical and graphical tools, e.g. FindMinimum, are

available.

References

[1] A. Pilaftsis, Phys. Rev. D 58 (1998) 096010;  Phys. Lett.  B 435 (1998) 88.

[2] T. Hahn, S. Heinemeyer, W. Hollik, G. Weiglein,  in preparation; see also:

S. Heinemeyer, W. Hollik, G. Weiglein,  Comp. Phys. Comm. 124 2000 76; hep-ph/0002213.

The codes are accessible from www.feynhiggs.de.

[3] S. Heinemeyer, Eur. Phys. Jour. C 22 (2001) 521;

M. Frank, S. Heinemeyer, W. Hollik, G. Weiglein, hep-ph/0212037.

[4] M. Frank, S. Heinemeyer, W. Hollik, G. Weiglein, hep-ph/0202166.

[5] G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich, G. Weiglein, Eur. Phys. Jour. C 28 (2003) 133.

[6] S. Heinemeyer, W. Hollik, G. Weiglein, Eur. Phys. Jour. C 16 (2000) 139.

[7] A. Djouadi, P. Gambino, S. Heinemeyer, W. Hollik, C. Jünger, G. Weiglein,   Phys. Rev. Lett.  78

(1997) 3626; Phys. Rev. D 57 (1998) 4179;

S. Heinemeyer, G. Weiglein, JHEP 0210 (2002) 072; hep-ph/0301062.

[8] S. Heinemeyer, D. Stöckinger, G. Weiglein, hep-ph/0312264.

[9] A. Djouadi, J. Kalinowski, M. Spira, Comput. Phys. Commun. 108 (1998) 56.

[10] J. Lee, A. Pilaftsis et al., hep-ph/0307377.

[11] P. Skands et al., hep-ph/0311123.

[12] B. Allanach et al., Eur. Phys. Jour. C 25 (2002) 113.

[13] M. Carena, S. Heinemeyer, C. Wagner and G. Weiglein, Eur. Phys. Jour. C 26 (2003) 601.

[14] T. Hahn, M. Pérez-Victoria,  Comput. Phys. Commun. 118 (1999) 153.