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HDECAY/CHANGES
Basil Bruhn 4884213286 initial
Signed-off-by: Basil Bruhn <basil.bruhn@psi.ch>
2025-11-17 10:04:29 +01:00

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This is a list of changes to hdecay.f since April 1997:
July 24 2025: - extension of the grids for the NLO quark mass effects
in H -> gg to 3 TeV (for BSM studies)
February 21 2025: - removed link to FeynHiggsFast due to compilation
problems (thanks to M. Vos)
April 04 2022: - bug fix (lines to be commented out) in calculation of
MSSM Higgs decays to bb for the genuine SUSY-QCD
corrections
(thanks to E. Bagnaschi)
July 23 2021: - bug fix in off-shell H -> hh* decays for the 2HDM
(thanks to L. Friedrich)
July 12 2021: - bug fix in hsqsq.f (thanks to E. Bagnaschi)
March 12 2021: Version 6.61:
- additional option to input the scale choice mu=kappa*M_H
for Higgs decays into quarks for studies of QCD scale
dependence
- additional option to input alpha_s(kappa*M_H),
m_s(kappa*M_H), m_c(kappa*M_H) and m_b(kappa*M_H) at the
scale kappa*M_H at which Higgs decays into quarks are
calculated
- refinements in the treatment of Higgs decays into quarks
(impact small)
- for details of the new input lines see comment lines at
beginning of hdecay.f
February 18 2021: Version 6.60:
- extension of MSSM Delta_b effects to elw. 2-loop
corrections proportional to alpha_1 and alpha_2
according to arXiv:1711.02555
- inclusion of top-stop-induced corrections to H -> hh
within the MSSM and hMSSM in the full EFT approach
according to arXiv:1810.10979
- additional option to input the running MSbar quark masses
m_s(M_H), m_c(M_H) and m_b(M_H) instead of the default
input m_s(2 GeV), mc(3 GeV), m_b(m_b) (only for SM!)
April 3 2020: Version 6.53:
- modification of SUSY-QCD corrections to h/H/A -> bb for
proper Delta_b terms
October 1 2018: - removal of incomplete NNLO mass terms in scalar Higgs
decays into massive quarks (thanks to W. Kotlarski)
May 7 2018: - instability in scalar 2-point functions removed
January 12 2018: Version 6.52:
- extension of Delta_b terms by A_b at NNLO implemented
- extension to Delta_s terms at NNLO implemented
- corrections of inconsistencies in the interface for
the 2HDM
- small refinements in MSSM Higgs decays into gluons
October 11 2016: Version 6.511:
- typos corrected in the off-shell decays H -> AZ*,
A -> hZ* (thanks to J. Romao)
(numerical impact below thresholds in MSSM for these decays)
January 13 2016: Version 6.51:
- bug fixes of SLHA interface
- removal of superfluous flag NNLO(M) from input file
December 1 2015: - Version 6.50: Input for bottom and charm masses
changed to the MSbar masses mb(mb) and mc(3 GeV). The
impact on the partial decay widths and branching
ratios is far below 1%. (The charm and bottom pole
masses are calculated internally.)
November 27 2015: - Version 6.43: Flag for exclusion of elw. corrections
for SM Higgs (and for COUPVAR = 1) decays included
July 27 2015: - Initialization of variables for H -> gg, gamma gamma
completed (thanks to M. Sampaio)
June 15 2015: - Instability for mass degenerate neutralinos removed
(thanks to H. Prosper)
June 13 2015: - Bug in interpolation for H -> gg corrected causing stability
problems for Higgs masses beyond 1 TeV
(thanks to M. Rodriguez-Vazquez)
April 10 2015: - Version 6.41 -> 6.42: removing an instability for the
hMSSM at low tan(beta) values (thanks to N. Rompotis)
January 5 2015: - Version 6.40 -> 6.41: addition of radiative
corrections to Higgs self-interactions within the hMSSM?
December 24 2014: - Version 6.31 -> 6.40: addition of hMSSM? to the MSSM
part (see description at top of fortran file)
- implementation of rescaled couplings for the SM4
December 15 2014: - Version 6.30 -> 6.31: stabilization of two-loop
corrections to Delta_b terms
(thanks to F. Frensch and S. Heinemeyer)
December 10 2014: - Version 6.20 -> 6.30: corrections of instabilities
in the MSSM Higgs self-interactions
- correction of inconsistent scheme choices in SLHA
input with implementation of h/H/A -> bb
(thanks to S. Heinemeyer)
November 9 2014: - Version 6.12 -> 6.20: extension to full NLO elw.
corrections for SM Higgs decays into fermion pairs
October 23 2014: - Version 6.11 -> 6.12: inaccuracy corrected for
SUSY-QCD corrections to h/H/A -> bb within the MSSM.
Numerical impact sizeable for scenarios with large
Delta_b corrections.
July 31 2014: - Version 6.10 -> 6.11: removal of instabilities for 2HDM
runs. No effect on results (thanks to Travis Martin)
January 17 2014: - update of HDECAY: Version 6.00 -> 6.10
- extension of 2HDM to lambda input
- signs in Delta_tau/mu corrected, elw. corrections
extended
- elw. corrections to Delta_b/s added
December 16 2013: - Typo in calculation of top width for the 2HDM case
corrected. (thanks to R. Santos)
- Improvement of Delta_b corrections. Numerical impact
small.
December 9 2013: - Syntax corrected in HDECAY output. No effect.
December 6 2013: - Small typos in charged Higgs decays corrected.
Numerical impact small.
November 27 2013: - small bug in charged Higgs decays for the 2HDM
corrected. Numerical impact small.
(thanks to J. Rathsman)
November 24 2013: - Major update of HDECAY: Version 5.11 -> 6.00
- Extension to general 2HDM:
added flag 2HDM and the 2HDM input parameters to
input file
added many additional 2HDM decay modes including
off-shell contributions
- several typos corrected in the off-shell decays
H -> AZ*, H -> H+W*, A -> hZ*, H+ -> t*b and H -> t*t
(numerical impact below thresholds in MSSM)
- added MSSM charged Higgs decays H+ -> cd, ts, td
(including off-shell top quark contributions)
- modified the interpolation between threshold and
large charged Higgs range (running mass effects,
Delta_b/s corrections)
- implementation of full CKM mixings in charged Higgs
and top decays with extended input file
September 4 2013: - Typo corrected in H -> squark squark decays.
Numerical impact small.
August 22 2013: - Typo corrected in off-shell decays H -> hh. No
numerical impact.
August 2 2013: - Typo corrected in SUSY-QCD corrections to Higgs -> gg
within the MSSM. Numerical effect negligible.
May 23 2013: - Version 5.11: improvement of calculating input parameters
for subroutine SUBH1 by resumming SUSY-QCD effects (small
numerical impact)
April 2 2013: - SLHA interface extended to cover the case of vanishing
SUSY scale in SLHA input file
March 8 2013: - bug corrected in link to FeynHiggsFast
(thanks to D. Chowdhury)
February 27 2013: - bug corrected in H -> Z gamma for different top and
charm coupling factors
February 21 2013: - Version 5.10: Implemented the Delta_mu corrections to
the muon Yukawa couplings within the MSSM
- sneutrino masses of the first two generations are
properly split from those of the third generation
February 11 2013: - Version 5.09: 2-loop QCD corrections to top decay width
added
February 8 2013: - Version 5.08: Even further refinements of the treatment
of scaling factors of the Higgs couplings in the
NNLO QCD corrections to Higgs boson decays into quarks
January 17 2013: - Version 5.07: Further refinements of the treatment of
scaling factors of the Higgs couplings in the NNLO QCD
corrections to Higgs boson decays into quarks
December 3 2012: - Version 5.06: Treatments of novel point-like
couplings for H -> gg corrected for the case ELWK = 1
November 12 2012: - Version 5.05: Charged Higgs decay into tau nu
corrected (thanks to S. Lehti)
November 9 2012: - Version 5.04: Treatment of novel point-like couplings
for H -> Z gamma corrected
- sign mistake in pseudoscalar Higgs couplings to
charginos and neutralinos corrected (thanks to G.
Belanger and A. Pukhov)
November 7 2012: - Version 5.03: Treatments of novel point-like couplings for
H -> gg, gamma gamma corrected
November 5 2012: - Version 5.02: Bug in statement function DHGGQCD2
corrected. Numerical effect for a pointlike Hgg coupling
negligible.
November 2 2012: - Version 5.01: Bug in implemention of SLHA interface
corrected (thanks to G. Belanger and A. Pukhov)
October 31 2012: - Bug in feynhiggs.f corrected (not our fault)
October 16 2012: - Major update of HDECAY: Version 4.45 -> 5.00
- Added electroweak corrections to H -> gg in the SM4
for m_t' = 500 GeV, m_b' = 450 GeV, m_nu'=375 GeV,
m_l' = 450 GeV in addition to the previous scenario.
Added a flag for the choice of the scenario.
- Corrected a flag in the SLHA output for the light scalar h
- Implemented NLO quark mass effects to H -> gg within
the SM
- Implemented charm quark loops in H -> gg
- Implemented scaling factors for the Higgs couplings to
fermions and gauge bosons as well as point-like
couplings to gluons, photon and Z+photon along with an
extension of the input file (see comment card). The
rescaling can be switched on and off by the flag COUPVAR.
The treatment of elw. corrections can be controlled
by the flag ELWK.
- Implemented the Delta_tau corrections to the tau
Yukawa couplings within the MSSM
March 13 2012: - Update of HDECAY: Version 4.44 -> 4.45
- Improvement of the approximate NLO elw. corrections to
H -> gamma gamma within the SM4
February 27 2012: - Update of HDECAY: Version 4.43 -> 4.44
- Bug corrected in subroutine RUNM_HDEC for SM4 Higgs
bosons which affected the running masses for M_b' >
M_t'. (thanks to A. Mueck)
November 14 2011: - Update of HDECAY: Version 4.42 -> 4.43
- inclusion of block VCKMIN in SLHA input/output
according to SLHA2
November 11 2011: - Update of HDECAY: Version 4.41 -> 4.42
- corrections in SLHA input
(thanks to A. Pukhov)
November 10 2011: - Update of HDECAY: Version 4.40 -> 4.41
- inclusion of top decays in SLHA output
- inclusion of new blocks in SLHA input according to
SLHA2
- inclusion of approximate NLO elw. corrections to
H -> gamma gamma in the SM4
- small update of elw. corrections to H -> gg in the SM4
- small corrections in SLHA input and output
(thanks to G. Belanger)
October 11 2011: - Update of HDECAY: Version 4.31 -> 4.40
- inclusion of approximate NLO and NNLO elw. and
elw.+QCD corrections to H -> ff, WW, ZZ in the SM4
August 29 2011: - Update of HDECAY: Version 4.30 -> 4.31
- inclusion of refinements in the QCD corrections of top
decays
August 26 2011: - Update of HDECAY: Version 4.20 -> 4.30
- inclusion of running bottom Yukawa coupling effects
and finite bottom mass effects in top decays. The
running bottom Yukawa coupling effects are sizeable,
the finite bottom mass effects small.
August 18 2011: - Update of HDECAY: Version 4.11 -> 4.20
- small inconsistencies corrected in SLHA output (thanks
to M. Hauru)
- Delta_b corrections added to t -> bH+ decays
August 17 2011: - Update of HDECAY: Version 4.10 -> 4.11
- Bug corrected in new Delta_s corrections
August 16 2011: - Update of HDECAY: Version 4.01 -> 4.10
- Inclusion of Delta_s corrections to strange Yukawa
couplings within the MSSM
- Added Output of top quark branching ratios and total
width in file br.top within the MSSM.
- Added electroweak corrections to H -> gg in the SM4
for m_t' = m_b' + 50*(1+1/5*log(M_H/M_ref)) GeV with
M_ref=115 GeV and m_b'=m_l'=m_nu'=600 GeV using the
grid of the paper
%\cite{Passarino:2011kv}
\bibitem{Passarino:2011kv}
G.~Passarino, C.~Sturm and S.~Uccirati,
%``Complete Electroweak Corrections to Higgs production in a Standard
%Model
%with four generations at the LHC,''
arXiv:1108.2025 [hep-ph].
%%CITATION = ARXIV:1108.2025;%%
June 20 2011: - Update of HDECAY: Version 4.00 -> 4.01
- Adjustment of the renormalization of A_t in the NNLO
SUSY-elw. corrections to Delta_b for consistency with the
input parameter
- Addition of (tiny) mass effects to H -> qq at NNLO QCD
June 4 2011: - Update of HDECAY: Version 3.80 -> 4.00
- Inclusion of a SM 4th generation; output file br.sm3
added for decays into 4th generation fermions
- Inclusion of dominant elw. corrections to H -> WW,ZZ in
the fermiophobic and 4th generation SM
- Added 4-loop QCD corrections to H -> gg decays
- Added 3-loop QCD corrections to A -> gg decay
- Implementation of the NNLO running of alpha_s for
consistency with HO corrections beyond NLO. The input
value of alpha_s(M_Z) is now the value for the NNLO
alpha_s.
May 27 2011: - Update of HDECAY: Version 3.71 -> 3.80
- Several modifications of write and read statements to
make them compatile with the gfortran compiler
(thanks to N. Mahmoudi).
- Inclusion of double off-shell contributions of MSSM Higgs
decays into WW and ZZ above threshold
- Defining the MSbar strange quark mass at the scale 2 GeV
instead of 1 GeV as input
- Added 4-loop QCD corrections to H -> qq (q.ne.t) decays
May 13 2011: - Several corrections to allow for negative gluino masses
April 23 2011: - Update of HDECAY: Version 3.60 -> 3.70
- Implementation of fermiophobic Higgs model with SM
Higgs couplings to gauge and Higgs bosons
April 14 2011: - Update of HDECAY: Version 3.53 -> 3.60
- Implementation of SUSY-QCD corrections to Higgs decays
into squarks
- Implementation of NLO-improved squark sector (SUSY-QCD)
- Inclusion of QCD corrections to the top width
- Inclusion of subleading terms in the two-loop SUSY-QCD
corrections to the MSSM bottom Yukawa couplings related
to the stop mixing (thanks to L. Mihaila for comparison)
- Extension of elw. corrections to H -> gamma gamma to
M_H = 1 TeV (thanks to G. Passarino et al.)
- Adjustments of SLHA interface
November 5 2010: - Corrections of the interface to the SLHA (thanks to
M. Warsinski)
June 16 2010: - Changes to declarations of complex functions and reading
the SLHA (thanks to N. Mahmoudi).
June 8 2010: - Reordering variables in Common block DAVID.
May 18 2010: - Missing lines in subroutine SFERMION_HDEC added to define
all variables in the common block SQNLO_HDEC (thanks to J.
Zurita).
April 7 2010: - Update of HDECAY: Version 3.52 -> 3.53
- NNLO QCD corrections to H -> gg implemented according
to Chetyrkin et al., PRL79 (1997) 353
- Electroweak corrections to H -> gamma gamma implemented up
to MH=170 GeV (thanks to G. Passarino et al.).
Please, cite the following papers for these corrections:
%\cite{Passarino:2007fp}
\bibitem{Passarino:2007fp}
G.~Passarino, C.~Sturm and S.~Uccirati,
%``Complete Two-Loop Corrections to H -> gamma gamma,''
Phys.\ Lett.\ B {\bf 655} (2007) 298
[arXiv:0707.1401 [hep-ph]].
%%CITATION = PHLTA,B655,298;%%
%\cite{Actis:2008ts}
\bibitem{Actis:2008ts}
S.~Actis, G.~Passarino, C.~Sturm and S.~Uccirati,
%``NNLO Computational Techniques: the Cases H -> gamma gamma and H ->
%g g,''
Nucl.\ Phys.\ B {\bf 811} (2009) 182
[arXiv:0809.3667 [hep-ph]].
%%CITATION = NUPHA,B811,182;%%
April 1 2010: - Update of HDECAY: Version 3.51 -> 3.52
Electroweak corrections to H -> gg implemented in
factorized form (thanks to G. Passarino et al.).
Please, cite the following papers for these corrections:
%\cite{Actis:2008ts}
\bibitem{Actis:2008ts}
S.~Actis, G.~Passarino, C.~Sturm and S.~Uccirati,
%``NNLO Computational Techniques: the Cases H -> gamma gamma and H ->
%g g,''
Nucl.\ Phys.\ B {\bf 811} (2009) 182
[arXiv:0809.3667 [hep-ph]].
%%CITATION = NUPHA,B811,182;%%
%\cite{Actis:2008ug}
\bibitem{Actis:2008ug}
S.~Actis, G.~Passarino, C.~Sturm and S.~Uccirati,
%``NLO Electroweak Corrections to Higgs Boson Production at Hadron
%Colliders,''
Phys.\ Lett.\ B {\bf 670} (2008) 12
[arXiv:0809.1301 [hep-ph]].
%\cite{Actis:2008uh}
\bibitem{Actis:2008uh}
S.~Actis, G.~Passarino, C.~Sturm and S.~Uccirati,
%``Two-Loop Threshold Singularities, Unstable Particles and Complex
%Masses,''
Phys.\ Lett.\ B {\bf 669} (2008) 62
[arXiv:0809.1302 [hep-ph]].
%%CITATION = PHLTA,B669,62;%%
July 8 2009: - Update of HDECAY: Version 3.5 -> 3.51
Further refinements included in off-shell decays
H -> W*W*, Z*Z*. Now agreement within 1% with the elw.
corrected results of A. Bredenstein et al.,
PRD74 (2006) 013004 and JHEP 0702 (2007) 080.
(thanks to A. Bredenstein for providing numbers for
comparison)
Please, cite the following papers for these corrections:
%\cite{Bredenstein:2006rh}
\bibitem{Bredenstein:2006rh}
A.~Bredenstein, A.~Denner, S.~Dittmaier and M.~M.~Weber,
%``Precise predictions for the Higgs-boson decay H ---> WW/ZZ ---> 4
eptons,''
Phys.\ Rev.\ D {\bf 74} (2006) 013004
[hep-ph/0604011].
%%CITATION = HEP-PH/0604011;%%
%\cite{Bredenstein:2006ha}
\bibitem{Bredenstein:2006ha}
A.~Bredenstein, A.~Denner, S.~Dittmaier and M.~M.~Weber,
%``Radiative corrections to the semileptonic and hadronic Higgs-boson
ecays H ---> W W / Z Z ---> 4 fermions,''
JHEP {\bf 0702} (2007) 080
[hep-ph/0611234].
%%CITATION = HEP-PH/0611234;%%
June 25 2009: - Update of HDECAY: Version 3.4 -> 3.5
Inclusion of off-shell decays H -> W*W*, Z*Z* above
threshold and approximations for their electroweak
corrections according to A. Bredenstein et al.,
PRD74 (2006) 013004
November 24 2008: - Bugs in interpolation of off-shell decays
H -> hh,AA,AZ,H+W- for SLHA interface corrected
(thanks to J. Rathsman, T. Rizzo, C.F. Berger,
J. Hewett and J.S. Gainer)
- Minor improvements in SLHA interface
(neutralino/chargino masses and mixing)
- 2-Loop corrections to MSSM bottom Yukawa couplings
included (according to PRL 101 (2008) 181801)
- Squarkmasses calculated from quark pole masses
instead of running MSbar masses.
January 31 2008: - Bug in routine FINT1_HDEC corrected (thanks to K. Moenig)
October 10 2007: - Minor corrections in the SLHA in and output
September 13 2007: - Minor corrections in the SLHA output
September 12 2007: - Inclusion of delta_mb effects in charged Higgs
decays
June 14 2007: - Update of HDECAY: Version 3.200 -> 3.300
Inclusion of fully massive (SUSY-)QCD corrections to
Higgs -> gamma gamma
September 1 2006: - Update of HDECAY: Version 3.103 -> 3.200
Link to SUSY Les Houches Accord implemented.
M. Muehlleitner added to the authors.
February 15 2006: - Correcting typos in charged Higgs couplings to
sfermions (thanks to U. Ellwanger)
August 15 2005: - Correcting a typo in function QCDMI(X,Y) for charged
Higgs decays (thanks to A. Ferrari).
May 3 2005: - Uncommenting top Yukawa corrections to delta_mb (thanks to
S. Mrenna)
October 20 2003: - Removal of 'dreal' in feynhiggs.f at places causing
problems with alpha (OSF1) workstations (thanks to
A. Pukhov)
September 19 2003: - Small change of analytical structure of SUSY-QCD
corrections to Higgs -> bb (thanks to G. Weiglein).
The numerical effect is tiny.
- Addition of subroutines for loop integrals
- Addition of scale choice to subroutine SFERMION
February 24 2003: - Addition of COMMON block COMMON/FLAGS_HDEC/INDIDEC
to subroutine READ_HDEC for individual SUSY decays
October 16 2002: - Correction of typo in line 344 (thanks to T. Farris).
This does not affect the results at all.
September 27 2002: - Corrections in the link to FeynHiggsFast (thanks to
M. Schumacher and S. Heinemeyer)
September 24 2002: - Corrections in the link to FeynHiggsFast to make
the renormalization schemes consistent
September 20 2002: - Corrections in the link to FeynHiggsFast
- Shortening of line 1103 in hdecay.f
- Passing flag INDIDEC to read and write routines
September 19 2002: - Major update of HDECAY: version 2.0 -> 3.0.
The following things have been added:
1.) SUSY-QCD corrections to h,H,A -> bb including
resummation (thanks to J. Guasch and P.
Haefliger for checking)
2.) Links to more routines for MSSM Higgs masses:
subh, subhpole, Haber et al., FeynHiggsFast
3.) Extension of 2-loop RGE approach to Higgs
selfinteractions
4.) Addition of decays into gravitino + gaugino
5.) Reorganization of subroutines and main program
6.) Renaming of subroutines, functions and common blocks
in order to allow for simpler links to other programs
(all names have the extension _HDEC now)
The new input parameters are described at the
beginning of hdecay.f.
November 30 2001: - If branch in subroutine SUSYCP added to prevent a
program crash. This does not change any results
(thanks to Elena Accomando).
July 20 2001: - Typos in pseudoscalar decays into fermions corrected.
The numerical differences are small.
July 11 2001: - Instability for small pseudoscalar masses corrected in
subroutine SUBH and H -> hh decays. Numerical results
are unchanged (thanks to Vladimir Rykov).
March 10 2001: - Typos corrected in lines 1363-1364,1375-1377,1387-1389,
2268-2270,2280-2282,2292-2294. The typos affect the
branching ratios for h,H -> gg in the MSSM, but are
numerically small for conventional MSSM scenarios
(thanks to Tao Han).
December 12 2000: - Typos corrected in lines 1345,1509,2248 and 2468. The
numerical effect is small (thanks to S. Heinemeyer).
August 23 2000: - Typos corrected in lines 536 and 1284, which do not
cause any changes of the numerical results
(thanks to F. von der Pahlen and G. Polesello)
- If cases added to subroutine SFERMION, which do not
cause any changes of the numerical results.
June 22 2000: - Addition of lines 2254-2258, the omission of which caused
problems for HIGGS=2 and OFF-SUSY=1 (thanks to A. Freitas)
December 20 1999 : - Typos corrected in first generation squark-loops of
h,H -> gg, gamma gamma (thanks to M. Muehlleitner)
- Typos corrected in pseudoscalar Higgs decays into
squarks (thanks to J.-B. de Vivie)
December 1 1998 : - Typos corrected in off-shell decays H+ -> W*h, W*A
in lines 2000,2001,2010,2018,2020,2051 (thanks to
Abdeslam Arhrib).
- Evaluation of top quark decay width (GAMT1) shifted
into subroutine HDEC.
October 30 1998 : - Typos corrected in QCD corrections to charged Higgs
decays into quarks in lines 882,883,886,887 (thanks
to Hong-Jian He)
August 20 1998 : - Typo corrected in WRITE statement in line 418
June 18 1998 : - Modifications in subroutine HDEC for the SUSY decays
in order to allow for loops switching on and off the
SUSY decays (thanks to E. Richter-Was)
May 16 1998 : - Bug in paper of Carena et al. fixed. Subroutine SUSYCP
corrected for Higgs pole masses (bottom quark loops for large
tan(beta)).
April 22 1998 : - Removing an instability in H -> Z*A for large tan(beta) at
large Higgs masses M_H (thanks to W. Kilian).
April 15 1998 : - Change of variable names in line 634:
BHQSLQDL,BHQSLQDR -> BHLSQDL,BHLSQDR (Sorry!)
January 13 1998 : - Change of variable names in line 634:
BHQSLDL,BHQSLDR -> BHQSLQDL,BHQSLQDR
August 29 1997 : - Interchange of Fortran lines in subroutines HDECAY and RUNM
(thanks to T. Schoerner)
July 21 1997 : - Interpolation in H -> hh, AA modified in subroutine HDEC
(thanks to T. Schoerner)
- Sfermion mixing angles modified in subroutines SFERMION and
SUSYCP (thanks to F. Borzumati)