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Decay widths of all MSSM scalars at full one-loop level. Helmut Eberl together with Hana Hlucha and Wolfgang Frisch. Loops and Legs in QFT, Wörlitz, Germany, 29 th April 2010. Outline. Motivation MSSM, Sfermion/Higgs mass matrices Sfermion/Higgs decays

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Decay widths of all MSSM scalars

at full one-loop level

Helmut Eberl

together with Hana Hlucha and Wolfgang Frisch

Loops and Legs in QFT, Wörlitz, Germany, 29th April 2010


  • Motivation

  • MSSM, Sfermion/Higgs mass matrices

  • Sfermion/Higgs decays

  • Details of programs

  • Numerics

  • Outlook

Program Packages that calculate all MSSM Higgs1 and Sfermion2 decays at full one-loop level

  • Motivation:

    • All SUSY-QCD known, but full EW corr. only for some processes really calculated up to now

    • No complete one-loop code publicly available up to now

    • Total one-loop widths are necessary for 23 one-loop processes with resonant propagators

    • Loops -precision calculation - measurement underlying Lagrangian - next talk by Sven Heinemeyer

[1] PhD thesis W. Frisch

[2] PhD thesis H. Hlucha

The Minimal Supersymmetric Standard Model

  • To every SM particle a SUSY partner is introduced, both members of the same multiplet and the d.o.f. are more than doubled.

  • The structure of the SM is automatically included.

  • New particles are predicted, super partners (sparticles) of the SM particles – SUSY models have a rich phenomenology.

Superpotential – generalisation of the Yukawa interactions of the SM:

all fields are here chiral multiplets,

m can be complex

are the 3 x 3 Yukawa matrices

  • Work is done in the “real” 24-parameter MSSM

Chiral supermultiplets:

5 phys. Higgs bosons

can mix

can mix

4 neutralinos

2 charginos

Gauge supermultiplets:

Interaction states – physical states

Particle mixing: MSSM scalars: Higgs bosons, sfermions

MSSM fermions: charginos, neutralinos

Mass matrices – Eigenvalue problems

Two-body decays

possible tree-level structures:

Higgs bosons














Higgs couplings to gauge bosons

From the Lagrangian with the covariant derivatives

we get the gauge boson masses

and the couplings with one and two gauge bosons to the Higgs bosons, e.g.

couplings proportional to

In decoupling limit:



Higgs couplings to fermions

Yukawa couplings

Decoupling limit

[1] M. Carena et al, 1999, 2000


3 x









wave fct. CTs

coupling CTs

only UV div. parts

technical trick

DRbar scheme: UV divergence D = 0

(note: tree-level couplings given at scale Q)

automatic check of

RGE invariance

always on-shell masses

Status of calculations

  • flavor conserving MSSM for real input parameters

  • all necessary amplitudes are calculated using FeynArts 3.2/FormCalc 5.3

  • the renormalization is done in the DRbar-scheme following the SPA convention

  • own written counter term file for the whole MSSM

  • automatic generation of fortran code of each channel

  • general Rx gauge implementation

  • hard Bremsstrahlung included with generic formulas

  • MSSM.mod filter to coupling matrices with explicit Yukawa couplings Yuk(type,gen)

  • “naïve” hb = Yuk(4,3) resummation included

  • fortran programs for Higgs and Sfermion widths already work

  • Mathematica link programs exist

  • SUSY spectrum is calculated using SPHENO

    • In- and output in Les Houches Format

S usy p arameter a nalysis project
SUSY Parameter Analysis project*


In order to get information on fundamental SUSY parameters and

SUSY-breaking mechanism in the MSSM:

observables shall be measured with high accuracy.

LHC – explorer machine

will see SUSY with masses at ~ 1 TeV scale, squark and gluino decays

ILC - high precision machine – requires equally theor. calc. including higher orders

Need of a well-defined theoretical framework:

SPA convention provides a clear base for calculating masses, couplings,

mixing, decay widths and production cross sections.

Program repository

theor. and exp. analyses, LHC+ILC tools, Les Houches Accord

Reference point SPS1a’

*J. A. Aguillar-Saavedra et al., EPJ C46 (2006) 43; see also J. Kalinowski, Acta Phys. Polon. B37 (2006), 1215

Spa convention
SPA convention

  • Massesof SUSY particles and Higgs bosons defined as pole masses

  • All SUSY Lagrangian parameters are in the DRbar scheme at Q = 1TeV

  • All elements in mass matrices, rotation matrices and corresponding mixing angles are def. DRbar at Q, except (h0 –H0) mixing angle is defined on-shell with p = mh0

  • SM input parameters: GFermi, α, mZ, as(mZ) and fermion masses

  • Decay widths/branching ratios and production cross section are calculated for the set of parameters specified above

Linear Rx gauge


  • In order to cancel the IR divergencies we have included

  • real photon/gluon radiation:

  • soft radiation – dependent on cut DE, automatized in FC

  • hard radiation – analytic results for integrals used from [1] four generic structures analytically derived and used

The simplest case is scalar -> scalar scalar g/g:

[1] A. Denner, Fortschr. Phys. 41 (1993) 307


Program description:

The program code is written in Fortran 77

  • At the program start the input file is read with the following options:

  • name of Les Houches input file

  • selection of higgs particle: h0 = 1, H0 = 2, A0 = 3 ,H+ = 4, All = 5

  • contribution: tree = 0, full one loop = 1, SQCD = 2

  • bremsstrahlung: off = 0, hard bremsstrahlung = 1, soft bremsstrahlung = 2

  • Higgs masses calculator: tree level masses = 0, SPheno masses = 1, FeynHiggs masses = 2

  • Name of output file

Structure of “SfermionDecay” similar

Reference point sps1a
Reference point SPS1a’

DRbar parameter at Q = 1 TeV

mSUGRA benchmark points:

Low Mass points

High Mass points


First versions of decay programs will be on the web soon!

  • Bottom Yukawa coupling resummation to improve, see [1]

  • Decay with vanishing tree-level, use of (one-loop)2 [2]

  • Higgs sector, input aeff

  • Extension to complex MSSM

  • h0 loop decays – 2loop improvements?

  • leading (strong) 2loop contributions?

  • MSSM fermion decays?

  • developed technique applicable for 2 to 2 and 2 to 3 processes

[1] L. Hofer, U. Nierste, D. Scherer, 2009, [2] S. Bejar, talk at HEPTOOLS meeting, Lisbon 2009