Decay widths of all MSSM scalarsat full one-loop level

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

Helmut Eberl together with Hana Hlucha and Wolfgang Frisch

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Motivation

MSSM, Sfermion/Higgs mass matrices

Sfermion/Higgs decays

Details of programs

Numerics

Outlook

OutlineOutline

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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 23 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

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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, are the 3 x 3 Yukawa matrices

can be complex

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

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Gauge supermultiplets:

Chiral supermultiplets:

4 neutralinos 2 charginos

5 phys. Higgs bosons

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Interaction states – physical statesParticle mixing: MSSM scalars: Higgs bosons, sfermions

MSSM fermions: charginos, neutralinos

Mass matrices – Eigenvalue problems

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“decoupling limit”

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Sfermion sector in the MSSM

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Two-body decays Two-body decays

Higgs bosons

scalar

scalar

scalar

scalar

possible tree-level structures:

Sfermions

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Higgs couplings to gauge bosonsHiggs 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:0 1

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Higgs couplings to fermionsHiggs couplings to fermions

Yukawa couplings

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

Decoupling limit

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RenormalizationRenormalization

= + + +1loopren.

tree vertex

3 x

wave fct. CTs coupling CTs

DRbar scheme: UV divergence = 0 (note: tree-level couplings given at scale Q)

only UV div. partstechnical trick

automatic check of RGE invariance

always on-shell masses

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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 R 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

Status of calculationsStatus of calculations

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SUSY Parameter Analysis project*

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

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

Reference point SPS1a’

http//spa.desy.de/spa

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SPA convention

Masses of 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

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Linear R gaugeLinear R gauge

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BremsstrahlungBremsstrahlung

In order to cancel the IR divergencies we have includedreal photon/gluon radiation:• soft radiation – dependent on cut E, automatized in FC• hard radiation – analytic results for integrals used from [1] four generic structures analytically derived and used

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

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

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All numerical results preliminary

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The program code is written in Fortran 77

At the program start the input file config.in 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

“SusyHiggsDecay”“SusyHiggsDecay”

Structure of “SfermionDecay” similar

Program description:

Reference point SPS1a’

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DRbar parameter at Q = 1 TeV

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mSUGRA benchmark points:

Low Mass points

High Mass points

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Bottom Yukawa coupling resummation to improve, see [1]

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

Higgs sector, input eff

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

OutlookOutlook

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

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Thank you for your attention!