Decay widths of all MSSM scalars at full one-loop level

1. 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

2. Outline • Motivation • MSSM, Sfermion/Higgs mass matrices • Sfermion/Higgs decays • Details of programs • Numerics • Outlook

3. 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

4. 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

5. Chiral supermultiplets: 5 phys. Higgs bosons can mix can mix 4 neutralinos 2 charginos Gauge supermultiplets:

6. Interaction states – physical states Particle mixing: MSSM scalars: Higgs bosons, sfermions MSSM fermions: charginos, neutralinos Mass matrices – Eigenvalue problems

8. “decoupling limit”

9. Sfermion sector in the MSSM

10. Two-body decays possible tree-level structures: Higgs bosons scalar fermion scalar scalar fermion scalar vector scalar scalar scalar vector vector Sfermions

11. 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: 0 1

12. Higgs couplings to fermions Yukawa couplings Decoupling limit [1] M. Carena et al, 1999, 2000

13. Renormalization 3 x = + + + 1loop ren. tree vertex 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

14. 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

15. SUSY Parameter Analysis project* http//spa.desy.de/spa 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

16. 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

17. Linear Rx gauge

18. Bremsstrahlung • 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

19. All numerical results preliminary

20. “SusyHiggsDecay” Program description: 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 Structure of “SfermionDecay” similar

21. Reference point SPS1a’ DRbar parameter at Q = 1 TeV

25. mSUGRA benchmark points: Low Mass points High Mass points

26. Outlook 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

27. Thank you for your attention!