Decay widths of all MSSM scalars at full one-loop level Loops and Legs in QFT, Wörlitz, Germany, 29 th April 2010 Helmut Eberl together with Hana Hlucha and Wolfgang Frisch

H. Eberl29th April 2010 Motivation MSSM, Sfermion/Higgs mass matrices Sfermion/Higgs decays Details of programs Numerics Outlook Outline

H. Eberl29th April 2010 Program Packages that calculate all MSSM Higgs 1 and Sfermion 2 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

H. Eberl29th April 2010 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

H. Eberl29th April 2010 Gauge supermultiplets: Chiral supermultiplets: 4 neutralinos 2 charginos 5 phys. Higgs bosons

H. Eberl29th April 2010 Interaction states – physical states Particle mixing: MSSM scalars: Higgs bosons, sfermions MSSM fermions: charginos, neutralinos Mass matrices – Eigenvalue problems

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H. Eberl29th April 2010 “decoupling limit”

H. Eberl29th April 2010 Sfermion sector in the MSSM

H. Eberl29th April 2010 Two-body decays Higgs bosons scalar possible tree-level structures: Sfermions

H. Eberl29th April 2010 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: 01

H. Eberl29th April 2010 Higgs couplings to fermions Yukawa couplings [1] M. Carena et al, 1999, 2000 Decoupling limit

H. Eberl29th April 2010 Renormalization =+++ 1loop ren. treevertex 3 x wave fct. CTscoupling CTs DRbar scheme: UV divergence  = 0 (note: tree-level couplings given at scale Q) only UV div. parts technical trick automatic check of RGE invariance always on-shell masses

H. Eberl29th April 2010 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” h b = 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 calculations

H. Eberl29th April 2010 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 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’ http//spa.desy.de/spa

H. Eberl29th April 2010 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 (h 0 –H 0 ) mixing angle is defined on-shell with p = m h0 SM input parameters: G Fermi, α, m Z, a s (m Z ) and fermion masses Decay widths/branching ratios and production cross section are calculated for the set of parameters specified above

H. Eberl29th April 2010 Linear R  gauge

H. Eberl 29th April 2010 Bremsstrahlung In order to cancel the IR divergencies we have included real 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:

H. Eberl29th April 2010 All numerical results preliminary

H. Eberl29th April 2010 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: h 0 = 1, H 0 = 2, A 0 = 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” Structure of “SfermionDecay” similar Program description:

Reference point SPS1a’ H. Eberl29th April 2010 DRbar parameter at Q = 1 TeV

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H. Eberl29th April 2010 mSUGRA benchmark points: Low Mass points High Mass points

H. Eberl29th April 2010 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 h 0 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 Outlook First versions of decay programs will be on the web soon!

H. Eberl29th April 2010 Thank you for your attention!