FeynHiggs. Henning Bahl. TOOLS, , Corfu. Max-Planck Institut für Physik, Munich

Transcription

1 FeynHiggs Henning Bahl Max-Planck Institut für Physik, Munich TOOLS, , Corfu

2 Introduction Higgs mass calculation Other observables Running the code Conclusions 2 / 26

3 Purpose of FeynHiggs Calculation of masses, mixings etc. in the MSSM at highest level of accuracy. works with real and complex parameters written in Fortran standard tool for masses, couplings and some decays in the LHCHXSWG current version: FeynHiggs team HB, Sven Heinemeyer, Thomas Hahn, Wolfgang Hollik, Sebastion Paßehr, Heidi Rzehak, Georg Weiglein 3 / 26

4 Core of FeynHiggs: Higgs mass calculation MSSM includes two Higgs doublets Φ 1 = ( φ + 1 v (φ 1 + iχ 1 ) ), Φ 2 = five physical Higgs states: h, H, A, H ± Higgs potential: ( φ + 2 v (φ 2 + iχ 2 ) V H = m 2 1H 1iH 1i + m 2 2H 2iH 2i ɛ ij (m 12 H 1i H 2j + m 12H 1iH 2j) (g2 + g 2 )(H 1iH 1i H 2iH 2i ) g2 H 1iH 2i 2 ) Minimization of potential m 2 1 and m 2 2 eliminated Reexpress m 2 12 through mass of A boson Higgs sector at tree-level determined by only two variables: M A and tan β = v 2 /v 1 Mass of SM-like Higgs can be predicted 4 / 26

5 tree-level bound on SM-like Higgs boson mass: M 2 h M 2 Z at loop level mixing between h, H and A loop-corrections can be large (up to 100%) For precision studies higher order corrections are essential! 5 / 26

6 Fixed-order calculation Straightforward approach Calculate self-energy corrections! For MA 2 M Z 2 mixing negligible: Solve p2 ˆΣ hh (p 2 ) = 0! Full 1L and partial 2L results included Renormalization scheme: OS or DR Resummation of bottom Yukawa coupling for large tan β Includes all corrections at given order Precise for not too much separated scales For high SUSY scale, large logarithms spoil convergence e.g. M 2 h O(α t) m 2 h + 12k M 4 t v 2 ( ln(m 2 S /M 2 t ) +... ) 6 / 26

7 Code generation Full 1L and O(α 2 t ) corrections can be generated automatically relies on tools FeynArts, FormCalc and TwoCalc bash scripts run the tools and output compile-ready Fortran files Toolchain for O(α 2 t ) corrections: [Hahn & Paßehr] 1. Generate diagrams with FeynArts 2. Prepare for tensor reduction 3. Tensor reduction with TwoCalc and FormCalc 4. Simplify expressions 5. Calculate renormalization constants with FeynArts/FormCalc 6. Combine everything and simplify 7. Generate code 7 / 26

8 EFT calculation Alternative approach If all SUSY particles are heavy, integrate them out! M 2 h = 2λ(M t)v 2 State of the art EFT calculation: Full LL+NLL resummation O(α s, α t ) NNLL resummation separate chargino/neutralino threshold EFT calculation resums large logarithms precise prediction for high scales misses however terms suppressed by SUSY scale v/m S 8 / 26

9 Effect of resummation / 26

10 Hybrid approach Idea Combine EFT and fixed-order approach to allow for precise prediction for all scales. ˆΣ hh (m 2 h) ˆΣ hh (m 2 h) [ 2v 2 λ(m t ) ] log [ˆΣhh (m 2 h) ] log = = [ˆΣhh (m 2 h) ] nolog [ 2v 2 λ(m t ) ] log Have to avoid double-counting of 1L and 2L logarithms Have to avoid double-counting of non-log terms EFT uses DR, fixed-order calcalculation can be OS parameter conversion needed Benefits: precise prediction for all scales 10 / 26

11 Comparison to pure EFT calculation / 26

12 Summary of available self-energy corrections Need to find complex poles (M 2 = M 2 imγ) of inverse propagator matrix 1 : p 2 m 2 h + Σ hh Σ hh Σ ha Σ Hh p 2 m 2 H + Σ HH Σ HA Σ Ah Σ AH p 2 m 2 A + Σ AA and Σ H ± H ±, (Σ = Σ(p2 )) : full one-loop corrections (all phases, p 2 dependence, NMFV) : O(α s α t ) corrections (all phases, p 2 dependence), O(α 2 t ) corrections (all phases, p 2 = 0) : O(α t α b, α 2 b ) corrections (phases interpolated, p2 = 0) : resummed logarithms using EFT 12 / 26

13 Numerical determination of the poles? For M A M Z, M 2 h = m 2 h (1) ˆΣ hh (m2 (2) h) ˆΣ hh (m2 (1) h) + ˆΣ hh (m2 h)ˆσ (1) hh (m2 h) +... Non-SM contributions to (1) ˆΣ hh (m2 (1) h )ˆΣ hh (m2 h ) are cancelled (2) by subloop-renormalization in ˆΣ hh (m2 h ) vev-ct holds generally at 2L (probably also at higher orders) ˆΣ (2) but FH includes hh only for vanishing electroweak couplings incomplete cancellation Numerical determination of poles spoils calculation! Solution easy for M A M Z, but what to do for M A M Z? 13 / 26

14 Procedure for general M A At 1L level M 2 h = m2 h determine poles of 1 hh (p2 ) = p 2 m 2 h +ˆΣ (1) hh (m2 h) +ˆΣ (2) hh (0) 1 hh (p2 ) = +ˆΣ (1) hh (m2 h) +ˆΣ (2) hh (0) 1 HH(p 2 ) = p 2 m 2 H +ˆΣ (1) HH (m2 h) +ˆΣ (2) HH (0) For determination of M H expand around M 2 H = m2 H (1) ˆΣ hh (m2 h ) expand around 1L solution [ˆΣ(1) ] hh (m2 h)ˆσ (1) hh (m2 h) [ˆΣ(1) hh (m2 h)ˆσ (1) hh (m2 h) [ˆΣ(1) HH (m2 h)ˆσ (1) hh (m2 h) ˆΣ (1) HH (m2 H ) will be available in the next release (FH2.14.0) ] ] g=g Y =0 g=g Y =0 g=g Y =0 14 / 26

15 Numerical impact of improved pole determination / 26

16 Output Observables Higgs masses: M h1, M h2, M h3, M H ± Z ij -factors for calculating processes involving external Higgs bosons effective mixing angle α eff For all observables theory uncertainty is estimated by change of renormalization scheme scale variation switching off the resummation of the bottom Yukawa coupling 16 / 26

17 Neutral Higgs decays total decay width: Γ tot h i, Γ tot H + Branching ratios of h i SM fermions: h i f f gauge bosons: h i γγ, Z ( ) Z ( ), W ( ) W ( ), gg gauge and Higgs boson: h i Z ( ) h j two Higgs bosons: h i h j h k sfermions: h i f i fj charginos/neutralinos: h i χ ± j χ k, χ0 j χ0 k For comparison also SM branching ratios are calculated Branching ratios of H + SM fermions: H + ( ) f f gauge and Higgs boson: H + W +( ) h i sfermions: h i f i f j chargino and neutralino: h i χ 0 i χ0 j 17 / 26

18 Higgs production Available cross-sections: bb, gg h + X qq qqh + X qq, gg tth + X qq W h + X qq Zh + X pp t 1 t 1 h + X gb th + X t H + b for MH ± M t For comparison also SM cross-sections are calculated. 18 / 26

19 EWPO and flavour observables Electroweak precision observables: W boson mass M W effective weak mixing angle sin θ eff r, ρ Anomalous magnetic moment of the muon g µ 2 Electric dipole moments of the electron, neutron and mercury Flavour observables: b sγ M s B s µ + µ 19 / 26

20 Getting and running the code Download latest version at feynhiggs.de Install via:./configure, make, make install 4 ways to run the code Command line Call from Fortran/C++ code Mathematica interface Web interface feynhiggs.de/fhucc 20 / 26

21 Command line I Inputfile: MT MSusy 2000 MA0 400 TB 10 Abs(At) 500 Arg(At) FeynHiggs file [flags] Possible to define loops over parameters Possible to use interpolation tables Alternatively use SLHA files as input Screen output:... - HIGGS MASSES - Mh0 = MHH = MA0 = MHp = ESTIMATED UNC. - DeltaMh0 = DeltaMHH = DeltaMA0 = DeltaMHp = / 26

22 Command line II Example bash script #! /bin/sh FeynHiggs - ${4: } «- _EOF_ > FH.out MT MSusy $2 Xt $3 TB 10 MA MUE 1000 M_ M_ _EOF_ cat FH.out table $1 FH.out 2>/dev/null 22 / 26

23 Call from Fortran/C++ code Link static Fortran library FHlib.a For C/C++ prototype file available: CFeynHiggs.h Most important routines input FHSetFlags - options (accuracy, approximations,... FHSetPara - MSSM input parameters output FHHiggsCorr - Higgs masses and mixings FHUncertainties - theory uncertainty estimate for Higgs masses and mixings FHCouplings - Higgs couplings and BRs FHHiggsProd - Higgs production cross-sections FHEWPO - electroweak precision observables FHFlavour - flavour constraints FHConstraints - additional constraints 23 / 26

24 Call from Mathematica make all to generate MathLink executable uses it via: input: Install[ MFeynHiggs ]; FHSetFlags[...]; FHSetPara[...]; FHHiggsCorr[] output {MHiggs -> { , , 1000., }, SAeff -> , UHiggs ->..., ZHiggs ->...} allows to use Mathematica functions (ContourPlot,...) 24 / 26

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26 Summary: FeynHiggs calculates Higgs masses, mixings, decays, production cross-sections etc. in the MSSM Includes combined state-of-the-art fixed-order and EFT calculations Allows for precise predictions for low and high SUSY scales Near future outlook (version ): Improved pole mass determination Optional DR renormalization of stop sector To come later... Complete revamp of 2L corrections Improved resummation for low M A (eff. THDM) NMSSM extension 26 / 26