Higher order corrections to Higgs production in Weak Boson Fusion Sophy Palmer Institute for Particle Physics Phenomenology University of Durham Paul Scherrer Institute December 2008 Work in collaboration with G Weiglein and T Figy
Introduction Outline of Calculation Results Summary Outline Introduction 1 The Higgs Sector Weak Boson Fusion Higgs - Weak Boson coupling Outline of Calculation 2 WBF Corrections Renormalisation Calibration Process Results 3 Partonic Cross Sections Comparison with the literature Monte Carlo Calibration Process Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction The Higgs Sector Outline of Calculation Weak Boson Fusion Results Higgs - Weak Boson coupling Summary The MSSM Higgs Sector In the MSSM, the Higgs sector needs to contain two Higgs doublets, which leads to 5 physical Higgs states: h 0 , H 0 , A 0 , H + , H − At tree level the Higgs sector is described by tan β and M A The tree level masses m h and m H are found by diagonalising the Higgs mass matrix � M 2 A sin 2 β + M 2 Z cos 2 β � M 2 A + M 2 � � sin β cos β − M 2 , tree Z = M 2 A + M 2 M 2 A cos 2 β + M 2 Z sin 2 β H � � sin β cos β − Z ↓ diagonalisation, α � � m 2 , tree 0 M 2 , tree = H H m 2 , tree 0 h Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction The Higgs Sector Outline of Calculation Weak Boson Fusion Results Higgs - Weak Boson coupling Summary The Complex MSSM In general, some of the parameters of the MSSM can be complex. For instance, gluino mass parameter M 3 trilinear coupling parameter A When complex phases are included, interesting (non-excluded) phenomenology can result Complex phases allow mixing between all three neutral Higgs bosons h − ˆ − ˆ − ˆ m 2 Σ hh ( p 2 ) Σ hH ( p 2 ) Σ hA ( p 2 ) M ( p 2 ) = − ˆ H − ˆ − ˆ Σ hH ( p 2 ) m 2 Σ HH ( p 2 ) Σ HA ( p 2 ) − ˆ ˆ A − ˆ Σ hA ( p 2 ) Σ HA ( p 2 ) m 2 Σ AA ( p 2 ) Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction The Higgs Sector Outline of Calculation Weak Boson Fusion Results Higgs - Weak Boson coupling Summary Weak Boson Fusion Weak boson fusion is expected to be the second largest contributor to Higgs Boson production at the LHC q → Q ′ + h / H + ¯ SM Higgs production Q + ¯ q ′ 10 5 LHC σ [ fb ] gg → h 10 4 qq → qqh Q ′ Q 10 3 qq → Wh V bb → h gg,qq → tth H 10 2 qb → qth qq → Zh V TeV4LHC Higgs working group 100 200 300 400 500 m h [ GeV ] q q ′ ¯ ¯ From: hep-ph/0607308 , T Hahn, S Heinemeyer, F Maltoni, G Weiglein, S Willenbrock Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction The Higgs Sector Outline of Calculation Weak Boson Fusion Results Higgs - Weak Boson coupling Summary WBF - Status NLO QCD corrections in the SM have been implemented in public Monte Carlo codes (see, for instance, hep-ph/0407066 , T Figy, C Oleari, D Zeppenfeld) The QCD corrections to weak boson fusion are relatively small Full SM one-loop corrections have been obtained and implemented in a Monte Carlo program ( hep-ph/0710.4749, hep-ph/0806.3624 , M Ciccolini, A Denner, S Dittmaier) An estimation of O ( α 3 α 2 s ) contributions has been published ( hep-ph/0809.3693 , J Vollinga) The pure SUSY-loop corrections to the total cross section have been investigated ( hep-ph/0804.2676 , W Hollik, T Plehn, M Rauch, H Rzehak) Loop level interference effects have been calculated ( hep-ph/0709.3513 , J Andersen, T Binoth, G Heinrich, J Smillie; hep-ph/0801.4231 , A Bredenstein, K Hagiwara, B Jäger) Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction The Higgs Sector Outline of Calculation Weak Boson Fusion Results Higgs - Weak Boson coupling Summary vbfnlo By using Monte Carlo programs, cross section distributions can be calculated, providing a useful tool for experimentalists. vbfnlo * is a public parton level Monte Carlo program that provides predictions for weak boson fusion in the Standard Model and includes NLO QCD corrections. Arbitrary cuts can be implemented Various scales and PDF sets can be chosen Several relevant processes are included: Higgs production Single W/Z boson production with leptonic decay WW/ZZ pair production with subsequent leptonic decays of W/Z bosons * hep-ph/0306109 , T Figy, C Oleari, D Zeppenfeld Available at http://www-itp.particle.uni-karlsruhe.de/ ∼ vbfnloweb/ Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction The Higgs Sector Outline of Calculation Weak Boson Fusion Results Higgs - Weak Boson coupling Summary Effective Couplings The most general HVV coupling is: T µν ( q 1 , q 2 ) a 1 ( q 1 , q 2 ) g µν + a 2 ( q 1 , q 2 ) q 1 • q 2 g µν − q µ � � = 2 q ν 1 + a 3 ( q 1 , q 2 ) ǫ µνρσ q 1 σ q 2 ρ At tree level ieM W ieM W a SM a MSSM = sin ( θ W ); = sin ( θ W ) sin ( β − α ) ; a 2 = 0 ; a 3 = 0 ; 1 1 New physics (e.g. a heavy particle loop) can be represented by the effective coupling T µν V V V V ˜ t H H H H H ˜ + + ∼ b ˜ t V V V V Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction The Higgs Sector Outline of Calculation Weak Boson Fusion Results Higgs - Weak Boson coupling Summary VVH Coupling and Azimuthal Angles The LHC will (hopefully) provide information about Strength of the HVV coupling Tensor structure of the HVV coupling Figure from: hep-ph/0609075 , T Figy, V Hankele, G Klamke, D Zeppenfeld Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction WBF Corrections Outline of Calculation Renormalisation Results Calibration Process Summary Calculation of Higher Order Corrections to WBF The programs* FeynArts, FormCalc, LoopTools and FeynHiggs have been used Q Q Q ′ Q ′ V ˜ ˜ t b V t V H H b t V V q q ′ q q ′ ¯ ¯ ¯ ¯ Higgs vertex couplings and weak boson self energies are incorporated into an effective coupling T µν For these diagram-types, the full Standard Model corrections and all fermion/sfermion corrections in the MSSM are included *Programs available at www.feynarts.de and www.feynhiggs.de Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction WBF Corrections Outline of Calculation Renormalisation Results Calibration Process Summary Calculation of Higher Order Corrections to WBF When only (s)fermionic corrections are being considered, the corrections to qqV are calculated using the counterterm Q Q ′ coupling V When bosons are included too, the full H matrix element is calculated V qqV vertex corrections are included for the q ¯ q ′ ¯ full Standard Model and for fermions and sfermions in the MSSM Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction WBF Corrections Outline of Calculation Renormalisation Results Calibration Process Summary Bosonic Corrections to WBF Q ′′ Q Q ′ Q ′′ All bosonic Q Q ′ V V corrections have V H H been implemented V V V in the Standard V q ′ q Model q ′′ q ′ q Outlook: g γ Q Q ′ Q Q ′ Implementing Q ′ Q these V V H H diagram-types in V V the MSSM q q ′ ¯ ¯ q ′ q ¯ ¯ Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction WBF Corrections Outline of Calculation Renormalisation Results Calibration Process Summary Boxes and pentagons The boxes and pentagons are included by calculating the full matrix element squared, using code generated by a modified version of FormCalc In order to check this procedure, the Born amplitude and the corrections to the Higgs vertex were calculated using this method, and the results cross checked against the simpler formfactor calculation Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction WBF Corrections Outline of Calculation Renormalisation Results Calibration Process Summary Higgs propagator corrections in the MSSM Radiative corrections lead to further mixing between Higgs bosons Finite wavefunction normalisation factors have been used to give outgoing particles the correct on-shell properties to take this mixing into account Q Q ˆ ˆ Γ 1 Γ h V ˆ = ˆ ˆ h Γ 2 Z Γ H ˆ ˆ Γ 3 Γ A V q q ¯ ¯ Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction WBF Corrections Outline of Calculation Renormalisation Results Calibration Process Summary Higgs propagator corrections in the MSSM The non-unitary ˆ Z matrix is given by √ Z h √ Z h Z hH √ Z h Z hA √ Z H Z Hh √ Z H √ Z h Z HA ˆ Z = √ Z h Z Ah √ Z A Z AH √ Z A When producing a Higgs i , √ Z i is a normalisation factor (dependent on the ii propagator), and Z ij involves the ij propagator and takes account of diagrams where there is a tree level Higgs j connected directly to the vertex. These corrections can be very important numerically. They are calculated using FeynHiggs , which includes the dominant two-loop contributions as well as the full one-loop corrections. Sophy Palmer Loop Corrections to Weak Boson Fusion
Introduction WBF Corrections Outline of Calculation Renormalisation Results Calibration Process Summary ∆ m b corrections Higher order corrections can significantly affect the relation between the bottom quark mass and the Yukawa coupling λ b λ b = m b → m b 1 v 1 v 1 1 + ∆ m b ∆ m b is output by FeynHiggs These corrections can potentially be large, especially for the heavy Higgs Sophy Palmer Loop Corrections to Weak Boson Fusion
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