Electroweak effects in Higgs boson production Frank Petriello - PowerPoint PPT Presentation

Electroweak effects in Higgs boson production Frank Petriello University of Wisconsin, Madison w/C. Anastasiou, R. Boughezal 0811.3458 w/ W. Y . Keung, WIP

Outline Brief review of experiment, theory for SM Higgs Electroweak corrections and factorization Higgs EFT and check of factorization Updated numerics for the Tevatron and fun with PDFs The 1-jet bin

Why we expect a TeV scale Higgs Last undiscovered particle of the SM Many reasons to expect it (or something else) to be observed soon Λ NP ≤ 1 . 7 TeV

Higgs in SM extensions The uncertainty in EWSB mechanism makes Higgs a portal into new physics at the TEV scale S. Dawson Han, Logan, McElrath ‘03 Hewett, Rizzo ‘02 Loop-induced gluon, photon modes can have O(1) deviations

SM Higgs circa 2008 Current fit of EW parameters by m Limit = 154 GeV July 2008 6 Theory uncertainty !# (5) !# had = LEP EW working group predicts: 5 0.02758 ± 0.00035 0.02749 ± 0.00012 incl. low Q 2 data 4 M H = 84 +34 − 26 GeV !" 2 3 2 Precision EW upper bound and direct 1 search lower bound at 95% CL: Excluded Preliminary 0 30 100 300 114 < M H / GeV < 154 m H [ GeV ] News from the Tevatron : Combined result from CDF, D0 exclude 170 GeV SM Higgs at 95% CL arXiv:0808.0534 “Preliminary” exclusion at 160-170 GeV on Friday Carefully reconsider SM prediction in light of experimental sensitivity

SM Higgs at the Tevatron W,Z t,b gg fusion dominant by Associated production factor of 10 essential for M H < 130 GeV CDF Run II Preliminary, L=1.9-3.0 fb -1 95% CL Limit/SM WWW 1.9 fb -1 Obs WH+ZH ! bbMET 2.1 fb -1 Obs LEP WWW 1.9 fb -1 Exp WH+ZH ! bbMET 2.1 fb -1 Exp Exclusion limit entirely from Excl. H !"" 2.0 fb -1 Obs WH ! l # bb 2.7 fb -1 Obs H !"" 2.0 fb -1 Exp WH ! l # bb 2.7 fb -1 Exp ZH ! llbb 2.4 fb -1 Obs H ! WW 3.0 fb -1 Obs ZH ! llbb 2.4 fb -1 Exp H ! WW 3.0 fb -1 Exp 10 2 10 2 Combined Obs gg → H → WW Combined Exp 10 10 BR(H → WW) > 90% for SM 1 1 160-170 GeV Higgs 100 110 120 130 140 150 160 170 180 190 200 m H (GeV/c 2 )

QCD corrections at NLO Top-loop dominant; bottom loop gives t,b -10% correction from interference b ln 2 ( M H /m b ) � m 2 � What makes is sensitive to new physics (begins at 1- loop) also makes it tough to calculate E.g., need NLO corrections >100% at Tevatron Harlander, Kilgore; Anastasiou, Melnikov 2002

Effective theory for Higgs Full NLO with mass dependence known (Djouadi, Graudenz, Spira, Zerwas 1995) Difficult to go to NNLO and check convergence of expansion Use EFT instead for top (Shifman et al. 1979; Ellis et al. 1988; S. Dawson; Djouadi, Spira, Zerwas 1991) known through O( α s5 ): Schroder, Steinhauser; Chetyrkin, Kuhn, Sturm 2006 If normalized to full LO top mass dependence, good to <10% for 1 TeV Higgs; <1% below 200 GeV Harlander 2008

NNLO in the EFT Catani, de Florian, Grazzini, Nason 2003 Anastasiou, Melnikov, Petriello 2005 Harlander, Kilgore; Anastasiou, Melnikov; Ravindran, J. Smith, van Neerven 2002-3 Full NNLO differential results known Soft gluon resummation increase NNLO by 10% N 3 LO scale dependence indicates stability of expansion

Electroweak corrections Residual QCD uncertainty ~10% ➩ EW corrections potentially important to match QCD and experimental precision Light-quark terms: q Aglietti, Bonciani, Degrassi, Vicini 2004 ➩ Up to 9% at threshold relative Duhrssen et al. 2004 to LO QCD

Thresholds and factorizationn Actis, Passarino, Sturm, Uccirati 2008 Self-energy resummation needed near thresholds ➪ complex M W,Z Reduces corrections: K-factor at Tevatron is ~3.5; how does QCD affect this? Partial factorization : no QCD corrections, set K=1,1-2% of NNLO cross section Complete factorization : same K for EW terms, remain 5-6% of NNLO ➪ 20% of LO QCD!

Tevatron exclusion Combined CDF, D0 results (2008) M H =170 GeV excluded What went into the SM prediction: • Complete factorization assumed • Same QCD corrections for t,b • Old PDFs (MRST 2002) Goals: • Test complete factorization hypothesis • Provide updated SM prediction

Testing factorization Full test of CF would require O( αα s ) corrections 3-loop virtual + 2-loop real emission Can we instead test using an EFT approach?

EFT formulation C 1 L = − α s 4 v HG a µ ν G aµ ν Radius of convergence: M H ≤ M W However, top-quark EFT valid to 1 TeV>2m t ; reason to expect similar here ➪ exact for dominant radiation pieces in resummation limit τ =M H2 / Ŝ → 1 for all M H Marzani et al. ‘08

Factorization in EFT C 1 L = − α s 4 v HG a µ ν G aµ ν Factorization holds if C 1w =C 1q , C 2w =C 2q

Matching to the EFT I Matching at O( α ): α s = − 1 v λ EW M 0 3 π � � M 2 = A (2) ( M 2 H H = 0) M 0 + O M 2 W,Z ➪ Equate to get λ EW

Matching to the EFT II Matching at O( αα s ): = − 1 α s v λ EW ( α s C 1 w ) M 0 3 π � � M 2 g = A (3) ( M 2 H W, Z H = 0) M 0 + O H M 2 g W,Z g = − − W, Z H g ➪ gives C 1w

EFT justification Did we get all the needed operators? Only other same-order operator: H q/ Dq v ¯ ➪ vanishes when inserted into EFT graphs Large-mass Feynman integral expansion: V . Smirnov Check that all 0,1,2,3-loop subgaphs contained in EFT or higher power ✔ Reduced graph s: only light lines, Subgraphs : contain all massive props, quantum corrections to operators Taylor expand (EFT operators)

Calculational procedure Generate 3-loop diagrams for g(p 1 )+g(p 2 ) → H(p H ) Taylor expand each diagram in M H by applying: Leading term in A gives C 1w upon comparison with L EFT ; need through n=2

Structure of result k 3 Coeffiicents in expansion are 3-loop vacuum bubbles: k 2 k 1 3 1 � � d d k j I ( � ν i ) = k 2 ν 1 k 2 ν 2 ( k 2 3 − M 2 W,Z ) ν 3 ( k 1 − k 2 ) 2 ν 4 ( k 2 − k 3 ) 2 ν 5 ( k 3 − k 1 ) 2 ν 6 1 2 j =1 3 � � d d k j D = j =1 Use integration-by-parts identities Chetyrkin, Tkachov ‘81 ; 3 Lorentz invariance gives 9 eqs: � � d d k j ∂ i [ k k D ] = 0 j =1

Integration-by-parts In a simple case: 1-loop bubble diagrams 1 � p d d k I ( ν 1 , ν 2 ) = k 2 ν 1 ( k + p ) 2 ν 2 k µ � � � ∂ d d k Set = 0 ∂ k µ k 2 ν 1 ( k + p ) 2 ν 2 ( d − 2 ν 1 − ν 2 ) I ( ν 1 , ν 2 ) − ν 2 I ( ν 1 − 1 , ν 2 + 1) + ν 2 p 2 I ( ν 1 , ν 2 + 1) = 0 Derive I (1 , 1) ⇒ I (1 , 2) = − d − 3 Apply to I (1 , 1) p 2 Apply functional relation to progressively more complicated integrals; all in terms of I(1,1)

Integration-by-parts Example of IBP equation for 3-loop calculation: {- ν 4 1 - 4 + - ν 6 1 - 6 + + ν 4 2 - 4 + + ν 6 3 - 6 + + ν 6 6 + +(d-2 ν 1 - ν 4 - ν 6 )} I( ν 1, ν 2, ν 3, ν 4, ν 5, ν 6 )=0 Apply IBP eqs to list of seed Operators acting on integrals: I(1,0,1,1,1,0), the arguments of I I(1,0,1,2,-1,1), ... Solve resulting system of equations Laporta ‘01 >100000 seeds; express in terms of 2 master integrals : I(1,0,1,1,1,0) and I(1,1,1,0,1,1)

Some examples 2(3 d − 8)(3 d − 10) I (1 , 0 , 1 , 1 , 1 , 0) − 2( d − 3) I (1 , 1 , 1 , 1 , 1 , 1) = I (1 , 1 , 1 , 0 , 1 , 1) ( d − 4) 2 d − 4 d − 2 I (1 , − 1 , 1 , 1 , 1 , 1) = d − 4 I (1 , 0 , 1 , 1 , 1 , 0) − 3(3 d − 8)(3 d − 10)( d − 5) I (1 , 1 , 1 , 1 , 2 , 1) = I (1 , 0 , 1 , 1 , 1 , 0) + (2 d − 6) I (1 , 1 , 1 , 0 , 1 , 1) ( d − 6)( d − 4) d ( d − 2)(3 d − 8) I (1 , − 2 , 1 , 1 , 1 , 3) = ( d − 8)( d − 6)( d − 4) I (1 , 0 , 1 , 1 , 1 , 0) 9 (3 d − 14)(3 d − 20)(3 d − 10)(3 d − 16)(3 d − 8)( d − 7) I (1 , 1 , 3 , 1 , 2 , 3) = I (1 , 0 , 1 , 1 , 1 , 0) 16 ( d − 8)( d − 10) +3 8(3 d − 20)( d − 3)( d − 4)( d − 5)( d − 6) I (1 , 1 , 1 , 0 , 1 , 1) Can evaluate master integrals via simple Gamma functions

Analytical result No renormalization needed (finite renormalization needed for top quark case) C 1w =7/6, compared to factorization hypothesis C 1w =C 1q =11/4 (C 1q -C 1w )/C 1q ≈ 0.6 ⇒ O(1) violation of assumption Numerical effect on hadronic cross section?

Numerical test of CF QCD corrections in EFT partial factorization actual result complete factorization Tevatron Full mass-dependent 2-loop EW corrections 8 6 Difference between CF 4 and actual: ! EW [%] a s ( C 1 w − C 1 q ) 2 Small compared to a s G (1) ( z ) LO NLO 0 NNLO, C 2W = -10 NNLO, C 2W = 10 NNLO CF -2 110 120 130 140 150 160 170 180 m H [GeV]

Updated cross section NNLO large-m t K-factor, exact LO Exact NLO b 2 , t-b interferences K-factors result 1.4 ≤ K bb,tb ≤ 1.7 for 120 ≤ M H ≤ 180 GeV; 3.5 used for both in old Catani et al. study Choose μ =M H /2 to reproduce central value of resummation to better then 1% Catani, de Florian, Grazzini, Nason ‘03 Comparison of pole, MSbar b-quark mass (<1% change) Use of newer MRST PDFs ...

Circa December 2008 A short lesson on PDFs and their errors... MRST 2002 → 2006: increase of α s and gluon density For M H =170 GeV: Act constructively to increase by 7-10% True for 120 ≤ M H ≤ 180 GeV (Note: PDF systematic error ±5%, 90% CL)

Circa January 2009 MSTW 2008 PDF release arXiv:0901.0002 • Run II inclusive jet data • Decrease of α s (M Z ) from 0.119 → 0.117 • Gluon density decreased at x ∼ 0.1 • gg luminosity error increased from 5% → 10% M H =170 GeV: ∼ 10-15% decrease in predicted cross section !