Effective Higgs-Gauge Analyses

Transcription

1 Effective Higgs-Gauge Analyses Tilman Plehn Universität Heidelberg CERN, July 017

2 Higgs Couplings t W,Z Standard Model operators assume: narrow CP-even scalar Standard Model operators fundamental physics in terms of Lagrangian L = L SM + W gm W H W µ W µ + Z + gf G H v GµνGµν + γf A non-linear EWSB, no link to gauge sector g f m f v H ( fr f L + h.c. ) m Z H Z µ Z µ c w τ,b,t H v AµνAµν + invisible + unobservable b,t W,Z Only Run I results, not enough 13 TeV data... 1 electroweak renormalizability broken total rates only 3 hard to relate to electroweak sector [Corbett, Eboli, Goncalves, Gonzalez-Fraile, TP, Rauch] L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. data b/w b/τ Z/W g SM+NP γ SM+NP BR inv g γ τ b t Z W g x = g x SM (1+ x )

3 Higgs Couplings t W,Z Standard Model operators assume: narrow CP-even scalar Standard Model operators fundamental physics in terms of Lagrangian L = L SM + W gm W H W µ W µ + Z + gf G H v GµνGµν + γf A non-linear EWSB, no link to gauge sector g f m f v H ( fr f L + h.c. ) m Z H Z µ Z µ c w τ,b,t H v AµνAµν + invisible + unobservable b,t W,Z Only Run I results, not enough 13 TeV data... 1 electroweak renormalizability broken total rates only 3 hard to relate to electroweak sector [Corbett, Eboli, Goncalves, Gonzalez-Fraile, TP, Rauch] L= (7 TeV) (8 TeV) fb -1, ATLAS + CMS a B a G *10 Rates 68% CL Rates 95% CL Rates+dist. 68% CL Rates+dist. 95% CL a W a 4 a 5 c H a t a b a τ

4 D6 Higgs operators D6 Lagrangian at face value [HISZ, polish, Trott etal, Goncales-Garcia etal] set of Higgs operators [renormalizable, #1 solved] O GG = φ φg a µν Gaµν O WW = φ Ŵ µν Ŵ µν φ O BB = O BW = φ ˆBµν Ŵ µν φ O W = (D µφ) Ŵ µν (D νφ) O B = O φ,1 = (D µφ) φ φ ( D µ φ ) O φ, = 1 ( ) ( ) µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ

5 D6 Higgs operators D6 Lagrangian at face value [HISZ, polish, Trott etal, Goncales-Garcia etal] set of Higgs operators [renormalizable, #1 solved] O GG = φ φg a µν Gaµν O WW = φ Ŵ µν Ŵ µν φ O BB = O φ, = 1 ( ) ( ) µ φ φ µ φ φ O W = (D µφ) Ŵ µν (D νφ) O B = actual basis after equation of motion, etc L HVV = αsv 8π f g Λ O GG + f BB Λ O BB + f WW Λ Higgs couplings to SM particles [plus Yukawa structures, # solved] L HVV = g g HG a µν Gaµν + g γ HA µνa µν O WW + f B Λ O B + f W Λ O W + f φ, Λ O φ, + g (1) Z Z µνz µ ν H + g () HZ Z µνz µν + g (3) HZ Z µz µ ( ) + g (1) W + W µν W µ ν H + h.c. + g () W HW + µν W µν + g (3) W HW + µ W µ + 7 -like coupling modifications extended by 4 new Lorentz structures

6 Tilman Plehn D6 Higgs operators D6 Lagrangian at face value [HISZ, polish, Trott etal, Goncales-Garcia etal] set of Higgs operators [renormalizable, #1 solved] O GG = φ φg a µν Gaµν O WW = φ Ŵ µν Ŵ µν φ O BB = O φ, = 1 ( ) ( ) µ φ φ µ φ φ O W = (D µφ) Ŵ µν (D νφ) O B = 7 -like coupling modifications extended by 4 new Lorentz structures Run I legacy kinematics: p T,V, φ jj [# solved] Events/bin 10 3 leptons 10 SM (SM Higgs) x 70 (f W /Λ =0TeV - ) x p T V(GeV)

7 Tilman Plehn D6 Higgs operators D6 Lagrangian at face value [HISZ, polish, Trott etal, Goncales-Garcia etal] set of Higgs operators [renormalizable, #1 solved] O GG = φ φg a µν Gaµν O WW = φ Ŵ µν Ŵ µν φ O BB = O φ, = 1 ( ) ( ) µ φ φ µ φ φ O W = (D µφ) Ŵ µν (D νφ) O B = 7 -like coupling modifications extended by 4 new Lorentz structures Run I legacy kinematics: p T,V, φ jj [# solved] Events/bin 10 SM Higgs f WW /Λ =-f BB /Λ =0TeV - f WW /Λ =-f BB /Λ =-0TeV - γγ jj 10 0 π/3 π/3 π Φ jj

8 D6 Higgs operators D6 Lagrangian at face value [HISZ, polish, Trott etal, Goncales-Garcia etal] set of Higgs operators [renormalizable, #1 solved] O GG = φ φg a µν Gaµν O WW = φ Ŵ µν Ŵ µν φ O BB = O φ, = 1 ( ) ( ) µ φ φ µ φ φ O W = (D µφ) Ŵ µν (D νφ) O B = 7 -like coupling modifications extended by 4 new Lorentz structures Run I legacy kinematics: p T,V, φ jj [# solved] Run I Higgs limits L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS f/λ [TeV - ] Λ/ f [TeV] f/λ [TeV - ] O GG rate only rate+distributions O WW O BB O W O B O φ O t O b O τ Λ/ f [TeV]

9 D6 Higgs operators D6 Lagrangian at face value [HISZ, polish, Trott etal, Goncales-Garcia etal] set of Higgs operators [renormalizable, #1 solved] O GG = φ φg a µν Gaµν O WW = φ Ŵ µν Ŵ µν φ O BB = O φ, = 1 ( ) ( ) µ φ φ µ φ φ O W = (D µφ) Ŵ µν (D νφ) O B = 7 -like coupling modifications extended by 4 new Lorentz structures Run I legacy kinematics: p T,V, φ jj [# solved] Run I Higgs limits but not easy... f B /Λ 40 [TeV - ] f W /Λ [TeV - ]

10 D6 Higgs operators D6 Lagrangian at face value [HISZ, polish, Trott etal, Goncales-Garcia etal] set of Higgs operators [renormalizable, #1 solved] O GG = φ φg a µν Gaµν O WW = φ Ŵ µν Ŵ µν φ O BB = O φ, = 1 ( ) ( ) µ φ φ µ φ φ O W = (D µφ) Ŵ µν (D νφ) O B = 7 -like coupling modifications extended by 4 new Lorentz structures Run I legacy kinematics: p T,V, φ jj [# solved] Run I Higgs limits but not easy... f B /Λ 40 [TeV - ] f W /Λ [TeV - ]

11 D6 Higgs-gauge operators Triple gauge couplings [Butter, Eboli, Gonzalez-Fraile, Gonzalez-Garcia, TP, Rauch] just one more gauge operator [#3 solved] ) O W = (D µφ) Ŵ µν (D νφ) O B = (D µφ) ˆBµν (D νφ) O WWW = Tr (Ŵµν Ŵ νρ Ŵ µ ρ

12 D6 Higgs-gauge operators Triple gauge couplings just one more gauge operator [#3 solved] [Butter, Eboli, Gonzalez-Fraile, Gonzalez-Garcia, TP, Rauch] O W = (D µφ) Ŵ µν (D νφ) O B = (D µφ) ˆBµν (D νφ) O WWW = Tr (Ŵµν Ŵ νρ Ŵ µ ρ pre-gauge invariance known as DeltaKappaLambda L TGV = ie κ γ W + µ W ν γµν ieλγ m W ig Z κ Z W + µ W ν Z µν ig Z g Z 1 κ Z = g v ( ) c 8cw Λ w f W s w f B W + µν W νρ γ µ ρ ig Z λ Z mw W + µν W νρ Z µ ρ (W + µν W µ Z ν W + µν) µ ZνW g Z 1 = g v 8c w Λ f W ) λ Z = 3g M W f Λ WWW

13 Tilman Plehn D6 Higgs-gauge operators Triple gauge couplings just one more gauge operator [#3 solved] [Butter, Eboli, Gonzalez-Fraile, Gonzalez-Garcia, TP, Rauch] O W = (D µφ) Ŵ µν (D νφ) O B = (D µφ) ˆBµν (D νφ) O WWW = Tr (Ŵµν Ŵ νρ Ŵ µ ρ kinematics: p T,l in VV production Events/bin SM WW Background f W /Λ =5TeV - f B /Λ =5TeV - f WWW /Λ =5TeV - Data ) p T lead(gev)

14 D6 Higgs-gauge operators Triple gauge couplings just one more gauge operator [#3 solved] [Butter, Eboli, Gonzalez-Fraile, Gonzalez-Garcia, TP, Rauch] O W = (D µφ) Ŵ µν (D νφ) O B = (D µφ) ˆBµν (D νφ) O WWW = Tr (Ŵµν Ŵ νρ Ŵ µ ρ kinematics: p T,l in VV production combined LHC channels ] - [TeV f B Λ CMS ATLAS 7 WZ 7 semi 8 WW 8 WZ combined f W - [TeV ] Λ )

15 D6 Higgs-gauge operators Triple gauge couplings just one more gauge operator [#3 solved] [Butter, Eboli, Gonzalez-Fraile, Gonzalez-Garcia, TP, Rauch] O W = (D µφ) Ŵ µν (D νφ) O B = (D µφ) ˆBµν (D νφ) O WWW = Tr (Ŵµν Ŵ νρ Ŵ µ ρ kinematics: p T,l in VV production combined LHC channels cleaning Higgs-sector correlations ] - [TeV f B Λ 0 0 ) f W - [TeV ] Λ

16 D6 Higgs-gauge operators Triple gauge couplings [Butter, Eboli, Gonzalez-Fraile, Gonzalez-Garcia, TP, Rauch] just one more gauge operator [#3 solved] ) O W = (D µφ) Ŵ µν (D νφ) O B = (D µφ) ˆBµν (D νφ) O WWW = Tr (Ŵµν Ŵ νρ Ŵ µ ρ kinematics: p T,l in VV production combined LHC channels cleaning Higgs-sector correlations complete Higgs-gauge analysis f/λ [TeV - ] LHC-Higgs, 95% CL LHC-Higgs + LHC-TGV + LEP-TGV, 95% CL Λ/ f [TeV] f/λ [TeV - ] Λ/ f [TeV] O GG O WW O BB O W O B O φ O WWW O t O b O τ

17 D6 Higgs-gauge operators Triple gauge couplings [Butter, Eboli, Gonzalez-Fraile, Gonzalez-Garcia, TP, Rauch] just one more gauge operator [#3 solved] ) O W = (D µφ) Ŵ µν (D νφ) O B = (D µφ) ˆBµν (D νφ) O WWW = Tr (Ŵµν Ŵ νρ Ŵ µ ρ kinematics: p T,l in VV production combined LHC channels cleaning Higgs-sector correlations complete Higgs-gauge analysis LHC vs LEP [AdamF, FrancescoR,...] triple gauge vertices g 1, κ, λ vs operators LEP limits from precision LHC limits from energy semileptonic analyses missing for 8 TeV LHC beating LEP, but what does it mean? ] - [TeV f B Λ LHC LHC+LEP 60 LEP f W - [TeV ] Λ

18 D6 Higgs-gauge operators [AdamF]

19 That other gauge theory The most nasty D6 operator [Krauss, Kuttimalai, TP; ChrisH] making sense of black hole searches S T jets E T dimension-6 operators [MichelangeloM: check more 4-fermions] O qq = qγ µq q γ µ q } {{ } 3 jets new physics M 5 TeV Events per bin Ratio to SM SHERPA CMS data SM SM + OG O G = f abc G aν µ Gbλ ν Gcµ λ }{{} Njet 5 5jets cg Λ = 5 TeV ST [GeV] CLs N jet 5 L =. fb 1 Observed Expected (±σ) Λ/ c G [TeV]

20 Self consistency Ideal LEP and flavor worlds unique EFT Lagrangian: linear realization matching unbroken phase chain of well separated energy scales E Λ 1... Λ N systematic expansions in E/Λ and α [example: ew precision data]

21 Self consistency Ideal LEP and flavor worlds unique EFT Lagrangian: linear realization matching unbroken phase chain of well separated energy scales E Λ 1... Λ N systematic expansions in E/Λ and α [example: ew precision data] Rotten LHC world range of (partonic) energy scales [H+jets production, etc] electroweak symmetry breaking at v E LHC low precision, reach from energy σ BR 1 (σ BR) SM = g m h 10% Λ systematic EFT probably not valid cutoff scale dependent on UV completion g=1 g= 4π [FrancescoR] Λ 400 GeV Λ 1.4 TeV

22 Matching matters Example: oblique parameters from Higgs portal vs D6 L EFT [Freitas, Lopez-Val, TP; Trott etal] c H Λ µ (φ φ) µ(φ φ) + c T Λ (φ D µ φ)(φ D µφ) + igc W Λ (φ σ k D µ φ)d ν W k µν predictions of Higgs portal model [m H λ v s, s α λ 3 v /(λ m H )] S λ 3 v 4πλ mh log m H mh 3λ 3 T v 3π sw λ mw ( m Z mh m W mh ) log m H m h leading log for tree-insertion of loop operators O T,B,W [Λ = λ v s ] c H Λ = λ 3 λ Λ c T Λ = 3αews w λ 3 3πc w λ Λ Λ c B,W log = µ Λ λ 3 19π λ Λ log Λ µ

23 Matching matters Example: oblique parameters from Higgs portal vs D6 L EFT [Freitas, Lopez-Val, TP; Trott etal] c H Λ µ (φ φ) µ(φ φ) + c T Λ (φ D µ φ)(φ D µφ) + igc W Λ (φ σ k D µ φ)d ν W k µν predictions of Higgs portal model [m H λ v s, s α λ 3 v /(λ m H )] S λ 3 v 4πλ mh log m H mh 3λ 3 T v 3π sw λ mw ( m Z mh m W mh ) log m H m h leading log for tree-insertion of loop operators O T,B,W [Λ = λ v s ] c H Λ = λ 3 λ Λ c T Λ = 3αews w λ 3 3πc w λ Λ Λ c B,W log = µ Λ λ 3 19π λ Λ log Λ µ v-improvement: Λ = m H and full model in terms of c α c H Λ = (1 cα) v c T Λ = 3αews w (1 cα) 8πcw v log m H c B,W µ Λ = 1 cα 48π v log m H µ

24 Matching matters Example: oblique parameters from Higgs portal vs D6 L EFT [Freitas, Lopez-Val, TP; Trott etal] c H Λ µ (φ φ) µ(φ φ) + c T Λ (φ D µ φ)(φ D µφ) + igc W Λ (φ σ k D µ φ)d ν W k µν predictions of Higgs portal model [m H λ v s, s α λ 3 v /(λ m H )] S λ 3 v 4πλ mh log m H mh 3λ 3 T v 3π sw λ mw ( m Z mh m W mh ) log m H m h leading log for tree-insertion of loop operators O T,B,W [Λ = λ v s ] c H Λ = λ 3 λ Λ c T Λ = 3αews w λ 3 3πc w λ Λ Λ c B,W log = µ Λ λ 3 19π λ Λ log Λ µ v-improvement: Λ = m H and full model in terms of c α c H Λ = (1 cα) v c T Λ = 3αews w (1 cα) 8πcw v log m H c B,W µ Λ broken-phase matching: systematically all terms v/λ ( c T Λ = αews w (1 cα) 8πcw v 5 ) + 3 log m H c B,W = 1 cα µ Λ 144π v = 1 cα 48π v log m H µ ( log m H µ )

25 Matching matters Example: oblique parameters from Higgs portal vs D6 L EFT [Freitas, Lopez-Val, TP; Trott etal] c H Λ µ (φ φ) µ(φ φ) + c T Λ (φ D µ φ)(φ D µφ) + igc W Λ (φ σ k D µ φ)d ν W k µν predictions of Higgs portal model [m H λ v s, s α λ 3 v /(λ m H )] S λ 3 v 4πλ mh log m H mh 3λ 3 T v 3π sw λ mw ( m Z mh m W mh leading log for tree-insertion of loop operators O T,B,W [Λ = λ v s ] c H Λ = λ 3 λ Λ c T Λ = 3αews w λ 3 3πc w λ Λ Λ log c B,W = µ -3 Λ ) log m H m h λ 3 19π λ Λ log Λ µ T parameter v-improvement: Λ = m H and full model in terms of c α Full λ 1 = 1.8x10-1 LL-L c H Λ = (1 cα) c T v Λ = 3αews w (1 cα) 8πcw v log m H c B,W = 1 λ LL-TL = 6.6x10-3 cα µ Λ 48π v log m H LL-TLv BP-TL µ BP-TLv broken-phase matching: systematically all terms 10 0 v/λ ( c T Λ = αews w (1 cα) 8πcw v 5 ) + 3 log m S3 H c B,W = 1 cα sinα µ Λ 144π v Γ (H > hh) [GeV] δ r [%] 10-1 I I S ( m H [GeV] ) log m H µ D8 effects testing what? tanβ

26 Self consistency at LHC D6 Lagrangian at face value [Brehmer, Freitas, Lopez-Val, TP] 1 push (simplified) models to visible deviations at LHC Higgs portal, HDM, stops, vector triplet construct and match D6-Lagrangian to model [weakly interacting] coupling modifications v /Λ vs new kinematics /Λ? 3 LHC simulations: D6-Lagrangian vs full model production: WBF, VH, HH decays: H γγ, 4l check for peaks in p T,j or m VH,...

27 Self consistency at LHC D6 Lagrangian at face value [Brehmer, Freitas, Lopez-Val, TP] 1 push (simplified) models to visible deviations at LHC Higgs portal, HDM, stops, vector triplet construct and match D6-Lagrangian to model [weakly interacting] coupling modifications v /Λ vs new kinematics /Λ? 3 LHC simulations: D6-Lagrangian vs full model production: WBF, VH, HH decays: H γγ, 4l check for peaks in p T,j or m VH,... Ensuring self consistency [Monday discussion] not use high-virtuality data [Mawatari] psychologically bad for sensitive experimentalists define theory hypothesis with form factors [cutoff?] not the theory we want to test D6 Lagrangian at face value, but matching uncertainties well-defined, complete, just a little more work for theorists

28 Kinematic distributions Kinematical information for example on effective Lagrangian simple p T, m ij, φ ij trivially included [Butter etal] correlations hard, check impact full phase space: BDT/NN-variable-weighting phase space patterns understood?

29 Kinematic distributions Kinematical information for example on effective Lagrangian simple p T, m ij, φ ij trivially included [Butter etal] correlations hard, check impact full phase space: BDT/NN-variable-weighting phase space patterns understood? Kinematics for gauge boson production [Panico, Pomarol, Riva, Wulzer]

30 Kinematic distributions Kinematical information for example on effective Lagrangian simple p T, m ij, φ ij trivially included [Butter etal] correlations hard, check impact full phase space: BDT/NN-variable-weighting phase space patterns understood? Beyond distributions [That was 90s] Log-likelihood estimator for hypothesis testing [MadMax: Cranmer, Kling, TP, Schichtel, Wiegand] Neyman-Pearson lemma phase space integration statistics limiting factor significance distribution [HH b bγγ] dσ/d R γγ [10 bbγγ bbjγ ccγγ ZH Significance pb] Significance λ SM λ SM ( 0) R γγ

31 Kinematic distributions Kinematical information for example on effective Lagrangian simple p T, m ij, φ ij trivially included [Butter etal] correlations hard, check impact full phase space: BDT/NN-variable-weighting phase space patterns understood? Beyond distributions [That was 90s] Log-likelihood estimator for hypothesis testing [MadMax: Cranmer, Kling, TP, Schichtel, Wiegand] Neyman-Pearson lemma phase space integration statistics limiting factor significance distributions Fisher information for parameter estimate [MadFisher: Brehmer, Cranmer, Kling, TP] Cramer-Rao bound phase space integration statistics limiting factor information distributions LHC theorists: smell the coffee...

32 Information geometry Applied to D6 in WBF H ττ 0.10 [Brehmer, Cranmer, Kling, TP] 0.05 correlations in Wilson coefficient space fww v /Λ fw v /Λ

33 Information geometry Applied to D6 in WBF H ττ [Brehmer, Cranmer, Kling, TP] correlations in Wilson coefficient space information distribution Normalized distribution Background SM Information OW pt, j1 [GeV] (det Iij) 1/5

34 Information geometry Applied to D6 in WBF H ττ [Brehmer, Cranmer, Kling, TP] correlations in Wilson coefficient space information distribution 1D, D distributions vs full phase space pt, j1 d fww v /Λ full combined φjj fw v /Λ

35 Information geometry Applied to D6 in WBF H ττ [Brehmer, Cranmer, Kling, TP] correlations in Wilson coefficient space information distribution 1D, D distributions vs full phase space full statistical analysis: multi-variate wins

36 Information geometry Applied to D6 in WBF H ττ [Brehmer, Cranmer, Kling, TP] correlations in Wilson coefficient space information distribution 1D, D distributions vs full phase space full statistical analysis: multi-variate wins Combined with decay H 4l precision vs energy energy wins Iij eigenvalues WBF, H 4l, L ε = 100 fb Eigenvector composition: Oφ, OW OWW OB OBB Reach Λ/ f [TeV] (det Iij/det I ij full ) 1/ full xsec pt, l1 pt, 4l mz θ1 θ Φ pt, j1 mjj ηjj φjj Restricted to OW, OWW, Oφ, pt, j1, pt, j pt, j1, φjj pt, l1, pt, j1 pt, l1, φjj pt, 4l, pt, j1 pt, 4l, φjj Reach Λ/ f [TeV]

37 Bottom line Higgs and electroweak sectors same thing [linear representation] dimension-6 Higgs-gauge LHC analysis working effective Lagrangian validated through full models uncertainties part of matching distributions the key, not obviously easy... [Butter etal, Falkowski etal]