The Rise of Effective Lagrangians at the LHC

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1 The Rise of Effective Lagrangians at the LHC Universität Heidelberg Brookhaven, May 2016

2 750 GeV the finger to particle theory taste not true taste wide X γγ impossible spin-0 actual model X aa 4γ NMSSM narrow m γγ spin-1 2 effective couplings vector quarks Furry not true spin-2 taste not true A 750 GeV elefant in the Higgs room key question: another Higgs scalar? [Dawson & Lewis] largely EFT exercise [problem: large signal rate] dimension-5 operators XG µν G µν and XA µν A µν avoid di-jet constraints gauge invariant XB µν B µν and XW µν W µν avoid VV constraints no clear link to other data great to play with, but only for fun, please

3 Theory in data-driven era Same old theory motivation WIMP dark matter still best choice hierarchy problem (probably) a problem but: data in driving seat

4 Theory in data-driven era Same old theory motivation WIMP dark matter still best choice hierarchy problem (probably) a problem but: data in driving seat Theory tool box Lagrangian language established by Higgs discovery 1- full new physics model [built to solve problems] 2- simplified models [capturing experimental features, theoretically poor] 3- effective field theory [symmetries and particles fixed, non-renormalizable operators] matter of convenience and taste bottom-up EFT simplified models full models agnostic ( ) data-driven ( ) ( ) theory-driven ( )

5 Theory in data-driven era Same old theory motivation WIMP dark matter still best choice hierarchy problem (probably) a problem but: data in driving seat Theory tool box Lagrangian language established by Higgs discovery 1- full new physics model [built to solve problems] 2- simplified models [capturing experimental features, theoretically poor] 3- effective field theory [symmetries and particles fixed, non-renormalizable operators] matter of convenience and taste bottom-up EFT simplified models full models agnostic ( ) pre-lhc data-driven ( ) ( ) theory-driven ( ) pre-lhc

6 Theory in data-driven era Same old theory motivation WIMP dark matter still best choice hierarchy problem (probably) a problem but: data in driving seat Theory tool box Lagrangian language established by Higgs discovery 1- full new physics model [built to solve problems] 2- simplified models [capturing experimental features, theoretically poor] 3- effective field theory [symmetries and particles fixed, non-renormalizable operators] matter of convenience and taste bottom-up EFT simplified models full models agnostic ( ) dishonest pre-lhc data-driven boring ( ) ( ) theory-driven pointless ( ) pre-lhc

7 Agnostic: why super-simple SM-Higgs sector? or: all couplings proportional to masses? assume: narrow CP-even scalar Standard Model operators total production/decay rates only Lagrangian L = L SM + W gm W H W µ W µ + Z + gf G H v GµνGµν + γf A g [SFitter] f m f v H ( fr f L + h.c. ) m Z H Z µ Z µ 2c w τ,b,t H v AµνAµν + invisible + unobservable electroweak renormalizability through some UV completion QCD renormalizability not an issue gg H qq qqh gg t th qq VH g HXX = g SM HXX (1 + X ) t b,t H ZZ H WW H b b H τ + τ H γγ W,Z W,Z

8 Agnostic: why super-simple SM-Higgs sector? or: all couplings proportional to masses? assume: narrow CP-even scalar Standard Model operators total production/decay rates only Lagrangian L = L SM + W gm W H W µ W µ + Z + gf G H v GµνGµν + γf A g [SFitter] f m f v H ( fr f L + h.c. ) m Z H Z µ Z µ 2c w τ,b,t H v AµνAµν + invisible + unobservable t b,t W,Z W,Z Total width coupling extraction impossible without width assumption observed partial widths: N = σ BR g2 p Γtot g 2 d Γtot g 4 g 2 Γ i (g 2 ) g 2 + Γ unobs g 2 0 = 0 gives constraint from Γ i (g 2 ) < Γ tot Γ H min WW WW unitarity: g WWH g SM WWH Γ H max [HiggsSignals] our assumption Γ tot = obs Γ j [plus generation universality]

9 after Run I Run I legacy [Corbett, Eboli, Goncalves, Gonzalez-Fraile, Lopez-Val, TP, Rauch] assume SM-like [secondary solutions possible] SFitter: correct theory uncertainties L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. SM g x = g x (1+ x ) data H V f W Z t b τ Z/W b/τ b/w

10 after Run I Run I legacy [Corbett, Eboli, Goncalves, Gonzalez-Fraile, Lopez-Val, TP, Rauch] assume SM-like [secondary solutions possible] SFitter: correct theory uncertainties g γ with new loops L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. SM g x = g x (1+ x ) data W Z t b τ γ γ SM+NP Z/W b/τ b/w

11 after Run I Run I legacy [Corbett, Eboli, Goncalves, Gonzalez-Fraile, Lopez-Val, TP, Rauch] assume SM-like [secondary solutions possible] SFitter: correct theory uncertainties g γ with new loops g g vs g t barely possible L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. SM g x = g x (1+ x ) data W Z t b τ γ g b/w b/τ Z/W g SM+NP γ SM+NP

12 after Run I Run I legacy [Corbett, Eboli, Goncalves, Gonzalez-Fraile, Lopez-Val, TP, Rauch] assume SM-like [secondary solutions possible] SFitter: correct theory uncertainties g γ with new loops g g vs g t barely possible including invisible decays Standard Model within 25% L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. SM g x = g x (1+ x ) data W Z t b τ γ g b/w b/τ Z/W g SM+NP γ SM+NP BR inv

13 after Run I Run I legacy [Corbett, Eboli, Goncalves, Gonzalez-Fraile, Lopez-Val, TP, Rauch] assume SM-like [secondary solutions possible] SFitter: correct theory uncertainties g γ with new loops g g vs g t barely possible including invisible decays Standard Model within 25% Future [SFitter; Cranmer, Kreiss, Lopez-Val, TP] L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. SM g x = g x (1+ x ) data g γ τ b t Z W b/τ Z/W g SM+NP γ SM+NP BR inv b/w LHC extrapolations unclear systematic/theory uncertainties large e + e linear collider much better unobserved decays avoided width measured from σ ZH H c c accessible invisible decays hugely improved QCD theory error bars avoided % CL: 3000 fb -1, 14 TeV LHC and 250 fb -1, 250 GeV LC 3000 fb -1, 14 TeV LHC 250 fb -1, 250 GeV LC LHC + LC LHC + LC ( t c ) g x = g x SM (1+ x ) H W Z t c b τ γ g

14 after Run I Run I legacy [Corbett, Eboli, Goncalves, Gonzalez-Fraile, Lopez-Val, TP, Rauch] assume SM-like [secondary solutions possible] SFitter: correct theory uncertainties g γ with new loops g g vs g t barely possible including invisible decays Standard Model within 25% Future [SFitter; Cranmer, Kreiss, Lopez-Val, TP] L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. SM g x = g x (1+ x ) data g γ τ b t Z W b/w b/τ Z/W g SM+NP γ SM+NP BR inv LHC extrapolations unclear systematic/theory uncertainties large e + e linear collider much better unobserved decays avoided width measured from σ ZH H c c accessible invisible decays hugely improved QCD theory error bars avoided Higgs factory case obvious GeV LC, 250 fb GeV TLEP, 4 exp. 2.5 ab -1 68% CL g x = g x SM (1+ x ) -0.1 H W Z c b τ γ g

15 after Run I Run I legacy [Corbett, Eboli, Goncalves, Gonzalez-Fraile, Lopez-Val, TP, Rauch] assume SM-like [secondary solutions possible] SFitter: correct theory uncertainties g γ with new loops g g vs g t barely possible including invisible decays Standard Model within 25% L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. SM g x = g x (1+ x ) data Three major problems with approach W Z t b τ γ g b/w b/τ Z/W g SM+NP γ SM+NP BR inv 1 theory: no electroweak renormalizability 2 experiment: no kinematic distributions 3 phenomenology: no link to other sectors

16 D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ

17 D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ relevant part after equation of motion, etc L HVV = αsv 8π f g Λ 2 O GG + f BB Λ O 2 BB + f WW Λ 2 O WW + f B Λ 2 O B + f W Λ 2 O W + f φ,2 Λ 2 O φ,2

18 D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ relevant part after equation of motion, etc L HVV = αsv 8π f g Λ 2 O GG + f BB Λ O 2 BB + f WW Λ 2 to SM particles [derivatives = momentum, #2 solved] L HVV = g g HG a µν Gaµν + g γ HA µνa µν O WW + f B Λ 2 O B + f W Λ 2 O W + f φ,2 Λ 2 O φ,2 + g (1) Z Z µνz µ ν H + g (2) HZ Z µνz µν + g (3) HZ Z µz µ ( ) + g (1) W + W µν W µ ν H + h.c. + g (2) W HW + µν W µν + g (3) W HW + µ W µ +

19 D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ relevant part after equation of motion, etc L HVV = αsv 8π f g Λ 2 O GG + f BB Λ O 2 BB + f WW Λ 2 to SM particles [derivatives = momentum, #2 solved] L HVV = g g HG a µν Gaµν + g γ HA µνa µν O WW + f B Λ 2 O B + f W Λ 2 O W + f φ,2 Λ 2 O φ,2 + g (1) Z Z µνz µ ν H + g (2) HZ Z µνz µν + g (3) HZ Z µz µ ( ) + g (1) W + W µν W µ ν H + h.c. + g (2) W HW + µν W µν + g (3) W HW + µ W µ + plus Yukawa structure f τ,b,t 9 operators for Run I data

20 D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ linked to g g = f GGv Λ 2 g (1) Z g (2) Z = g2 v 2Λ 2 = g2 v 2Λ 2 αs f gv 8π Λ 2 c 2 w f W + s 2 w f B 2c 2 w g (3) Z = M 2 Z ( 2G F ) 1/2 g f = m f v ( s 4 w f BB + c 4 w f WW 2cw 2 ( 1 v 2 1 v 2 2Λ 2 f φ,2 ) 2Λ f 2 φ,2 ) + v 2 f f 2Λ 2 g γ = g2 vs 2 w 2Λ 2 g (1) W g (2) W = g2 v 2Λ 2 f W 2 = g2 v 2Λ f 2 WW f BB + f WW 2 g (3) W = M2 W ( 2G F ) 1/2 ( 1 v ) 2 2Λ f 2 φ,2

21 EFT@LHC D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ Run 1 legacy kinematics: p T,V, φ jj [remember #2] Events/bin leptons 10 2 SM (SM Higgs) x 70 (f W /Λ 2 =20TeV -2 ) x p T V(GeV)

22 EFT@LHC D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ Run 1 legacy kinematics: p T,V, φ jj [remember #2] Events/bin 10 2 SM Higgs f WW /Λ 2 =-f BB /Λ 2 =20TeV -2 f WW /Λ 2 =-f BB /Λ 2 =-20TeV -2 γγ jj 10 0 π/3 2π/3 π Φ jj

23 D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ Run 1 legacy kinematics: p T,V, φ jj [remember #2] with impact... f B /Λ 2 40 [TeV -2 ] f W /Λ 2 [TeV -2 ]

24 D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ Run 1 legacy kinematics: p T,V, φ jj [remember #2] with impact......in last bin f B /Λ 2 40 [TeV -2 ] f W /Λ 2 [TeV -2 ]

25 D6 Higgs operators Higgs sector effective field theory [Eboli, Goncales-Garcia,...] 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,2 = 1 ( ) ( ) 2 µ φ φ µ φ φ O φ,3 = 1 3 ( φ φ) 3 O φ,4 = (D µφ) ( D µ φ ) ( ) φ φ Run 1 legacy kinematics: p T,V, φ jj [remember #2] with impact......in last bin Run I sensitivity limited L= (7 TeV) (8 TeV) fb -1, 68% CL: ATLAS + CMS f/λ 2 [TeV -2 ] Λ/ f [TeV] f/λ 2 [TeV -2 ] 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]

26 EFT@LHC D6 Higgs-gauge operators Triple gauge couplings one more Higgs-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 Events/bin SM WW Background f W /Λ 2 =25TeV -2 f B /Λ 2 =25TeV -2 f WWW /Λ 2 =25TeV -2 Data p T lead(gev)

27 D6 Higgs-gauge operators Triple gauge couplings one more Higgs-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 ] -2 [TeV 2 f B Λ CMS ATLAS 7 WZ 7 semi 8 WW 8 WZ combined f W -2 [TeV ] 2 Λ

28 D6 Higgs-gauge operators Triple gauge couplings one more Higgs-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 affecting correlations ] -2 [TeV 2 f B Λ f W -2 [TeV ] 2 Λ

29 D6 Higgs-gauge operators Triple gauge couplings one more Higgs-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 affecting correlations complete Higgs-gauge analysis f/λ 2 [TeV -2 ] LHC-Higgs, 95% CL LHC-Higgs + LHC-TGV + LEP-TGV, 95% CL Λ/ f [TeV] f/λ 2 [TeV -2 ] Λ/ f [TeV] O GG O WW O BB O W O B O φ2 O WWW O t O b O τ

30 D6 Higgs-gauge operators Triple gauge couplings one more Higgs-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 affecting correlations complete Higgs-gauge analysis LHC vs LEP triple gauge vertices g 1, κ, λ vs operators semileptonic analyses missing for 8 TeV Run I LHC beating LEP ] -2 [TeV 2 f B Λ LHC LHC+LEP 60 LEP f W -2 [TeV ] 2 Λ

31 Exercise: higher-dimensional operators Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O φ,2 = 1 2 µ(φ φ) µ (φ φ), O φ,3 = 1 3 (φ φ) 3

32 Exercise: higher-dimensional operators Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O φ,2 = 1 2 µ(φ φ) µ (φ φ), O φ,3 = 1 3 (φ φ) 3 first operator, wave function renormalization O φ,2 = 1 2 µ(φ φ) µ (φ φ)= 1 2 ( H + v) 2 µ H µ H proper normalization of combined kinetic term [LSZ] L kin = 1 ( 2 µ H µ H 1 + f ) φ,2v 2! = 1 Λ 2 2 µh µ H H = H 1 + f φ,2v 2 Λ 2

33 Exercise: higher-dimensional operators Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O φ,2 = 1 2 µ(φ φ) µ (φ φ), O φ,3 = 1 3 (φ φ) 3 first operator, wave function renormalization O φ,2 = 1 2 µ(φ φ) µ (φ φ)= 1 2 ( H + v) 2 µ H µ H proper normalization of combined kinetic term [LSZ] L kin = 1 ( 2 µ H µ H 1 + f ) φ,2v 2! = 1 Λ 2 2 µh µ H H = H second operator, minimum condition giving v v 2 = µ2 λ f φ,3µ 4 4λ 3 Λ f φ,2v 2 Λ 2

34 Exercise: higher-dimensional operators Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O φ,2 = 1 2 µ(φ φ) µ (φ φ), O φ,3 = 1 3 (φ φ) 3 first operator, wave function renormalization O φ,2 = 1 2 µ(φ φ) µ (φ φ)= 1 2 ( H + v) 2 µ H µ H proper normalization of combined kinetic term [LSZ] L kin = 1 ( 2 µ H µ H 1 + f ) φ,2v 2! = 1 Λ 2 2 µh µ H H = H second operator, minimum condition giving v v 2 = µ2 λ f φ,3µ 4 4λ 3 Λ 2 both operators contributing to Higgs mass L mass = µ2 H λv 2 H2 f φ,3 15 Λ 2 24 v 4! H2 = m2 H 2 H2 m 2 H = 2λv 2 ( 1 f φ,2v 2 + f φ,3v 2 Λ 2 2Λ 2 λ ) 1 + f φ,2v 2 Λ 2

35 Exercise: higher-dimensional operators Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O φ,2 = 1 2 µ(φ φ) µ (φ φ), O φ,3 = 1 3 (φ φ) 3 Higgs self couplings momentum dependent [( L self = m2 H 1 f φ,2v 2 + 2f ) φ,3v 4 2v 2Λ 2 3Λ 2 mh 2 H 3 2f ] φ,2v 2 Λ 2 mh 2 H µh µ H [( m2 H 1 f φ,2v 2 + 4f ) φ,3v 4 8v 2 Λ 2 Λ 2 mh 2 H 4 4f ] φ,2v 2 Λ 2 mh 2 H 2 µ H µ H

36 Exercise: higher-dimensional operators Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O φ,2 = 1 2 µ(φ φ) µ (φ φ), O φ,3 = 1 3 (φ φ) 3 Higgs self couplings momentum dependent [( L self = m2 H 1 f φ,2v 2 + 2f ) φ,3v 4 2v 2Λ 2 3Λ 2 mh 2 H 3 2f ] φ,2v 2 Λ 2 mh 2 H µh µ H [( m2 H 1 f φ,2v 2 + 4f ) φ,3v 4 8v 2 Λ 2 Λ 2 mh 2 H 4 4f ] φ,2v 2 Λ 2 mh 2 H 2 µ H µ H alternatively, strong multi-higgs interactions ( H = 1 + f ) φ,2v 2 H + f φ,2v H2 + f φ,2 H3 + O( H 4 ) 2Λ 2 2Λ 2 6Λ 2

37 Exercise: higher-dimensional operators Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O φ,2 = 1 2 µ(φ φ) µ (φ φ), O φ,3 = 1 3 (φ φ) 3 Higgs self couplings momentum dependent [( L self = m2 H 1 f φ,2v 2 + 2f ) φ,3v 4 2v 2Λ 2 3Λ 2 mh 2 H 3 2f ] φ,2v 2 Λ 2 mh 2 H µh µ H [( m2 H 1 f φ,2v 2 + 4f ) φ,3v 4 8v 2 Λ 2 Λ 2 mh 2 H 4 4f ] φ,2v 2 Λ 2 mh 2 H 2 µ H µ H alternatively, strong multi-higgs interactions ( H = 1 + f ) φ,2v 2 H + f φ,2v H2 + f φ,2 H3 + O( H 4 ) 2Λ 2 2Λ 2 6Λ 2 operators and distributions linked to poor UV behavior

38 D6 top operators Same for tops [TopFitter: Buckley, Englert, Ferrando, Miller, Moore, Russell, White] single, pair-wise, and associated top production [plus decays] including anomalous A FB from Tevatron 4-quark, Yang-Mills, electroweak operators O qq = qγ µq tγ µ t profile likelihoods and individual limits Generic D6 reach 500 GeV [C = 1] O G = f ABC G Aν µ GBλ ν GCµ λ O φg = φ φg a µν Gaµν CG C 33 ug individual marginalized C 1 u C 2 u C 1 d C 2 d C 33 uw Ct C 3 φq C 33 ub Cφu C 1 φq Ci = Civ 2 /Λ 2

39 D6 top operators Same for tops [TopFitter: Buckley, Englert, Ferrando, Miller, Moore, Russell, White] single, pair-wise, and associated top production [plus decays] including anomalous A FB from Tevatron 4-quark, Yang-Mills, electroweak operators O qq = qγ µq tγ µ t profile likelihoods and individual limits Generic D6 reach 500 GeV [C = 1] O G = f ABC G Aν µ GBλ ν GCµ λ O φg = φ φg a µν Gaµν CG C 33 ug individual marginalized For theorists: in terms of models axigluon: M A > 1.4 TeV [t t resonance] SM-like W : M W > 1.2 TeV [t-channel,...] models less sensitive to correlations C 1 u C 2 u C 1 d C 2 d C 33 uw Ct C 3 φq C 33 ub Cφu C 1 φq Ci = Civ 2 /Λ 2

40 D6 dark matter operators Combining direct, indirect, collider results for WIMPs [Tait etal] choose dark matter candidate [Majorana/Dirac fermion, scalar, dark photon] consider D6 scattering process χχ SM SM relic density from annihilation [mχ/t 30] indirect detection even later direct detection non-relativistic [E 10 MeV] LHC tricky: single scale m χ m mediator? example: scalar dark matter LabelCoefficient Operator σ SI σannv Real scalar R1 λ 1 1/(2M 2 ) mq χ 2 qq s-wave R2 λ 2 1/(2M 2 ) imq χ 2 qγ 5 q s-wave R3 λ 3 αs /(4M 2 )χ 2 Gµν G µν s-wave R4 λ 4 αs /(4M 2 )iχ 2 Gµν G µν s-wave Complex scalar C1 λ 1 1/(M 2 ) mq χ χ qq s-wave C2 λ 2 1/(M 2 ) imq χ χ qγ 5 q s-wave C3 λ 3 1/(M 2 ) χ µχ qγ µ q p-wave C4 λ 4 1/(M 2 ) χ µχ qγ µ γ 5 q p-wave C5 λ 5 αs /(8M 2 )χ χgµν G µν s-wave C6 λ 6 αs /(8M 2 )iχ χgµν G µν s-wave

D6 dark matter operators Relic density plus Hooperon default input: relic density scalar dark matter LabelCoefficient Operator σ SI σannv Real scalar R1 λ 1 1/(2M 2 ) mq χ 2 qq s-wave R2 λ 2 1/(2M 2

41 D6 dark matter operators Relic density plus Hooperon default input: relic density scalar dark matter LabelCoefficient Operator σ SI σannv Real scalar R1 λ 1 1/(2M 2 ) mq χ 2 qq s-wave R2 λ 2 1/(2M 2 ) imq χ 2 qγ 5 q s-wave R3 λ 3 αs /(4M 2 )χ 2 Gµν G µν s-wave R4 λ 4 αs /(4M 2 )iχ 2 Gµν G µν s-wave profile likelihood [Liem, Bertone, Calore, Ruiz de Austri, Tait, Trotta, Weniger] flat prior on log λ i [prior 1/λ i ] Dirichlet prior prefering similar-sized Wilson coefficients

42 D6 dark matter operators Relic density plus Hooperon default input: relic density scalar dark matter LabelCoefficient Operator σ SI σannv Real scalar R1 λ 1 1/(2M 2 ) mq χ 2 qq s-wave R2 λ 2 1/(2M 2 ) imq χ 2 qγ 5 q s-wave R3 λ 3 αs /(4M 2 )χ 2 Gµν G µν s-wave R4 λ 4 αs /(4M 2 )iχ 2 Gµν G µν s-wave profile likelihood [Liem, Bertone, Calore, Ruiz de Austri, Tait, Trotta, Weniger] flat prior on log λ i [prior 1/λ i ] Dirichlet prior prefering similar-sized Wilson coefficients Fermi: GCE plus dwarf galaxies with data, the method hardly matters...

43 (Simplified) scalar/gauge extensions Higgs singlet/doublet extensions [Higgs portal] one or more new (pseudo-) scalars mixing with SM-like Higgs

44 (Simplified) scalar/gauge extensions Higgs singlet/doublet extensions [Higgs portal] one or more new (pseudo-) scalars mixing with SM-like Higgs Scalar top partners, non-higgs [simplfied supersymmetry] Lagrangian with scalar top partner, singlet plus doublet µ L (D µ ) (D Q) + (Dµ t R ) (D µ t R ) Q M 2 Q M2 t R t R κ LL (φ Q) (φ Q) [ κ RR ( t R t R )(φ φ) κ LR M t R (φ Q) ] + h.c. contribution through loops all over Higgs-gauge sector

45 (Simplified) scalar/gauge extensions Higgs singlet/doublet extensions [Higgs portal] one or more new (pseudo-) scalars mixing with SM-like Higgs Scalar top partners, non-higgs [simplfied supersymmetry] Lagrangian with scalar top partner, singlet plus doublet µ L (D µ ) (D Q) + (Dµ t R ) (D µ t R ) Q M 2 Q M2 t R t R κ LL (φ Q) (φ Q) [ κ RR ( t R t R )(φ φ) κ LR M t R (φ Q) ] + h.c. contribution through loops all over Higgs-gauge sector Triplet gauge extension [whatever that becomes in the UV] additional vector triplet field V µ L 1 Ṽ a 4 µνṽµνa + M2 Ṽ Ṽ a 2 µṽ µa + i g [ V 2 c H Ṽ a µ φ σ a ] D µ φ + g2 w Ṽ a µ c F F L γ µ σ a F L 2g V fermions + g V 2 c VVV ɛ abc Ṽ a µṽ b ν D[µ Ṽ ν]c + g 2 V c VVHH Ṽ a µṽ µa (φ φ) gw 2 c VVW ɛ abc W µν Ṽ b µṽ c ν new states, mixing with W ± and Z weak gauge coupling to W, Z mass eigenstates

46 Higgs D6 breakdown D6-Lagrangian breakdown [Brehmer, Freitas, Lopez-Val, TP] phenomenology: does D6 capture all model features at LHC? theory: how do D6 vs EFT vs full model differences appear?

47 Higgs D6 breakdown D6-Lagrangian breakdown [Brehmer, Freitas, Lopez-Val, TP] phenomenology: does D6 capture all model features at LHC? theory: how do D6 vs EFT vs full model differences appear? push (simplified) models to visible deviations at 13 TeV Higgs portal, 2HDM, stops, vector triplet [weakly interacting, Eq.(2)] σ BR 1 (σ BR) SM = g2 m 2 h 10% Λ 2 Λ 400 GeV no scale hierarchy for testable models?!

48 Higgs D6 breakdown D6-Lagrangian breakdown [Brehmer, Freitas, Lopez-Val, TP] phenomenology: does D6 capture all model features at LHC? theory: how do D6 vs EFT vs full model differences appear? push (simplified) models to visible deviations at 13 TeV Higgs portal, 2HDM, stops, vector triplet [weakly interacting, Eq.(2)] σ BR 1 (σ BR) SM = g2 m 2 h 10% Λ 400 GeV Λ 2 no scale hierarchy for testable models?! construct and match D6-Lagrangian to model coupling modifications v 2 /Λ 2 vs new kinematics /Λ? matching conditions with v Λ, v-improved matching

49 Higgs D6 breakdown D6-Lagrangian breakdown [Brehmer, Freitas, Lopez-Val, TP] phenomenology: does D6 capture all model features at LHC? theory: how do D6 vs EFT vs full model differences appear? push (simplified) models to visible deviations at 13 TeV Higgs portal, 2HDM, stops, vector triplet [weakly interacting, Eq.(2)] σ BR 1 (σ BR) SM = g2 m 2 h 10% Λ 400 GeV Λ 2 no scale hierarchy for testable models?! construct and match D6-Lagrangian to model coupling modifications v 2 /Λ 2 vs new kinematics /Λ? matching conditions with v Λ, v-improved matching LHC simulations: D6-Lagrangian vs full model production: WBF, VH, HH decays: H γγ, 4l check where differences appear at 13 TeV kinematic distributions like p T,j or m VH? resonance peaks of new states?

50 Higgs D6 breakdown Higgs portal testable benchmarks for LHC Singlet EFT EFT (v-improved) m H sin α v s/v singlet x Λ c H EFT x c H EFT x effects in WBF and hh + - miss u d u d l l E T (S5) p p h h (S4) σ [fb/bin] SM full σ [fb/bin] 1.5 SM 1 σ EFT - σ full σ full EFT 0 EFT error m T [GeV] σ EFT - σ full σ full full (no H) EFT error full EFT m hh [GeV]

51 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC 2HDM EFT Type tan β α/π m 12 m H 0 m A 0 m H ± Λ [GeV] c u c d,l I II II I

52 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC 2HDM EFT Type tan β α/π m 12 m H 0 m A 0 m H ± Λ [GeV] c u c d,l I II II I effects in H γγ σ [fb/bin] EFT 0 p p h γ γ (D1) SM full σ EFT - σ full σ full 1 0 EFT error m γγ [GeV]

53 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC effects in H γγ Top partners testable benchmarks for LHC Scalar top-partner model EFT M κ LL κ RR κ LR m t 1 m t 2 c H c W c HW

54 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC effects in H γγ Top partners testable benchmarks for LHC Scalar top-partner model EFT p p V h (P2) M κ LL κ RR κ LR m t 1 m t c H c W c HW 2 80 SM EFT full effects in WBF and Vh σ [fb/bin] σ EFT - σ full σ full EFT error m Vh [GeV]

55 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC effects in H γγ Top partners testable benchmarks for LHC effects in WBF and Vh Vector triplet [Brehmer, Biekötter, Krämer, TP] testable benchmarks for LHC Triplet model EFT M V g V c H c F c VVHH m ξ c W c H c 6 c f

56 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC effects in H γγ Top partners testable benchmarks for LHC effects in WBF and Vh Vector triplet [Brehmer, Biekötter, Krämer, TP] testable benchmarks for LHC Triplet model M V g V c H c F c VVHH m ξ c W c H c 6 c f EFT full (no ξ) SM effects in Vh and WBF σ [fb/bin] σ EFT - σ full σ full EFT EFT error p p V h (T4) full [GeV] m Vh

57 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC effects in H γγ Top partners testable benchmarks for LHC effects in WBF and Vh Vector triplet [Brehmer, Biekötter, Krämer, TP] testable benchmarks for LHC Triplet model M V g V c H c F c VVHH m ξ c W c H c 6 full c f 1 EFT full (no ξ) SM EFT error m Vh [GeV] effects in Vh and WBF σ [fb/bin] σ EFT - σ full σ full EFT p p V h (T4')

58 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC effects in H γγ Top partners testable benchmarks for LHC effects in WBF and Vh Vector triplet [Brehmer, Biekötter, Krämer, TP] testable benchmarks for LHC Triplet model EFT 1 M V g V c H c F c VVHH m ξ c W c H c 6 c f effects in Vh and WBF σ [fb/bin] u d u d h (T5) SM EFT full (no ξ) full EFT error σ EFT - σ full σ full p [GeV] T,j1

59 Higgs D6 breakdown Higgs portal testable benchmarks for LHC effects in WBF and hh 2HDM testable benchmarks for LHC effects in H γγ Top partners testable benchmarks for LHC effects in WBF and Vh Vector triplet [Brehmer, Biekötter, Krämer, TP] testable benchmarks for LHC Triplet model EFT 1 M V g V c H c F c VVHH m ξ c W c H c 6 c f SM EFT full (no ξ) full EFT error effects in Vh and WBF σ [fb/bin] σ EFT - σ full σ full u d u d h (T5') p [GeV] T,j1

60 Higgs D6 breakdown Reasons for D6-breakdown in Higgs sector at LHC Model Process EFT failure resonance kinematics matching singlet on-shell h 4l, WBF, Vh,... off-shell WBF,... ( ) hh 2HDM on-shell h 4l, WBF, Vh,... off-shell H γγ,... ( ) hh top partner WBF, Vh vector triplet WBF ( ) Vh ( )

61 Higgs D6 breakdown Reasons for D6-breakdown in Higgs sector at LHC Model Process EFT failure resonance kinematics matching singlet on-shell h 4l, WBF, Vh,... off-shell WBF,... ( ) hh 2HDM on-shell h 4l, WBF, Vh,... off-shell H γγ,... ( ) hh top partner WBF, Vh vector triplet WBF ( ) Vh ( ) Lessons from Higgs sector start with D6 description [data-driven era of particle physics] EFT expansion in E/Λ known to be dodgy test D6 in comparison to (simplified) models all relevant effect at tree level resonance peaks the key feature

62 Questions Questions waiting to be answered is it really the Standard Model Higgs? [No] is there WIMP dark matter? [Yes] is there TeV-scale physics beyond the Standard Model? [Yes] are EFT analyses boring? [Yes] will we stop EFT analyses once we find new states [Hopefully] welcome to a data-driven era! Lectures on LHC Physics and dark matter updated under plehn/ Much of this work was funded by the BMBF Theorie-Verbund which is ideal for relevant LHC work

Kinematics in Higgs Fits

Kinematics in Higgs Fits Universität Heidelberg LHCHXS Meeting, November 2015 Higgs Couplings Standard Model operators [SFitter: Gonzalez-Fraile, Klute, TP, Rauch, Zerwas] Lagrangian [in terms of non-linear