Higgs Physics for the LHC

Transcription

1 Higgs Physics for the LHC Universität Heidelberg Brookhaven, 9/2013

2 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2

3 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution

4 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution

5 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution 1966: original Higgs phenomenology

6 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution 1966: original Higgs phenomenology

7 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution 1966: original Higgs phenomenology

8 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution 1966: original Higgs phenomenology 1976 etc: collider phenomenology

9 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution 1966: original Higgs phenomenology 1976 etc: collider phenomenology

10 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution 1966: original Higgs phenomenology 1976 etc: collider phenomenology 1989 Higgs hunter s guide

11 Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2) L U(1) Y U(1) Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 2 Higgs-related papers [also Brout & Englert; Guralnik, Hagen, Kibble] 1964: combining two problems to one predictive solution 1966: original Higgs phenomenology 1976 etc: collider phenomenology 1989 Higgs hunter s guide predicted from mathematical field theory

12 Higgs Physics Two problems for spontaneous gauge symmetry breaking problem 1: Goldstone s theorem SU(2)L U(1)Y U(1)Q gives 3 massless scalars problem 2: massive gauge theories massive gauge bosons have 3 polarizations, and 3 6= 2 In terms of Higgs potential V =µ2 φ 2 + λ φ 4 minimum at v φ= 2 V v2 µ2 =µ2 + 2λ φ 2 = 2 φ 2 2λ excitation φ = 2 mh = 2V H 2 v +H 2 = 2λv 2 minimum

13 Higgs signatures Higgs decays easy [Hdecay] weak-scale scalar coupling proportional to mass off-shell decays below threshold decay to γγ via W and top loop [destructive interference] m H = 126 GeV perfect 1 bb _ BR(H) WW ZZ τ + τ cc _ gg tt γγ Zγ M H [GeV]

14 Higgs signatures Higgs decays easy [Hdecay] weak-scale scalar coupling proportional to mass off-shell decays below threshold decay to γγ via W and top loop [destructive interference] m H = 126 GeV perfect Higgs production hard [7-8 TeV, 5-15/fb] quantum effects needed gluon fusion production loop induced weak boson fusion production with jets [σ fb] [σ 1200 fb] t W,Z b,t W,Z

15 Higgs signatures Higgs decays easy [Hdecay] weak-scale scalar coupling proportional to mass off-shell decays below threshold decay to γγ via W and top loop [destructive interference] m H = 126 GeV perfect Higgs production hard [7-8 TeV, 5-15/fb] quantum effects needed gluon fusion production loop induced weak boson fusion production with jets easy channels for pp H ZZ 4l fully reconstructed pp H γγ fully reconstructed pp H WW (l ν)(l + ν) large BR [σ fb] [σ 1200 fb] t b,t W,Z W,Z

16 Higgs signatures Higgs decays easy [Hdecay] weak-scale scalar coupling proportional to mass off-shell decays below threshold decay to γγ via W and top loop [destructive interference] m H = 126 GeV perfect Higgs production hard [7-8 TeV, 5-15/fb] quantum effects needed gluon fusion production loop induced weak boson fusion production with jets easy channels for pp H ZZ 4l fully reconstructed pp H γγ fully reconstructed pp H WW (l ν)(l + ν) large BR fun still waiting pp H ττ plus jets pp ZH (l + l )(b b) boosted pp t th waiting for a good idea... [σ fb] [σ 1200 fb] t b,t W,Z W,Z

17 Higgs discovery 4th of July fireworks [no theory input needed beyond basic Pythia/Herwig] silver channel H γγ local significance 4.5σ (ATLAS), 4.1σ (CMS) golden channel H ZZ 4l local significance 3.4σ (ATLAS), 3.2σ (CMS) WW and ττ, bb adding little (CMS) combined 5.0σ (ATLAS), 4.9σ (CMS) [LEE 4.3σ]

18 Higgs discovery 4th of July fireworks [no theory input needed beyond basic Pythia/Herwig] silver channel H γγ local significance 4.5σ (ATLAS), 4.1σ (CMS) golden channel H ZZ 4l local significance 3.4σ (ATLAS), 3.2σ (CMS) WW and ττ, bb adding little (CMS) combined 5.0σ (ATLAS), 4.9σ (CMS) [LEE 4.3σ] Rolf Heuer: We have him

19 Higgs discovery 4th of July fireworks [no theory input needed beyond basic Pythia/Herwig] silver channel H γγ local significance 4.5σ (ATLAS), 4.1σ (CMS) golden channel H ZZ 4l local significance 3.4σ (ATLAS), 3.2σ (CMS) WW and ττ, bb adding little (CMS) combined 5.0σ (ATLAS), 4.9σ (CMS) [LEE 4.3σ] Rolf Heuer: We have it

20 Questions 1. What is the Higgs? psychologically: looked for Higgs, so found a Higgs CP-even spin-0 scalar expected, what about D6 operators? spin-1 vector unlikely spin-2 graviton unexpected

21 Questions 1. What is the Higgs? psychologically: looked for Higgs, so found a Higgs CP-even spin-0 scalar expected, what about D6 operators? spin-1 vector unlikely spin-2 graviton unexpected 2. What are the coupling values? coupling after fixing operator basis Standard Model Higgs vs anomalous couplings

22 Questions 1. What is the Higgs? psychologically: looked for Higgs, so found a Higgs CP-even spin-0 scalar expected, what about D6 operators? spin-1 vector unlikely spin-2 graviton unexpected 2. What are the coupling values? coupling after fixing operator basis Standard Model Higgs vs anomalous couplings 3. What does all this tell us? two-higgs-doublet models? models predicting weak-scale new physics? renormalization group based Hail-Mary passes?

23 Example: Higgs potential Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O 1 = 1 2 µ(φ φ) µ (φ φ), O 2 = 1 3 (φ φ) 3

24 Example: Higgs potential Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O 1 = 1 2 µ(φ φ) µ (φ φ), O 2 = 1 3 (φ φ) 3 first operator, wave function renormalization O 1 = 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 ) 1v 2! = 1 Λ 2 2 µh µ H H = H 1 + f 1v 2 Λ 2

25 Example: Higgs potential Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O 1 = 1 2 µ(φ φ) µ (φ φ), O 2 = 1 3 (φ φ) 3 first operator, wave function renormalization O 1 = 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 ) 1v 2! = 1 Λ 2 2 µh µ H H = H 1 + f 1v 2 Λ 2 second operator, minimum condition to fix v ( ) v 2 µ2 2 = 2λ f 2µ 4 8λ 3 Λ + 2 O(Λ 4 ) = µ2 1 + f 2µ 2 2λ 4λ 2 Λ 2 2λΛ2 f2 2 + O(Λ 0 )

26 Example: Higgs potential Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O 1 = 1 2 µ(φ φ) µ (φ φ), O 2 = 1 3 (φ φ) 3 first operator, wave function renormalization O 1 = 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 ) 1v 2! = 1 Λ 2 2 µh µ H H = H 1 + f 1v 2 Λ 2 second operator, minimum condition to fix v ( ) v 2 µ2 2 = 2λ f 2µ 4 8λ 3 Λ + 2 O(Λ 4 ) = µ2 1 + f 2µ 2 2λ 4λ 2 Λ 2 2λΛ2 f2 2 + O(Λ 0 ) physical Higgs mass L mass = µ2 H λv 2 H2 f 2 15 Λ 2 24 v 4! H2 = m2 H 2 H2 m 2 H = 2λv 2 ( 1 f 1v 2 Λ 2 + f 2v 2 2Λ 2 λ )

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

28 Example: Higgs potential Higgs sector including dimension-6 operators L D6 = 2 i=1 f i Λ 2 O i with O 1 = 1 2 µ(φ φ) µ (φ φ), O 2 = 1 3 (φ φ) 3 Higgs self couplings momentum dependent [( L self = m2 H 1 f 1v 2 2v 2Λ + 2f ) 2v 4 2 3Λ 2 mh 2 H 3 2f ] 1v 2 Λ 2 mh 2 H µh µ H m2 H 8v 2 [( 1 f 1v 2 Λ 2 + 4f 2v 4 Λ 2 m 2 H ) H 4 4f 1v 2 Λ 2 mh 2 H 2 µ H µ H field renormalization, strong multi-higgs interactions ( H = 1 + f ) 1v 2 H + f 1v H2 + f 1 H3 + O( H 4 ) 2Λ 2 2Λ 2 6Λ 2 ].

29 Higher-dimensional operators Light Higgs as a Goldstone boson [Contino, Giudice, Grojean, Mühlleitner, Pomarol, Rattazzi,...] strongly interacting models predicting heavy broad resonance(s) light state if protected by Goldstone s theorem [Georgi & Kaplan] interesting if v f < 4πf m ρ [little Higgs v g 2 f /(2π)] adding specific D6 operator set

30 Higher-dimensional operators Light Higgs as a Goldstone boson [Contino, Giudice, Grojean, Mühlleitner, Pomarol, Rattazzi,...] strongly interacting models predicting heavy broad resonance(s) light state if protected by Goldstone s theorem [Georgi & Kaplan] interesting if v f < 4πf m ρ [little Higgs v g 2 f /(2π)] adding specific D6 operator set L SILH = c ( ) ( ) H 2f 2 µ H H µ H H + c ( T 2f 2 ) ( 3 cy y f + c 6λ f 2 ( H H + ic W g 2m 2 ρ ( H σ i D µ H f 2 H H f L Hf R + h.c. ) (D ν W µν) i + ic Bg H ) ( D µ H ) 2m 2 ρ H ) D µh ( H ) D µ H ( ν B µν) + ic HW g 16π 2 f 2 (Dµ H) σ i (D ν H)W i µν + ic HBg 16π 2 f 2 (Dµ H) (D ν H)B µν + cγg 2 g 2 H HB µνb µν + cgg2 S y 2 t H HG a 16π 2 f 2 gρ 2 16π 2 f 2 gρ 2 µν Gaµν.

31 Higher-dimensional operators Light Higgs as a Goldstone boson [Contino, Giudice, Grojean, Mühlleitner, Pomarol, Rattazzi,...] strongly interacting models predicting heavy broad resonance(s) light state if protected by Goldstone s theorem [Georgi & Kaplan] interesting if v f < 4πf m ρ [little Higgs v g 2 f /(2π)] adding specific D6 operator set L SILH = c ( ) ( ) H f 2 µ H H µ H H + c ( T H ) ( D µ H H ) D µh f 2 c ( ) ( ) 6 H 3 cy y f H + (3f ) 2 f 2 H H f L Hf R + h.c. + ic ( W H σ i ) D µ H (D ν W µν) i + ic ( B H ) D µ H ( ν B µν) (16f ) 2 (16f ) 2 + ic HW (16f ) 2 (Dµ H) σ i (D ν H)W i µν + ic HB (16f 2 ) (Dµ H) (D ν H)B µν + cγ (256f ) 2 H HB µνb µν + cg (256f ) 2 H HG a µν Gaµν.

32 Higher-dimensional operators Light Higgs as a Goldstone boson [Contino, Giudice, Grojean, Mühlleitner, Pomarol, Rattazzi,...] strongly interacting models predicting heavy broad resonance(s) light state if protected by Goldstone s theorem [Georgi & Kaplan] interesting if v f < 4πf m ρ [little Higgs v g 2 f /(2π)] adding specific D6 operator set collider phenomenology of mostly (H H) terms

33 Higher-dimensional operators Light Higgs as a Goldstone boson [Contino, Giudice, Grojean, Mühlleitner, Pomarol, Rattazzi,...] strongly interacting models predicting heavy broad resonance(s) light state if protected by Goldstone s theorem [Georgi & Kaplan] interesting if v f < 4πf m ρ [little Higgs v g 2 f /(2π)] adding specific D6 operator set collider phenomenology of mostly (H H) terms Anomalous Higgs couplings [Hagiwara etal; Corbett, Eboli, Gonzales-Fraile, Gonzales-Garcia] assume Higgs is largely Standard Model additional higher-dimensional couplings L eff = αsv 8π f g Λ 2 (Φ Φ)G µνg µν + f WW Λ 2 Φ W µνw µν Φ + f W Λ 2 (DµΦ) W µν (D νφ) + f B Λ 2 (DµΦ) B µν (D νφ) + f WWW Λ 2 Tr(W µνw νρ W µ ρ ) + f b Λ 2 (Φ Φ)(Q 3 Φd R,3 ) + fτ Λ 2 (Φ Φ)(L 3 Φe R,3 ) plus e-w precision data and triple gauge couplings remember what your operators are!

34 Angular Correlations Measurements of operator structures Cabibbo Maksymowicz Dell Aquila Nelson angles for H ZZ [Melnikov etal; Lykken etal; v d Bij etal; Choi etal] Ze Zµ cos θ e = ˆp e ˆp Zµ cos θ µ = ˆp µ ˆp Ze cos θ X = ˆp Ze ˆp beam cos φ e = (ˆp beam ˆp Zµ ) (ˆp Zµ ˆp e ) Ze p cos φ = (ˆp e ˆp e + ) (ˆp µ ˆp µ + ) X 1 p e j e + X µ µ ê z 0 ` Z Z j e µ + h ê z µ + e p? p

35 Angular Correlations Measurements of operator structures Cabibbo Maksymowicz Dell Aquila Nelson angles for H ZZ [Melnikov etal; Lykken etal; v d Bij etal; Choi etal] Ze Zµ cos θ e = ˆp e ˆp Zµ cos θ µ = ˆp µ ˆp Ze cos θ X = ˆp Ze ˆp beam cos φ e = (ˆp beam ˆp Zµ ) (ˆp Zµ ˆp e ) Ze p cos φ = (ˆp e ˆp e + ) (ˆp µ ˆp µ + ) X 1 p e j e + X µ µ ê z 0 ` Z Z j e µ + h ê z µ + e p? p

36 Angular Correlations Measurements of operator structures Cabibbo Maksymowicz Dell Aquila Nelson angles for H ZZ [Melnikov etal; Lykken etal; v d Bij etal; Choi etal] Breit frame or hadron collider (η, φ) in WBF [Breit: boost into space-like] [Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP]

37 Angular Correlations Measurements of operator structures Cabibbo Maksymowicz Dell Aquila Nelson angles for H ZZ [Melnikov etal; Lykken etal; v d Bij etal; Choi etal] Breit frame or hadron collider (η, φ) in WBF [Breit: boost into space-like] [Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP] cos θ 1 = ˆp j1 ˆp V2 cos θ 2 = ˆp j2 ˆp V1 V1 Breit V2 Breit cos φ 1 = (ˆp V2 ˆp d ) (ˆp V2 ˆp j1 ) V1 Breit cos φ = (ˆp q1 ˆp j1 ) (ˆp q2 ˆp j2 ). X cos θ = ˆp V1 ˆp d X 1 ( Q V 1 d j 1 V 2 Q (? j 2 2

38 Angular Correlations Measurements of operator structures Cabibbo Maksymowicz Dell Aquila Nelson angles for H ZZ [Melnikov etal; Lykken etal; v d Bij etal; Choi etal] Breit frame or hadron collider (η, φ) in WBF [Breit: boost into space-like] [Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP] possible scalar couplings L (φ φ)w µ W µ 1 Λ 2 (φ φ)w µν W µν 1 Λ 2 (φ φ)ɛ µνρσw µν W ρσ different channels, same physics dγ Γ d φ dσ σ d φ dσ σ d φ jj 0 + D D D5 0 + SM D D SM D SM

39 Angular Correlations Measurements of operator structures Cabibbo Maksymowicz Dell Aquila Nelson angles for H ZZ [Melnikov etal; Lykken etal; v d Bij etal; Choi etal] Breit frame or hadron collider (η, φ) in WBF [Breit: boost into space-like] [Rainwater, TP, Zeppenfeld; Hagiwara, Li, Mawatari; Englert, Mawatari, Netto, TP] possible scalar couplings L (φ φ)w µ W µ 1 Λ 2 (φ φ)w µν W µν 1 Λ 2 (φ φ)ɛ µνρσw µν W ρσ different channels, same physics

40 t W,Z Standard Model operators [SFitter: Klute, Lafaye, TP, Rauch, Zerwas] assume: narrow CP-even scalar Standard Model operators couplings proportional to masses? couplings from production & decay rates gg H qq qqh gg t th qq VH g HXX = g SM HXX (1 + X ) b,t H ZZ H WW H b b H τ + τ H γγ W,Z

41 t W,Z Standard Model operators [SFitter: Klute, Lafaye, TP, Rauch, Zerwas] assume: narrow CP-even scalar Standard Model operators couplings proportional to masses? couplings from production & decay rates gg H qq qqh gg t th qq VH g HXX = g SM HXX (1 + X ) b,t H ZZ H WW H b b H τ + τ H γγ W,Z Total width non-trivial scaling N = σ BR gives constraint from g2 p Γtot g 2 d Γtot g 4 g 2 Γi (g 2 ) g 2 Γ i (g 2 ) < Γ tot Γ H min + Γ unobs WW WW unitarity: g WWH g SM WWH Γ H max SFitter assumption Γ tot = obs Γ j [plus generation universality] g 2 0 = 0

42 Error analysis Sources of uncertainty statistical error: Poisson systematic error: Gaussian, if measured theory error: not Gaussian simple argument LHC rate 10% off: no problem LHC rate 30% off: no problem LHC rate 300% off: Standard Model wrong theory likelihood flat centrally and zero far away profile likelihood construction: RFit [CKMFitter] 2 log L = χ 2 = χ T d C 1 χ d 0 d i d i < σ (theo) i χ d,i = d i d i σ (theo) i d σ (exp) i d i > σ (theo) i i

43 now and in the future Now [Aspen/Moriond 2013; Lopez-Val, TP, Rauch] focus SM-like [secondary solutions possible] six couplings and ratios from data g b from width g g vs g t not yet possible Moriond [similar: Ellis etal, Djouadi etal, Strumia etal, Grojean etal] 1 L= (7 TeV)+12-21(8 TeV) fb -1, 68% CL: ATLAS + CMS SM exp. data data (+ γ ) g x = g x SM (1+ x ) poor man s analyses: H, V, f Tevatron H b b with little impact H f V W t Z τ b γ b/w τ/b Z/W

44 now and in the future Now [Aspen/Moriond 2013; Lopez-Val, TP, Rauch] focus SM-like [secondary solutions possible] six couplings and ratios from data g b from width g g vs g t not yet possible Moriond [similar: Ellis etal, Djouadi etal, Strumia etal, Grojean etal] 1 L= fb -1 ( TeV), 68% CL: ATLAS+CMS+Tevatron SM exp. data data (+ γ ) g x = g x SM (1+ x ) poor man s analyses: H, V, f Tevatron H b b with little impact H f V W t Z τ b γ b/w τ/b Z/W

45 now and in the future Now [Aspen/Moriond 2013; Lopez-Val, TP, Rauch] focus SM-like [secondary solutions possible] six couplings and ratios from data g b from width g g vs g t not yet possible [similar: Ellis etal, Djouadi etal, Strumia etal, Grojean etal] poor man s analyses: H, V, f Tevatron H b b with little impact Future LHC extrapolations unclear theory extrapolations tricky ILC case obvious interplay in loop-induced couplings % CL: 3000 fb -1, 14 TeV LHC and 500 fb -1, 500 GeV LC 3000 fb -1, 14 TeV LHC 500 fb -1, 500 GeV LC HL-LHC + LC500 HL-LHC + LC500 ( t c ) g x = g x SM (1+ x ) H W Z t c b τ γ g

46 now and in the future Now [Aspen/Moriond 2013; Lopez-Val, TP, Rauch] focus SM-like [secondary solutions possible] six couplings and ratios from data g b from width g g vs g t not yet possible [similar: Ellis etal, Djouadi etal, Strumia etal, Grojean etal] poor man s analyses: H, V, f Tevatron H b b with little impact Future LHC extrapolations unclear theory extrapolations tricky ILC case obvious interplay in loop-induced couplings fundamental e + e advantages: unobserved decays avoided width measured from rates including σ ZH H c c accessible invisible decays hugely improved QCD theory error bars avoided H 68% CL: 3000 fb -1, 14 TeV LHC and 500 fb -1, 500 GeV LC 3000 fb -1, 14 TeV LHC 500 fb -1, 500 GeV LC HL-LHC + LC500 HL-LHC + LC500 ( t c ) W Z t c b g x = g x SM (1+ x ) τ γ g

47 as a weakly interacting new physics Extended Higgs models [Lopez-Val, TP, Rauch; Chen & Dawson, many, many papers] assume the Higgs really is a Higgs allow for coupling modifications consider portals/singlet extensions boring [Englert TP, Rauch, Zerwas, Zerwas] how would s look? [ ] V (Φ 1, Φ 2 ) = m11 2 Φ 1 Φ 1 + m22 2 Φ 2 Φ 2 m12 2 Φ 1 Φ 2 + h.c. + λ 1 2 (Φ 1 Φ 1) 2 + λ 2 2 (Φ 2 Φ 2) 2 + λ 3 (Φ 1 Φ 1) (Φ 2 Φ 2) + λ 4 Φ 1 Φ 2 2 [ ] λ5 + 2 (Φ 1 Φ 2) 2 + λ 6 (Φ 1 Φ 1) (Φ 1 Φ 2) + λ 7 (Φ 2 Φ 2) (Φ 1 Φ 2) + h.c.

48 as a weakly interacting new physics Extended Higgs models [Lopez-Val, TP, Rauch; Chen & Dawson, many, many papers] assume the Higgs really is a Higgs allow for coupling modifications consider portals/singlet extensions boring [Englert TP, Rauch, Zerwas, Zerwas] how would s look? Physical parameters angle β = atan(v 2 /v 1 ) angle α defining h 0 and H 0 gauge boson coupling g W,Z = sin(β α)g SM W,Z type-i: all fermions with Φ 2 type-ii: up-type fermions with Φ 2 lepton-specific: type-i quarks and type-ii leptons flipped: type-ii quarks and type-i leptons Yukawa aligned: y b cos(β γ b ) = 2m b /v compressed masses m h 0 m H 0 [thanks to Berthold Stech] single hierarchy m h 0 m H 0,A 0,H ± protected by custodial symmetry PQ-violating terms m 12 and λ 6,7

49 as a weakly interacting new physics Extended Higgs models [Lopez-Val, TP, Rauch; Chen & Dawson, many, many papers] assume the Higgs really is a Higgs allow for coupling modifications consider portals/singlet extensions boring [Englert TP, Rauch, Zerwas, Zerwas] how would s look? Facing data fit including single heavy Higgs mass decoupling regime sin 2 α 1/(1 + tan 2 β) little impact of additional theoretical and experimental constraints s generally good fit, but decoupling heavy Higgs type-i type-ii lepton specific flipped

50 as a consistent UV completion How to think of SFitter coupling results x 0 violating renormalization, unitarity,... experimentally irrelevant, only QCD matters theoretically (supposedly) of great interest EFT approach: (1) define consistent, decouple heavy states (2) fit model parameters, plot range of SM couplings (3) compare to free SM couplings fit

51 as a consistent UV completion How to think of SFitter coupling results x 0 violating renormalization, unitarity,... experimentally irrelevant, only QCD matters theoretically (supposedly) of great interest EFT approach: (1) define consistent, decouple heavy states (2) fit model parameters, plot range of SM couplings (3) compare to free SM couplings fit Yukawa-aligned V (β α) b,t,τ {β, γ b,τ } γ m H ± g not free parameter, top partner? custodial symmetry built in at tree level V < 0 Higgs-gauge quantum corrections enhanced V < 0 fermion quantum corrections large for tan β 1 g x /g x SM [%] Type I tt ττ ZZ sin(β α) = 1 sin(β α) = 0.95 sin(β α) = 0.90 sin(β α) = 0.85 Unitarity bb _ B d -B d WW _ B d -B d ττ tt bb WW ZZ m h 0 = 126 GeV m H 0 = 200 GeV _ B d -B d ZZ WW Vacuum stability ττ tt bb m A 0 = 250 GeV m H + = 280 GeV _ B d -B d bb ZZ WW Vacuum stability ττ tt

52 as a consistent UV completion How to think of SFitter coupling results x 0 violating renormalization, unitarity,... experimentally irrelevant, only QCD matters theoretically (supposedly) of great interest EFT approach: (1) define consistent, decouple heavy states (2) fit model parameters, plot range of SM couplings (3) compare to free SM couplings fit Consistent coupling fits pretty good at tree level W Z > 0 through loops free SM couplings fine? direct fit aligned aligned (constr.) measured data V t b τ γ

53 TeV scale fourth chiral generation excluded strongly interacting models retreating [Goldstone protection] extended Higgs sectors wide open no final verdict on the MSSM hierarchy problem worse than ever [light fundemental scalar discovered] do not know

54 TeV scale fourth chiral generation excluded strongly interacting models retreating [Goldstone protection] extended Higgs sectors wide open no final verdict on the MSSM hierarchy problem worse than ever [light fundemental scalar discovered] do not know High scales Planck-scale extrapolation [Holthausen, Lim, Lindner; Buttazzo etal] d λ d log Q 2 = 1 16π 2 vacuum stability right at edge λ = 0 at finite energy? [12λ 2 + 6λλ 2t 3λ 4t 32 ( ) λ 3g g (2g (g2 2 + g2 1 )2)] IR fixed point for λ/λ 2 t fixing m 2 H /m2 t [with gravity: Shaposhnikov, Wetterich] mt αs m H = IR fixed points phenomenological nightmare do not know

55 Example: top Higgs renormalization group Running of coupling/mass ratios Higgs self coupling and top Yukawa with stable zero IR solutions d λ d log Q = 1 ( ) 12λ 2 + 6λy π 2 t 3y 4 d y 2 t t d log Q = π y 4 2 t

56 Example: top Higgs renormalization group Running of coupling/mass ratios Higgs self coupling and top Yukawa with stable zero IR solutions d λ d log Q = 1 ( ) 12λ 2 + 6λy π 2 t 3y 4 d y 2 t t d log Q = π y 4 2 t running ratio R = λ/y 2 t dr d log Q = 3λ 2 32π 2 R ( 8R 2 + R 2)! = 0 R =

57 Example: top Higgs renormalization group Running of coupling/mass ratios Higgs self coupling and top Yukawa with stable zero IR solutions d λ d log Q = 1 ( ) 12λ 2 + 6λy π 2 t 3y 4 d y 2 t t d log Q = π y 4 2 t running ratio R = λ/y 2 t dr d log Q = 3λ 2 32π 2 R ( 8R 2 + R 2)! = 0 R = numbers in the far infrared, better for Q v λ yt 2 = m2 H v 2 2v 2 2mt 2 = m2 H 4m 2 = 0.44 IR t IR m H = 1.33 m t IR

58 Questions Big questions is it really the Standard Model Higgs? is there space for new physics outside the Higgs sector? when will we finally kiss stronly interacting models good bye? Small questions what are good alternative test hypotheses? how can we improve the couplings fit precision? how can we measure the bottom Yukawa? how can we measure the top Yukawa? how can we measure the Higgs self coupling? how do we avoid theory dominating uncertainties which backgrounds do we need to know better?... Lectures on LHC Physics, Springer, arxiv: updated under plehn/ Much of this work was funded by the BMBF Theorie-Verbund which is ideal for relevant LHC work

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