Tilman Plehn. Mainz, July 2015

Transcription

1 Testing the Universität Heidelberg Mainz, July 2015

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 lots of collider phenomenology starting in 1976

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 lots of collider phenomenology starting in 1976 Adding in Glashow Weinberg Salam t Hooft Veltman massive, minimal Standard Model complete renormalizability unique for particle physics [and cosmology] Higgs sector the perfect way to test structure [remember LEP for gauge structure] bias: no strongly interacting Higgs sector!

10 Questions for Run 2+x 1. What is the Higgs Lagrangian? psychologically: looked for Higgs, so found a Higgs CP-even spin-0 scalar expected, which operators? spin-1 vector unlikely spin-2 graviton unexpected ask Stephie and Uli [Cabibbo Maksymowicz Dell Aquila Nelson angles]

11 Questions for Run 2+x 1. What is the Higgs Lagrangian? psychologically: looked for Higgs, so found a Higgs CP-even spin-0 scalar expected, which operators? spin-1 vector unlikely spin-2 graviton unexpected ask Stephie and Uli [Cabibbo Maksymowicz Dell Aquila Nelson angles] 2. What is the Lagrangian? naive-but-useful: set of couplings given Lagrangian bottom-up: Higgs effective theory top-down: modified Higgs sectors

12 Questions for Run 2+x 1. What is the Higgs Lagrangian? psychologically: looked for Higgs, so found a Higgs CP-even spin-0 scalar expected, which operators? spin-1 vector unlikely spin-2 graviton unexpected ask Stephie and Uli [Cabibbo Maksymowicz Dell Aquila Nelson angles] 2. What is the Lagrangian? naive-but-useful: set of couplings given Lagrangian bottom-up: Higgs effective theory top-down: modified Higgs sectors 3. What does all this tell us? strongly interacting models? weakly interacting extensions? TeV-scale new physics? hierarchy problem, vacuum stability, Higgs inflation, etc

13 t W,Z Standard Model operators assume: narrow CP-even scalar Standard Model operators couplings proportional to masses? Lagrangian L = L SM + W gm W H W µ W µ + Z + gf G H v GµνGµν + γf A 2nd generation Yukawas µ,c,s? [ask MatthiasN] g 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 b,t W,Z

14 t W,Z Standard Model operators assume: narrow CP-even scalar Standard Model operators couplings proportional to masses? Lagrangian L = L SM + W gm W H W µ W µ + Z + gf G H v GµνGµν + γf A 2nd generation Yukawas µ,c,s? [ask MatthiasN] g 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 b,t W,Z total rates only [on-shell and off-shell, Keith or Kirill around?] 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 ) H ZZ H WW H b b H τ + τ H γγ

15 Higgs Portal Higgs portal to new physics [dark matter, etc] all-renormalizable extended potential [with or without VEV] V (Φ, S) =µ 2 1 (Φ Φ) + λ 1 Φ Φ 2 + µ 2 2 S 2 + λ 2 S 4 + λ 3 Φ Φ S 2 mixing to the observed Higgs mass eigenstate visible and invisible decays H 1 = cos χ H Φ + sin χ S Γ 1 = cos 2 χ Γ SM 1 + sin 2 χ Γ hid 1 sin 2 χ Γ hid 1 BR inv = cos 2 χ Γ SM 1 + sin 2 χ Γ hid 1 event rate (σ BR) H1 cos 2 χ = (σ BR) SM H tan 2 χ Γhid 1 Γ SM 1 collider reach

16 Higgs Portal Higgs portal to new physics [dark matter, etc] all-renormalizable extended potential [with or without VEV] V (Φ, S) =µ 2 1 (Φ Φ) + λ 1 Φ Φ 2 + µ 2 2 S 2 + λ 2 S 4 + λ 3 Φ Φ S 2 mixing to the observed Higgs mass eigenstate visible and invisible decays H 1 = cos χ H Φ + sin χ S Γ 1 = cos 2 χ Γ SM 1 + sin 2 χ Γ hid 1 sin 2 χ Γ hid 1 BR inv = cos 2 χ Γ SM 1 + sin 2 χ Γ hid 1 event rate (σ BR) H1 cos 2 χ = (σ BR) SM H tan 2 χ Γhid 1 Γ SM 1 invisible Higgs the key

17 Two Higgs doublets Two doublets [no flavor, CP, custodial troubles] angle β = atan(v 2 /v 1 ) angle α defining h and H gauge boson coupling g W,Z = sin(β α)gw SM,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 single hierarchy m h m H,A,H ± [custodial symmetry]

18 Two Higgs doublets Two doublets [no flavor, CP, custodial troubles] angle β = atan(v 2 /v 1 ) angle α defining h and H gauge boson coupling g W,Z = sin(β α)gw SM,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 single hierarchy m h m H,A,H ± [custodial symmetry] Facing data decoupling regime sin 2 α 1/(1 + tan 2 β) 2HDMs good fit with decoupling heavy Higgs type-i type-ii lepton specific flipped

19 Two Higgs doublets Two doublets [no flavor, CP, custodial troubles] angle β = atan(v 2 /v 1 ) angle α defining h and H gauge boson coupling g W,Z = sin(β α)gw SM,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 single hierarchy m h m H,A,H ± [custodial symmetry] Yukawa-aligned 2HDM V (β α) b,t,τ {β, γ b,τ } γ m H ± g not free parameter, add top partner custodial symmetry at tree level V < direct fit direct fit ( V <0) aligned 2HDM measured data realistic model not yet in reach 0.4 aligned 2HDM (constr.) V t b τ γ

20 Extended Higgs sectors Decoupling in one dimension [Cranmer, Kreiss, Lopez-Val, TP] decoupling defined through the massive gauge sector g V = 1 ξ2 g SM 2 + O(ξ3 ) V = ξ2 2 + O(ξ3 ) V

21 Extended Higgs sectors Decoupling in one dimension [Cranmer, Kreiss, Lopez-Val, TP] decoupling defined through the massive gauge sector dark singlet g V = 1 ξ2 g SM 2 + O(ξ3 ) V = ξ2 2 + O(ξ3 ) V Γ inv = ξ 2 Γ SM µ p,d = Γ SM Γ SM + Γ inv = 1 ξ 2 + O(ξ 3 ) < 1

22 Extended Higgs sectors Decoupling in one dimension [Cranmer, Kreiss, Lopez-Val, TP] decoupling defined through the massive gauge sector dark singlet g V = 1 ξ2 g SM 2 + O(ξ3 ) V = ξ2 2 + O(ξ3 ) V Γ inv = ξ 2 Γ SM µ p,d = Γ SM Γ SM + Γ inv = 1 ξ 2 + O(ξ 3 ) < 1 mixing singlet [no anomalous decays] 1 + x = cos θ = 1 ξ 2 µ p,d = 1 ξ 2 + O(ξ 3 ) < 1

23 Extended Higgs sectors Decoupling in one dimension [Cranmer, Kreiss, Lopez-Val, TP] decoupling defined through the massive gauge sector dark singlet g V = 1 ξ2 g SM 2 + O(ξ3 ) V = ξ2 2 + O(ξ3 ) V Γ inv = ξ 2 Γ SM µ p,d = Γ SM Γ SM + Γ inv = 1 ξ 2 + O(ξ 3 ) < 1 mixing singlet [no anomalous decays] composite Higgs ξ = v f 1 + x = cos θ = 1 ξ 2 µ p,d = 1 ξ 2 + O(ξ 3 ) < 1 µ WBF,d µ GF,d = (1 ξ 2 ) 2 (1 2ξ 2 ) 2 = 1 + 2ξ 2 + O(ξ 3 ) > 1

24 Extended Higgs sectors Decoupling in one dimension [Cranmer, Kreiss, Lopez-Val, TP] decoupling defined through the massive gauge sector dark singlet g V = 1 ξ2 g SM 2 + O(ξ3 ) V = ξ2 2 + O(ξ3 ) V Γ inv = ξ 2 Γ SM µ p,d = Γ SM Γ SM + Γ inv = 1 ξ 2 + O(ξ 3 ) < 1 mixing singlet [no anomalous decays] composite Higgs ξ = v f 1 + x = cos θ = 1 ξ 2 µ p,d = 1 ξ 2 + O(ξ 3 ) < 1 µ WBF,d µ GF,d = additional doublet [type-x fermion sector] 1 + V = sin(β α) = 1 ξ 2 (1 ξ 2 ) 2 (1 2ξ 2 ) 2 = 1 + 2ξ 2 + O(ξ 3 ) > 1

25 Extended Higgs sectors Decoupling in one dimension [Cranmer, Kreiss, Lopez-Val, TP] decoupling defined through the massive gauge sector dark singlet g V = 1 ξ2 g SM 2 + O(ξ3 ) V = ξ2 2 + O(ξ3 ) V Γ inv = ξ 2 Γ SM µ p,d = Γ SM Γ SM + Γ inv = 1 ξ 2 + O(ξ 3 ) < 1 mixing singlet [no anomalous decays] composite Higgs ξ = v f 1 + x = cos θ = 1 ξ 2 µ p,d = 1 ξ 2 + O(ξ 3 ) < 1 µ WBF,d µ GF,d = additional doublet [type-x fermion sector] 1 + V = sin(β α) = 1 ξ 2 MSSM [plus tan β] ξ 2 = m2 h (m2 Z m2 h ) m 2 A (m2 H m2 h ) m4 Z sin2 (2β) m 4 A (1 ξ 2 ) 2 (1 2ξ 2 ) 2 = 1 + 2ξ 2 + O(ξ 3 ) > 1

26 Extended Higgs sectors Decoupling in one dimension [Cranmer, Kreiss, Lopez-Val, TP] decoupling defined through the massive gauge sector dark singlet g V = 1 ξ2 g SM 2 + O(ξ3 ) V = ξ2 2 + O(ξ3 ) V Γ inv = ξ 2 Γ SM µ p,d = Γ SM Γ SM + Γ inv = 1 ξ 2 + O(ξ 3 ) < 1 mixing singlet [no anomalous decays] composite Higgs γγ µ VBF ξ = v f ξ < x = cos θ = 1 ξ 2 µ p,d = 1 ξ 2 + O(ξ 3 ) < 1 ξ = 0.2 MSSM MCHM5 singlet 2HDM I 2HDM II µ WBF,d µ GF,d = VV µ VBF ξ < 0.4 ξ = 0.2 MSSM (1 ξ 2 ) 2 (1 2ξ 2 ) 2 = 1 + 2ξ 2 + O(ξ 3 ) > 1 MCHM5 singlet 2HDM I 2HDM II µ ττ VBF ξ < 0.4 ξ = 0.2 MCHM5 2HDM II singlet MSSM 2HDM I γγ 2 µ GF VV 2 µ GF µ ττ GF

27 Higgs Limits in terms of effective field theory in Higgs sector set of Higgs-gauge operators 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

28 Higgs Limits in terms of effective field theory in Higgs sector set of Higgs-gauge operators 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 plus Yukawa structure f τ,b,t 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

29 Higgs Limits in terms of effective field theory in Higgs sector set of Higgs-gauge operators 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 plus Yukawa structure f τ,b,t Higgs couplings to SM particles Λ O 2 BB + f WW Λ 2 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 +

30 Higgs Limits in terms of effective field theory in Higgs sector set of Higgs-gauge operators 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 observable Higgs couplings 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

31 Higgs Limits in terms of effective field theory in Higgs sector set of Higgs-gauge operators 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 SFitter analysis same setup and data as before f/λ 2 [TeV -2 ] L= (7 TeV) (8 TeV) fb -1, ATLAS + CMS O GG O WW O BB O W O B O φ2 Λ/ f f/λ 2 [TeV] [TeV -2 ] Λ/ f [TeV] SM exp. 68% CL SM exp. 95% CL data 68% CL data 95% CL O t O b O τ

32 Higgs Limits in terms of effective field theory in Higgs sector set of Higgs-gauge operators 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 SFitter analysis same setup and data as before correlations a problem [diagonalization means 1 + ] f B /Λ 2 40 [TeV -2 ] f W /Λ 2 [TeV -2 ]

33 Higgs Limits in terms of effective field theory in Higgs sector set of Higgs-gauge operators 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 Including distributions some operators momentum-dependent example: p T,V or Φ jj just a start... f B /Λ 2 40 [TeV -2 ] f W /Λ 2 [TeV -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

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 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

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 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

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 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

38 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

39 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

40 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

41 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] whatever...

42 High scales [Lindner etal, Wetterich etal, Bauer etal] Planck-scale extrapolation d λ d log Q 2 = 1 16π 2 [12λ 2 + 6λλ 2t 3λ 4t 32 ( ) λ 3g g (2g (g2 2 + g2 1 )2)]

43 High scales [Lindner etal, Wetterich etal, Bauer etal] Planck-scale extrapolation d λ d log Q = 1 [ ] 12λ 2 + 6λλ π 2 t 3λ 4 t Landau pole: exploding λ for large Q, small λ t stability issue: sign change in λ for large Q, large λ t IR fixed point for λ/λ 2 t fixing m 2 H /m2 t [with gravity: Shaposhnikov, Wetterich] mt αs m H =

44 Exercise: top Higgs renormalization group Running of coupling/mass ratios [Wetterich] 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

45 Exercise: top Higgs renormalization group Running of coupling/mass ratios [Wetterich] 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 =

46 Exercise: top Higgs renormalization group Running of coupling/mass ratios [Wetterich] 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 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 ( 8R 2! R 2) = 0 R = m H = 1.33 m t IR

47 High scales [Lindner etal, Wetterich etal, Bauer etal] Planck-scale extrapolation d λ d log Q = 1 [ ] 12λ 2 + 6λλ π 2 t 3λ 4 t Landau pole: exploding λ for large Q, small λ t stability issue: sign change in λ for large Q, large λ t IR fixed point for λ/λ 2 t fixing m 2 H /m2 t [with gravity: Shaposhnikov, Wetterich] mt αs m H =

48 High scales [Lindner etal, Wetterich etal, Bauer etal] Planck-scale extrapolation d λ d log Q = 1 [ ] 12λ 2 + 6λλ π 2 t 3λ 4 t Landau pole: exploding λ for large Q, small λ t stability issue: sign change in λ for large Q, large λ t IR fixed point for λ/λ 2 t fixing m 2 H /m2 t [with gravity: Shaposhnikov, Wetterich] mt αs m H = Vacuum stability [Giudice etal; Eichhorn, Gies, Jaeckel, TP, Scherer, Sondenheimer] RG running of Higgs potential λ < 0 at GeV? [Buttazo etal] 1.0 yt g SM couplings g 2 g y b l m in TeV RGE scale m in GeV

49 High scales [Lindner etal, Wetterich etal, Bauer etal] Planck-scale extrapolation d λ d log Q = 1 [ ] 12λ 2 + 6λλ π 2 t 3λ 4 t Landau pole: exploding λ for large Q, small λ t stability issue: sign change in λ for large Q, large λ t IR fixed point for λ/λ 2 t fixing m 2 H /m2 t [with gravity: Shaposhnikov, Wetterich] mt αs m H = Vacuum stability [Giudice etal; Eichhorn, Gies, Jaeckel, TP, Scherer, Sondenheimer] RG running of Higgs potential λ < 0 at GeV? [Buttazo etal] new physics at GeV? running couplings Λ 4 Λ 6 g 3 y RGE scale k in GeV

50 High scales [Lindner etal, Wetterich etal, Bauer etal] Planck-scale extrapolation d λ d log Q = 1 [ ] 12λ 2 + 6λλ π 2 t 3λ 4 t Landau pole: exploding λ for large Q, small λ t stability issue: sign change in λ for large Q, large λ t IR fixed point for λ/λ 2 t fixing m 2 H /m2 t [with gravity: Shaposhnikov, Wetterich] mt αs m H = Vacuum stability [Giudice etal; Eichhorn, Gies, Jaeckel, TP, Scherer, Sondenheimer] RG running of Higgs potential λ < 0 at GeV? [Buttazo etal] new physics at GeV? new physics at GeV? running couplings Λ 4 Λ 6 g 3 y RGE scale k in GeV

51 High scales [Lindner etal, Wetterich etal, Bauer etal] Planck-scale extrapolation d λ d log Q = 1 [ ] 12λ 2 + 6λλ π 2 t 3λ 4 t Landau pole: exploding λ for large Q, small λ t stability issue: sign change in λ for large Q, large λ t IR fixed point for λ/λ 2 t fixing m 2 H /m2 t [with gravity: Shaposhnikov, Wetterich] mt αs m H = Vacuum stability [Giudice etal; Eichhorn, Gies, Jaeckel, TP, Scherer, Sondenheimer] RG running of Higgs potential λ < 0 at GeV? [Buttazo etal] new physics at GeV? new physics at GeV? TeV-scale DM portal? running couplings g 3 y Λ HS 0.0 Λ RG scale k in GeV

52 Questions Big questions is it really the Standard Model Higgs? is there new physics in/outside the Higgs sector? does fundamental theory hold to Planck scale? Practical questions can we define interesting extended models? can we set general limits in effective theories? are there links to other interesting sectors? how can we increase the precision? are there any good ideas out there? Lectures on LHC Physics, Springer, arxiv: updated under plehn/

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54 Longitudinal WW scattering WW scattering at high energies [Tao etal; Dawson] historically alternative to light Higgs WW scattering at high energies [via Goldstones] g V H ( a L V Lµ V µ L + a T V T µ V µ ) T still useful after Higgs discovery?

55 Longitudinal WW scattering WW scattering at high energies [Tao etal; Dawson] historically alternative to light Higgs WW scattering at high energies [via Goldstones] g V H ( a L V Lµ V µ L + a T V T µ V µ ) T still useful after Higgs discovery? high energy signal reduced by Higgs tagging jets as Higgs pole observables instead

56 Longitudinal WW scattering WW scattering at high energies [Tao etal; Dawson] historically alternative to light Higgs WW scattering at high energies [via Goldstones] g V H ( a L V Lµ V µ L + a T V T µ V µ ) T still useful after Higgs discovery? high energy signal reduced by Higgs tagging jets as Higgs pole observables instead Tagging jet observables [Brehmer, Jäckel, TP] polarization defined in Higgs frame transverse momenta 1 + (1 x)2 P T (x, p T ) x P L (x, p T ) 1 x x p 3 T ((1 x)m 2 W + p2 T )2 2(1 x)m 2 W p T ((1 x)m 2 W + p2 T )2

57 Longitudinal WW scattering WW scattering at high energies [Tao etal; Dawson] historically alternative to light Higgs WW scattering at high energies [via Goldstones] g V H ( a L V Lµ V µ L + a T V T µ V µ ) T still useful after Higgs discovery? high energy signal reduced by Higgs tagging jets as Higgs pole observables instead Tagging jet observables [Brehmer, Jäckel, TP] polarization defined in Higgs frame transverse momenta azimuthal angle A φ = σ( φ jj < π 2 ) σ( φ jj > π 2 ) σ( φ jj < π 2 ) + σ( φ jj > π 2 )

58 Longitudinal WW scattering WW scattering at high energies [Tao etal; Dawson] historically alternative to light Higgs WW scattering at high energies [via Goldstones] g V H ( a L V Lµ V µ L + a T V T µ V µ ) T still useful after Higgs discovery? high energy signal reduced by Higgs tagging jets as Higgs pole observables instead Tagging jet observables [Brehmer, Jäckel, TP] polarization defined in Higgs frame transverse momenta azimuthal angle total rate σ (A L al 2 + A T at 2 ) simple question, clear answer a T Rate Combined p, A T,j φ % CL, 300 fb No systematics a L

59 Hierarchy problem Tuning in Lagrangian [Giudice ] electron Yukawa m e/v 1 a problem? (1) no, it s just a number (2) no, m e = 0 is chiral symmetry

60 Hierarchy problem Tuning in Lagrangian [Giudice ] electron Yukawa m e/v 1 a problem? (1) no, it s just a number (2) no, m e = 0 is chiral symmetry so what about ratio? G F G N c2

61 Hierarchy problem Tuning in Lagrangian [Giudice ] electron Yukawa m e/v 1 a problem? (1) no, it s just a number (2) no, m e = 0 is chiral symmetry so what about ratio? Quantum field theory G F G N c2 stability with respect to quantum corrections G F 1 v 1 2 mh 2 with scale hierarchy unstable effective field theory broken symmetries welcome δm 2 H Λ2

62 Hierarchy problem Tuning in Lagrangian [Giudice ] electron Yukawa m e/v 1 a problem? (1) no, it s just a number (2) no, m e = 0 is chiral symmetry so what about ratio? Quantum field theory G F G N c2 stability with respect to quantum corrections G F 1 v 1 2 mh 2 with scale hierarchy unstable effective field theory broken symmetries welcome δm 2 H Λ2 SUSY little hierarchy quadratic Higgs divergence gone logarithmic dependence left δm 2 H v 2 log m t 1 m t 2 m 2 t