The Composite Nambu-Goldstone Higgs Andrea Wulzer
Natural or Unnatural ? One sure goal of the LHC is to answer the question: “Is EWSB scale Natural of Fine-tuned?” ◆ 2 ✓ ◆ 2 ∆ � δ m 2 ✓ 126 GeV M P H ' m 2 500 GeV m h H = New Physics (Top Partners) scale M P
Natural or Unnatural ? One sure goal of the LHC is to answer the question: “Is EWSB scale Natural of Fine-tuned?” ◆ 2 ✓ ◆ 2 ∆ � δ m 2 ✓ 126 GeV M P H ' m 2 500 GeV m h H = New Physics (Top Partners) scale M P ∆ Optimistic view: 4 1 M P [TeV] 0 . 5 1
Natural or Unnatural ? One sure goal of the LHC is to answer the question: “Is EWSB scale Natural of Fine-tuned?” ◆ 2 ✓ ◆ 2 ∆ � δ m 2 ✓ 126 GeV M P H ' m 2 500 GeV m h H = New Physics (Top Partners) scale M P ∆ ∆ Optimistic view: Pessimistic view: 4 4 1 1 M P [TeV] M P [TeV] 0 . 5 0 . 5 1 1
Natural or Unnatural ? One sure goal of the LHC is to answer the question: “Is EWSB scale Natural of Fine-tuned?” ◆ 2 ✓ ◆ 2 ∆ � δ m 2 ✓ 126 GeV M P H ' m 2 500 GeV m h H = New Physics (Top Partners) scale M P ∆ ∆ Optimistic view: Pessimistic view: 4 4 1 1 M P [TeV] M P [TeV] 0 . 5 0 . 5 1 1 In both cases we will learn something!
Composite Higgs Composite Higgs scenario: 1. Higgs is hadron of new strong force Corrections to screened above 1 /l H m H The Hierarchy Problem is solved 2. Higgs is a Goldstone Boson , this is why it is light 3. Partial Fermion Compositeness: linear coupling to strong sector
Composite Higgs Composite Higgs scenario: 1. Higgs is hadron of new strong force Corrections to screened above 1 /l H m H The Hierarchy Problem is solved 2. Higgs is a Goldstone Boson , this is why it is light 3. Partial Fermion Compositeness: linear coupling to strong sector
Composite Higgs Composite Higgs scenario: 1. Higgs is hadron of new strong force Corrections to screened above 1 /l H m H The Hierarchy Problem is solved 2. Higgs is a Goldstone Boson , this is why it is light 3. Partial Fermion Compositeness: linear coupling to strong sector Indirect effects from sigma-model couplings A) Corrections to SM: B) New Non-ren. Couplings: O ( v 2 f 2 ) � 20% � ⇥ / e.g. Double His gg → hh Higgs Br. Ratios Higgs Production c Indirect, but “direct” (robust) signature of compositeness
Composite Higgs Composite Higgs scenario: 1. Higgs is hadron of new strong force Corrections to screened above 1 /l H m H The Hierarchy Problem is solved 2. Higgs is a Goldstone Boson , this is why it is light 3. Partial Fermion Compositeness: linear coupling to strong sector Composite Sector Elementary Sector W 1 , 2 , 3 , B µ µ f L , f R L int gauge: L int = gJ µ W µ fermions: L int = y L q L O L + y R q R O R
Composite Higgs Low energy Higgs physics from symmetries L π = f 2 2( @ h ) 2 + g 2 i π = 1 4 f 2 sin 2 h ✓ 1 ◆ | W | 2 + µ d µ 4 d i Z 2 2 c 2 f w ξ ⌘ v 2 f 2 =sin 2 h h i = i g 2 p 1 − ξ 4 v g HV V f
Composite Higgs Low energy Higgs physics from symmetries L π = f 2 2( @ h ) 2 + g 2 i π = 1 4 f 2 sin 2 h ✓ 1 ◆ | W | 2 + µ d µ 4 d i Z 2 2 c 2 f w ξ ⌘ v 2 f 2 =sin 2 h h i = i g 2 p 1 − ξ 4 v g HV V f Fermion couplings are less sharply predicted. c = 1 − 2 ξ MCHM 5 √ 1 − ξ = i m f p v c 1 − ξ c = MCHM 4 MCHM 10 . . . Do depend on fermionic operator representations
Composite Higgs courtesy of R.Torre A rough comparison with data: Higher order effects, from resonances exchange, should be also taken into account
Top Partners In the IR, fermionic operators correspond to particles: h 0 |O| Q i 6 = 0 O L,R ↔ Q L,R Q = “vector-like colored fermions” and carry color ! Q O (partners)
Top Partners In the IR, fermionic operators correspond to particles: h 0 |O| Q i 6 = 0 O L,R ↔ Q L,R Q = “vector-like colored fermions” and carry color ! Q O (partners) gives a mass-mixing in the IR: L int = y L q L O L + y R q R O R L mass = m ∗ Q QQ + y fqQ physical particles are partially composite | SM n i =cos φ n | elementary n i + sin φ n | composite n i tan φ n = yf m ∗ | BSM n i =cos φ n | composite n i � sin φ n | elementary n i Q
Top Partners | SM n i =cos φ n | elementary n i + sin φ n | composite n i P.C. generates Yukawas ... y f = ... and the Higgs Potential Top loop dominate because the top is largely composite.
Top Partners Top partners cancel divergence, thus are m H directly bounded by Naturalness ◆ 2 ✓ ◆ 2 ∆ � δ m 2 ✓ 125 GeV M P H ' m 2 400 GeV m H H SUSY: Composite Higgs: light stops light fermionic partners
Top Partners Top partners cancel divergence, thus are m H directly bounded by Naturalness ◆ 2 ✓ ◆ 2 ∆ � δ m 2 ✓ 125 GeV M P H ' m 2 400 GeV m H H 4 In a class of explicit CH models Ξ� 0.2 3 MCHM 4 , 5 , 10 Q =2 / 3 2 : (low tuning) ξ = 0 . 2 1 0 0 1 2 3 4 5 6 m H ∈ [115 , 130] Q =5 / 3 Light Higgs plus Low Tuning need Light Partners (Matsedonsky,i Panico, AW 2012)
Top Partners Top partners cancel divergence, thus are m H directly bounded by Naturalness ◆ 2 ✓ ◆ 2 ∆ � δ m 2 ✓ 125 GeV M P H ' m 2 400 GeV m H H 4 In a class of explicit CH models Ξ� 0.1 3 MCHM 4 , 5 , 10 Q =2 / 3 2 : (larger tuning) ξ = 0 . 1 1 0 0 1 2 3 4 5 6 m H ∈ [115 , 130] Q =5 / 3 Light Higgs plus Low Tuning need Light Partners (Matsedonsky,i Panico, AW 2012)
Top Partners ✓ T ◆ X 5 / 3 Fourplet of custodial SO(4) B X 2 / 3 Spectrum: Couplings: B X T V ∼ M X /f t X 2 / 3 because Goldstones are derivatively coupled X 5 / 3 Unlike e e Singlet of custodial T SO(4) Unlike e e T W sizeable coupling to bottom quark b
Top Partners Three possible production mechanisms X QCD pair prod . comparing production rates: model indep., (14 TeV LHC) relevant at low mass e T 1000 X 100 single prod . with t Σ @ fb D X model dep. coupling 10 pdf-favoured at high mass t 1 600 800 1000 1200 1400 1600 1800 2000 M @ GeV D single prod . with b X favoured by small b mass dominant when allowed b
Top Partners Current limits (rough): ξ = 0 . 2 4 Ξ� 0.2 3 Q =2 / 3 2 1 0 0 1 2 3 4 5 6 Q =5 / 3
Top Partners Current limits (rough): ξ = 0 . 1 4 Ξ� 0.1 3 Q =2 / 3 2 1 0 0 1 2 3 4 5 6 Q =5 / 3
Top Partners Current limits, simplified model approach: 1.0 s = 8 TeV X 5 ê 3 ê B excl . L d 20 fb - 1 0.8 x = 0.2 c = 0 sin f L c = 1 ê 2 0.6 charge 2 ê 3 0.4 excl . Theoretically excl . 0.2 0.5 1.0 1.5 2.0 m 5 ê 3 H TeV L
Top Partners Current limits, simplified model approach: 1.0 s = 8 TeV L d 20 fb - 1 0.8 X 5 ê 3 ê B excl . x = 0.1 c = 0 c = 1 ê 2 0.6 sin f L charge 2 ê 3 0.4 excl . Theoretically 0.2 excl . 1 2 3 4 5 m 5 ê 3 H TeV L
Top Partners Projections, simplified model approach: 1.0 s = 13 TeV L = 20 fb - 1 X 5 ê 3 ê B excl . 0.8 x = 0.1 c = 0 c = 1 ê 2 0.6 sin f L charge 2 ê 3 0.4 excl . Theoretically 0.2 excl . 1 2 3 4 5 m 5 ê 3 H TeV L H
Top Partners Projections, simplified model approach: 1.0 s = 13 TeV L = 100 fb - 1 0.8 X 5 ê 3 ê B excl . x = 0.05 c = 0 c = 1 ê 2 0.6 sin f L charge 2 ê 3 0.4 excl . Theoretically 0.2 excl . 1 2 3 4 5 H m 5 ê 3 H TeV L
Conclusions and Outlook •Composite Higgs is the perfect benchmark for present and future studies of Higgs couplings modifications •Important playground for (Un-)Naturalness tests from fermionic Top Partner searches •Direct searches win over coupling determinations •Much to be learned (on both) from the 13 TeV run!
Backup Reach on CH vectors 5 theoretically Model B H.L.S. model EWPT excluded (arXiv:1109.1570) 4 V>WZ>2lv g V 3 V>WZ>jj V>lvu 2 1 500 1000 1500 2000 2500 3000 3500 eV D
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