Beyond the Higgs

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Beyond the Higgs

E = mc 2Beyond the Higgsnew ideas on electroweaksymmetry breakingHiggs mechanism. The Higgs as a UV moderator of EWinteractions. Needs for New Physics beyond the Higgs.Dynamics of EW symmetry breakingE = ¯hνReview of possible scenarios :Gauge-Higgs Unification, LittleHiggs, Composite Higgs, (5D) Higgsless models.R µν − 1 2 Rg µν = 16πG T µνCh!"ophe GrojeanCERN-TH & CEA-Saclay/IPhT( christophe.grojean@cern.ch )


A decade of experimental successestop discoverysolar and atmospherical neutrino oscillationsdirect CP violation in the K system (ds) (K-long decaying into 2 pions)CP violation in the B system (db)evidence of an accelerated phase in the expansion of the Universemeasure of the dark energy/dark matter composition of the UniverseThese results have strengthened the SM as a successfuldescription of Nature ... butCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


... these experimental results also concluded that there is aphysics beyond the Standard Model.Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


The questions addressed in these lectureswe expect new physics to play a crucial role inthe mechanism of electroweak symmetry breaking.After LEP, what is the current bound on the scale of newphysics in the EWSB sector?What can we infer about the population of the TeV scale?What are the potentials to discover new physics in theEWSB sector at LHC ?Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Bounds on (Dangerous) New PhysicsHeavy Particles ➾ new interactions for SM particlesbroken symmetry operators scale ΛB, L (QQQL)/Λ 2 10 13 TeVflavor (1,2 nd family), CP ( ¯ds ¯ds)/Λ 2 1000 TeVflavor (2,3 rd family) m b (¯sσ µν F µν b)/Λ 2 50 TeVAt colliders, it will be difficult to find direct evidenceof new physics in these sectors...Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


New Physics in the EW sector((h † σ a h)W a µνB µν) /Λ 2 |h † D µ h| 2 /Λ 2 (h † h ) 3/Λ2Λ ∼ few TeV onlyhigh potential for direct detection at LHC, ILC !!!Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


EW “unification” and EWSBZEUSd"/dQ 2 (pb/GeV 2 )10110 -110 -2ZEUS (prel.) e + p NC 99-00ZEUS e ! p NC 98-99SM e + p NC (CTEQ6D)SM e ! p NC (CTEQ6D)EMAbove ~ 100 GeV,electromagnetic andweak interactions areunified10 -310 -410 -5ZEUS e + p CC 99-00ZEUS e ! p CC 98-99SM e + p CC (CTEQ6D)FaibleBelow 100 GeV, γ andZ behave differently10 -6SM e ! p CC (CTEQ6D)m γ < 6 × 10 −17 eV10 -710 3 10 4Q 2 (GeV 2 )m W ±m Z 0= 80.425 ± .038 GeV= 91.1876 ± .0021 GeVCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Higgs MechanismSymmetry of the LagrangianSymmetry of the VacuumSU(2) L × U(1) YHiggs Doublet( ) H+H =H 0U(1) e.m.Vacuum Expectation Value( ) 0〈H〉 = √2 v with v ≈ 246 GeVD µ H = ∂ µ H − i ( √ ) gW3µ + g ′ B µ 2gW+√ µ2 2gW−µ −gWµ 3 + g ′ H with W ± (µ = √ 1B µ 2 W1µ ∓ Wµ2 )|D µ H| 2 = 1 4 g2 v 2 W + µ W − µ + 1 8(W3µ B µ) ( g 2 v 2 −gg ′ v 2−gg ′ v 2 g ′2 v 2 )( W3 µB µ )Gauge boson spectrumelectrically charged bosonsM 2 W = 1 4 g2 v 2 M γ =0electrically neutral bosonsZ µ = cWµ 3 − sB µ c =γ µ = −sWµ 3 + cB µWeak mixing angle√gg2 +g ′2s =g ′√g 2 +g ′2M 2 Z = 1 4 (g2 + g ′2 )v 2Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Custodial SymmetryRho parameterρ ≡M 2 WM 2 Z cos2 θ w=14 g2 v 2=114 (g2 + g ′2 )v 2 g 2g 2 +g ′2H =Consequence of an approximate global symmetry of the Higgs sector( H+H 0 )Higgs doublet = 4 real scalar fieldsV (H) =λ(H † H − v22) 2is invariant under the rotation of the four real componentsSU(2) RSO(4) ∼ SU(2) L × SU(2) RΦ † Φ= H † H(11)SU(2) L(iσ 2 H ⋆ H ) =ΦV (H) = λ 4(trΦ † Φ − v 2) 22x2 matrixexplicitly invariant under SU(2) L × SU(2) RCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Counting the degrees of freedomSU(2) l × U(1) y → U(1) em3 broken gauge directions = 3 eaten Goldstone bosonsH =( h+h 0 )Higgs doublet = 4 real scalar fields3 eaten Goldstone bosons which become thelongitudinal polarizations of the massive gaugebosons( )H = e iπa T a 0v+h √2One physical degree of freedomthe Higgs bosonIn the unitary gauge, theπ a are non-physical.V (H) =λ(H † H − v22) 2= m2 h2 h2 + m2 h2v h3 + m2 h8v 2 h4mass termself-couplingswithm 2 h =2λv 2Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Higgs as a UV moderatorCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Indeed a massivespin 1 particle has3 physical polarizations:A µ = ɛ µ e ik µx µɛ µ ɛ µ = −1 k µ ɛ µ =0Why do we need a Higgs ?The W and Z masses are inconsistent with the known particlecontent! Need more particles to soften the UV behavior ofmassive gauge bosons.k µ =(E,0, 0,k)InwithBlack k µ k µ = E 2 − k 2 = M 2{ ɛµ1 = (0, 1, 0, 0)2 transverse:= (0, 0, 1, 0)1 longitudinal:ɛ µ 2Exerciseɛ µ ⊥ =(k M , 0, 0, E M ) ≈ kµM + O( E M )( in the R-ξ gauge, the time-like polarization ( ɛ µ ɛ µ =1,k µ ɛ µ = M ) is arbitrarily massive and decouple )Bad UV behavior forthe scattering of the longitudinalpolarizationsW LW LW LW Lcontact interactionCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Why do we need a Higgs ?Bad UV behavior forthe scattering of the longitudinalpolarizationsW LW Lk µl νp ρq σW LW Lcontact interactionA = ɛ µ l (k)ɛν l (l) ig 2 (2η µρ η νσ − η µν η ρσ − η µσ η νρ ) ɛ ρ l (p)ɛσ l (q)In WhiteA∝ g 2 E4M 4violations of perturbative unitarity around E ~ MCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


A QCD antecedentQCD pions are Goldstone bosons associated to SU(2) L xSU(2) R /SU(2) VU = e iπa σ a /f π(0f π √2)kinetic terms for U interaction terms for π aL = |∂ µ U| 2 = 1 2 (∂ µπ a ) 2 − 16f 2 π((π a ∂ µ π a ) 2 − (π a ) 2 (∂ µ π a ) 2) + . . .π aπ bπ cπ dcontact interaction growing with energyA ( π a π b → π c π d) = A(s, t, u)δ ab δ cd + A(t, s, u)δ ac δ bd + A(u, t, s)δ ad δ bcA(s, t, u) = sf 2 πf π = 93 MeVunitarity bound√ √ s ∼ 4 πfπ = 660 MeVrho meson (m=770 MeV) is restoring unitarityCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


γ, Z 0Why do we need a Higgs ?+W −W −W + γ, Z 0 W +s channel exchangeW −W + W +t channel exchangeW −W −W + W +W −contact interactionW −3H 0W −W −γ, Z 0W + W +t channel exchange4W −A = g 2 ( EM W) 2+A = −g 2 ( EM W) 2W −W + H 0 W +W −Higgs in s channelW + W +Higgs in t channelThe Higgs boson unitarize the W scattering4(if its mass is below ~ 700 GeV)A = g 2 (MH2M W) 2W + W +W L scattering = pion scatteringGoldstone equivalence theoremcontact interactionLewellyn Smith ‘73Dicus, Mathur ‘73Cornwall, Levin, Tiktopoulos ‘733Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Partial wave amplitude decomposition:A = 16πOptical theorem:Unitarity BoundLee, Quigg, Thacker ‘77dσdΩ = 1Chanowitz, Gaillard ‘8564π 2 s |A|2∞∑(2l + 1)P l (cos θ)a l a l = 132πl=0σ = 16s∞∑(2l + 1)|a l | 2l=0∫ 1−1d(cos θ)P l (cos θ)AP 0 (x) =1,P 1 (x) =x, P 2 (x) =3x 2 /2 − 1/2 ...σ = 1 sIm (A(θ = 0))Im (a l )=|a l | 2(Im (a l ) − 1/2) 2 + (Re (a l )) 2 =1/4|Re (a l ) |≤ 1/2SM without a Higgs a 0 = g2 E 216πMW2SM with a Higgsa 0 =g2 M 2 H64πM 2 W√ s =2E ≤ 1.7 TeVM H ≤ 1.2 TeVStronger Bound2W + W − + ZZ scatteringM H ≤ 780 GeVCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Can we replace the Higgs by a vector?scalar exchangevector exchangeA(s, t, u) = sv 2 − g2 σv 2 s 2s − m 2 σA(s, t, u) = sv 2 − g2 ρ( s − ut − m 2 ρ+ s − tu − m 2 ρ+3 s m 2 ρ)growing amplitude cancelledfor g=1 (Higgs)growing amplitude cancelledfor g 2 =m 2 /3v 254gbut this is not enougha vector resonance canonly postpone unitarity breakdown321m500 1000 1500 2000 2500 3000➾region where unitarity is maintained up to 3 TeVCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Physics Beyond the Higgs?Is the Standard Model with a Higgs a UV finite theory?i.e. valid to arbitrarily high energiesOf course, the SM will fail around the Planck scalebut the real question isIs there any reason to think there is new physicsbetween the weak scale and the Planck scale?Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Quantum corrections of % Higgs potentialCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Quantum Behavior of the Higgs 4 Coupling (I)V (h) =− 1 2 µ2 h 2 + 1 4 λh4vev : v 2 = µ 2 /λmass : m 2 H =2λv 2=16π 2dλd ln Q = 24λ2 − (3g ′2 +9g 2 − 12y 2 t )λ + 3 8 g′4 + 3 4 g′2 g 2 + 9 8 g4 − 6y 4 t +Large mass (λ dominated RGE)16π 2dλd ln Q = 24λ2λ increases with Q: IR-free couplingHigher loopsSmall Yukawaλ(Q) =m 2 H2v 2 − 32π 2 m 2 H ln(Q/v)Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Quantum Behavior of the Higgs 4 Coupling (I)V (h) =− 1 2 µ2 h 2 + 1 4 λh416π 2dλd ln Q = 24λ2 − (3g ′2 +9g 2 − 12y 2 t )λ + 3 8 g′4 + 3 4 g′2 g 2 + 9 8 g4 − 6y 4 t +Large mass (λ dominated RGE)Higher loopsSmall Yukawaλλ(Q) =Landau polem 2 H2v 2 − 32π 2 m 2 H ln(Q/v)Λ ≤ ve 4π2 v 2 /3m 2 Hm 2 H2v 2vQve 4π2 v 2 /3m 2 HNew physics should appear before that point to restore stabilityfor m H fixed, upper bound on for fixed, upper bound on m HNo microscopic description: forΛ →∞, trivial theory (λ=0)Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Quantum Behavior of the Higgs 4 Coupling (II)16π 2dλd ln Q = 24λ2 − (3g ′2 +9g 2 − 12y 2 t )λ + 3 8 g′4 + 3 4 g′2 g 2 + 9 8 g4 − 6y 4 t +Higher loopsSmall YukawaSmall mass (yt dominated RGE)16π 2dλd ln Q = −6y4 tλ decreases with Q.(dy t16π2Higher loopsSmall Yukawad ln Q = 9 2 y3 t + y 2 (Q) =y 2 (Q 0 )1 − 916π 2 y 2 (Q 0 ) ln Q Q 0(λ(Q) =λ 0 −38π 2 y 4 0 ln Q Q 01 − 916π 2 y 2 0 ln Q Q 02π 2 m 2 /3y 4 v 2Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Quantum Behavior of the Higgs 4 Coupling (II)16π 2dλd ln Q = 24λ2 − (3g ′2 +9g 2 − 12y 2 t )λ + 3 8 g′4 + 3 4 g′2 g 2 + 9 8 g4 − 6y 4 t +Higher loopsSmall YukawaSmall mass (yt dominated RGE)λ(Q) =λ 0 −38π 2 y 4 0 ln Q Q 01 − 916π 2 y 2 0 ln Q Q 0λm 2 H2v 20vQve 4π2 m 2 H /3y4 t v2λ< 0➾ potential unbounded from belowλ(Q) =0 for λ 0 ≈ 38π 2 y 4 0 ln Q Q 0New physics should appear before that point to restore stabilityΛ ≤ ve 4π2 m 2 H /3y4 t v2for fixed, lower bound on m HCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Higgs Mass [GeV]600500400300200Triviality Bound100Vacuum Stability Bound1 10 100Λ [TeV]the SM is not UV completeit is an effective theory of a more comprehensive theorythe cutoff of the SM can be rather lowCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Solution to the Higgs 4 Coupling Instabilitiesfind a symmetry such thatλ ≡ g 2the Higgs quartic will inherit the good UV asymptotically freebehavior of the gauge couplingExamples of such symmetry:supersymmetrygauge-Higgs unification: the Higgs is identified as a component ofthe gauge field along some extra-dimensions.Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Quantum Instability of the Higgs Massso far we looked only at the RG evolution of the Higgs quartic coupling (dimensionlessparameter). The Higgs mass has a totally different behavior: it is higly dependent on theUV physics, which leads to the so called hierarchy and little hierarchy problems.=+Higher loopsSmaller Yukawa∫d 4 k 1(2π) 4 k 2 − m 2 ∝ Λ2∫d 4 k k 2(2π) 4 (k 2 − m 2 ) 2 ∝ Λ2m 2 H ∼ m 2 0 − (115 GeV) 2 () 2Λ400 GeVA low-mass Higgs boson is imperiled by quantum corrections.The hierarchy problem is a technical problem in scalar theoriesCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Symmet!es for a natural EWSBCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


How to Stabilize the Higgs PotentialGoldstone’s Theoremspontaneously broken global symmetrymassless scalarThe spin tricka particle of spin s:... but the Higgs has sizable non-derivativecouplings2s+1 polarization states...with the only exception of a particle moving at the→→speed of light... fewer polarization statesSpin 1 Gauge invariance no longitudinal polarizationSpin 1/2Chiral symmetryonly one helicity... but the Higgs is a spin 0 particle→m=0→Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Symmetries to Stabilize a Scalar PotentialSupersymmetryHigher DimensionalLorentz invariancefermion ~ bosonA µ ∼ A 54D spin 1 4D spin 0These symmetries cannot be exact symmetry of the Nature.They have to be broken. We want to look for a soft breaking inorder to preserve the stabilization of the weak scale.Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Other symmetries?Ghost symmetry[Grinstein, O’Connell, Wise ‘07]SM particle ~ ghostIt was known since Pauli-Villars that ghosts can soften the UVbehavior of the propagators. But they are unstable per se.Lee-Wick in the 60’s proposed a trick to stabilize the ghosts (atthe price of of a violation of causality at the microscopic scale).Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


New physics and EW prec'ion testsCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


New Particles & EW Precision MeasurementsWe’ve seen that we need new particles to stabilize the weak scale.They have to be massive to evade direct searches.They still influence SM physics and can be “detected” trough precision measurements.DefineB in = B + B ′ , B out = B − B ′L = 1 2 W 3Example: Take an extra heavy B’ gauge bosonL = 1 2 W 3(p 2 − M 2 W )W 3 + t 0 M 2 W W 3 B + 1 2 B(p2 − t 2 0M 2 W )B + gJ 3 W 3 + g ′ J y B+ 1 2 B′ (p 2 − M 2 )B ′ + g ′ J y B ′ t 0 = g ′ /gand integrate out B out∂L=0 ⇔ B out = (t2 0MW 2 − M 2 )B in − 2t 0 MW 2 W 3∂B out 2p 2 − t 2 0 M W 2 − M 2+ 1 2 B in(p 2 − M 2 W + t 2 0MW4 )M 2W 3 + t 0 MW2(p 2 − t 2 0MW 2 + p4 − 2t 2 0MW 2 p2 + t 4 0MW4 )M 2+gJ 3 W 3 + g ′ J y B in + O(p6M 4 )+ O( )M6WM 4(1+ p2 − t 2 0MW2 )M 2holographic methodW 3 B inCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08B in


New Particles & EW Precision MeasurementsL = 1 2 W 3+ 1 2 B inMass matrix in the(p 2 − M 2 W + t 2 0MW4 )M 2 W 3 + t 0 MW2(1+ p2 − t 2 0MW2 )M 2 W 3 B in(p 2 − t 2 0MW 2 + p4 − 2t 2 0MW 2 p2 + t 4 0MW4 )M 2 B in + gJ 3 W 3 + g ′ J y B in(W 3 ,B in ) basis(1 − t 2 0M 2 WM 2This mass matrix is diagonalized byZ = cW 3 − sB inγ = sW 3 + cB inNote: det=0, so the photon is still massless!) ⎛ ⎝ M 2 W −t 0 M 2 Wwith masses−t 0 M 2 Wt 2 0M 2 W⎞⎠MZ 2 = ( 1−t 2 0 M 2 W /M 2 )c 2 0Mγ 2 =0M 2 Wunmodified weak mixing angles = s 0 , c = c 0that’s what you need to ensure that thephoton couples to T 3L +YRho and T parametersρ ≡ M W2MZ 2 ≈ 1+ s2 0c2 c 2 0M 2 WM 2 SM deviation: ρ ≡ 1+α em T T = s2 0α em c 2 0M 2 WM 2Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Experimental Constraints on TT ≤ 0.2⇔M ≥ 1.1 TeVThat’s rather genericbound on new physicsneeded to stabilize theweak scale is at least oneorder of magnitude abovethe weak scaleParticle Data Groupsection 10.3Little Hierarchy PbCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Model Independent BSM AnalysisDeviations from SM are measured by dimension 6 operatorsassuming flavor universality and CP, there are 20 such operatorsaffecting the gauge and the fermion sectors(linear case, similar results in the non-linear case)O S =(H † σ a H)W a µνB µν O T = |H † D µ H| 2[Buchmuller, Wyler ‘86][Han, Skiba ‘04]i(H † σ a D µ H)(f d γ µ σ a f d )+h.c.f d = L, Qi(H † D µ H)(fγ µ f)+h.c.(Lγ µ σ a L)(Lγ µ σ a L)f = L, E, Q, U, Dprobed byLEP1 and SLD(Lγ µ σ a L)(Qγ µ σ a Q)(fγ µ f)(f ′ γ µ f ′ )f = L, E f ′ = L, E, Q, U, Dprobed byLEP2e + e − → ¯ff(actually, there is another operator, but it is poorly constrained ɛ abc Wµ aν Wν bρ Wρcµ )Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Facing the LEP ParadoxL BSM = c iO iΛ 2c i ∼O(1) ⇒ Λ ≥ 5 ∼ 10 TeVLEP paradox: such a large cutoff will destabilize a light Higgs[Barbieri, Strumia ‘00]1Find points withreduced fine tuningimproved naturalness2Loop inducedEW corrections3Cancellations amongvarious operatorsor a combination of the three...Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


The Structure of the Oblique CorrectionsAssuming heaviness of new physics, flavor universality, CP[Peskin, Takeuchi ‘90,’92][Golden, Randall ‘90][Holdom, Terning ‘90]L = W µ + Π +− (p 2 ) W − µ + 1 2 W µ 3 Π 33(p 2 ) W 3 µ + W µ 3 Π 3B(p 2 ) B µ + 1 2 Bµ Π BB (p 2 ) B µ4 vacuum polarizations that we expand in powers of momentum:A priori 12 coefficients:Π V (p 2 )=Π V (0) + p 2 Π ′ V (0) + 1 2 (p2 ) 2 Π ′′ V (0) + O(p 6 )But 3 can be removed by canonically normalized the gauge bosons (g, g’ and v).Π ′ +−(0) = Π ′ BB(0) = 1, Π +− (0) = −M 2 W = −(80.425 GeV) 2And we need to impose the masslessness of the photon and its couplings to Q=T 3 +Y.We are left with 7 coefficientsCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


The Structure of the Oblique CorrectionsWe are left with seven coefficients[Grinstein, Wise ‘91][Barbieri, Pomarol, Rattazzi, Strumia ‘04]Coefficients Dim. 6 Operators SU(2) c SU(2) LŜ = g gΠ ′ ′ 3B (0) O WB = (H † τ a H)WµνB a µν /gg ′ + −1 ̂T = (ΠM 2 33 (0) − Π +− (0)) O H = |H † D µ H| 2 − −WÛ = Π ′ +−(0) − Π ′ 33(0) dim. 8 − −V = M 2 W2(Π′′33(0) − Π ′′ +−(0) ) dim. 10 − −X = M 2 W2Π ′′3B (0) dim. 8 + −Y = M 2 W2Π ′′ BB (0) O BB = (∂ ρ B µν ) 2 /2g ′2 + +W = M 2 W2Π ′′33(0) O WW = (D ρ Wµν) a 2 /2g 2 + +(S =4s 2 wŜ/α em ≈ 119 Ŝ, T = ̂T /α em ≈ 129 ̂T), U = −4s 2 wÛ/α em ≈−119 ÛFor universal models(couplings of BSM to SM fermionsonly through SM currents)Û ∼ M 2 WΛ 2̂T , V ∼ M 4 WΛ 4̂T , X ∼ M 2 WΛ 2only four oblique parameters dominateŜ[Barbieri, Pomarol, Rattazzi, Strumia ‘04][Cacciapaglia, Csaki, Marandella, Strumia ‘06]Ch!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Tools #1: Disguising the Oblique ParametersCertain linear combinations remain poorly constrainedIndeed massaging the eqs of motion, we obtain the two identities− 2gscv2α O S − g′ v 2α O T + g ′ ∑ y f O Hf =2iB µν D µ H † D ν Hf− 4g′ scv 2O S + g(O HL + O HQ )=4iWµνD a µ H † σ a D ν Hα[Grojean, Skiba, Terning ‘06]The RHS terms only affect the triple gauge boson couplings... which are poorly measuredSo it is possible to disguise oblique corrections into yet unconstrained operatorsIt is important to measure triple gauge boson verticesto fully identify new physics in the EWSB sectorCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


ools #2: The Benefits of the Custodial SymmetryCustodial symmetry and the T parameterV (H) =λ(H † H − v22) 2[Weinberg ‘79][Sikivie, Susskind, Voloshin, Zakharov ‘80]is invariant under SO(4) ∼ SU(2) L × SU(2) RSU(2) LSU(2) R(iσ 2 H ⋆ H ) =Φif New Physics respects SU(2) R , then it won’t generate the operator O T = |H † D µ H| 2Custodial symmetry andnewSU(2) L xSU(2) RembeddingQ L =⎛⎝ t2/3 Lt 5/3Lb −1/3Lb 2/3LZ bL¯bL[Agashe, Contino, Da Rold, Pomarol ‘06]then b L is an eigenstate of L R and this ensures that δZ bL¯bL =0but we expectZt L¯tdeviations in L Wt L¯bL Zb R¯bR(good for ?)⎞⎠ ≡ (2, ¯2) 2/3t R ≡ (1, 1) −2/3b R ≡ (1, 1) −2/3(H † D µ H)(b L γ µ b L )A b FBCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


Tools #3: T-parity for Loop Induced Correctionsheavy particles = oddlight particles = evenat each vertex, an even number of heavy fields are requiredno effective operator for light fields are generatedby tree-level exchange of heavy fields[Cheng, Low ‘03]tree-level exchange forbiddenloop exchange allowed✗✓c i ∼ α 4π⇒Λ ≥ 500 GeVCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


EW Precision Measurements & Higgs MassAt the loop level, SM degrees of freedom contribute to S and T➾ constraints on the Higgs mass0.50.40.30.2m top=171.4 GeV68 % CL95 % CLT0.10−0.1−0.2m HPlot100from scalarsm EWPT,eff500from cutofffrom fermions?−0.3−0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4SCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08


ConclusionsEW interactions need a UV moderatorto unitarize WW scattering amplitudethe SM with a light fundamental scalar cannot be (naturally)extended to very high energiesnew particles/symmetries are expected to populate the TeV scaleto trigger the breaking of the EW symmetryCh!"ophe Grojean Beyond the Higgs Ecole de Gif, September '08

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