The Higgs Scalar H. V (φ) φ 2. φ 1. unitary gauge. P529 Spring,

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1 The iggs Scalar V (φ) V (φ) φ 1 φ 2 φ 1 φ 2 φ = ( φ + φ 0 ) unitary gauge ( ν + ) P529 Spring,

2 Interactions of Gauge interactions: ZZ, ZZ 2, W + W, W + W 2 ϕ 1 2 ( 0 ν + ) (unitary gauge) L ϕ = (D µ ϕ) D µ ϕ V (ϕ) = 1 ( 2 ( µ) 2 + M 2 W W µ+ W µ 1 + ν + 1 ( 2 M 2 Z Zµ Z µ 1 + ) 2 V (ϕ) ν ) 2 (quartic and induced cubic interactions, (ν)m 2 /ν 2 ) P529 Spring,

3 W + µ W µ f 2igµν M2 W ν 2igµν M2 W ν 2 i m f ν W ν W + ν f Zµ Zµ 2igµν M2 Z ν 2igµν M2 Z ν 2 Zν Zν 3i M2 ν 3i M2 ν 2 Typeset by FoilTEX P529 Spring,

4 iggs potential: V (ϕ) = +µ 2 ϕ ϕ + λ(ϕ ϕ) 2 Fourth term: Quartic self-interaction Third: Induced cubic self-interaction µ4 4λ µ2 2 + λν 3 + λ 4 4 Second: (tree level) mass-squared, M = 2µ 2 = 2λν First: Constant (irrelevant until gravity added cosmological constant) λ λ ν P529 Spring,

5 Yukawa couplings of iggs to fermions L Yukawa = i ψ i ( m i gm ) i ψ i 2M W Coupling gm i /2M W is flavor diagonal and small except t quark bb dominates for M 2M W ( W + W, ZZ dominate when allowed because of larger gauge coupling) Flavor diagonal because only one doublet couples to fermions fermion mass and Yukawa matrices proportional Often flavor changing iggs couplings in extended models with two doublets coupling to same kind of fermion (not MSSM) Stringent limits, e.g., tree-level iggs contribution to K L K S mixing (loop in standard model) h ds/m < 10 6 GeV 1 P529 Spring,

6 No a priori constraint on λ except vacuum stability (λ > 0 0 < M < ) Theoretical bounds: triviality, tree unitarity, (meta) stability at loop level Experimental bounds: LEP 2 bound: e + e Z Z M GeV at 95% cl (can evade with singlet or in MSSM) Indirect (precision tests) + LEP 2: M < 150 GeV, 95% cl Tevatron (CDF, D0): 2M W excluded; enhancement GeV LC 2012: (CMS, ATLAS): observation of iggs-like state around 125 GeV; heavy excluded MSSM: much of parameter space has standard-like iggs with M < 130 GeV (150 in extensions) P529 Spring,

7 M [GeV] Γ Z, σ had, R l, R q (1σ) Z pole asymmetries (1σ) M W (1σ) m t (1σ) low energy precision data (90% CL) allowed by searches excl. by 1 experiment excl. by > 1 experiment m t [GeV] P529 Spring,

8 ! Broad"excess"consistent" with"produc.on"at"m "="125" '="125" CDF:""2.89"(1.46)" DØ:"""""2.92"(1.66) " `" iggs"measurements"at"the"tevatron" 11" P529 Spring,

9 Theoretical Bounds Theoretical M limits, ambye and Riesselmann, hep-ph/ P529 Spring,

10 M 2 = 2λν2, λ = g2 M 2 8M 2 W = G F M 2 2 Running gauge couplings (vacuum polarization) b gs = 1 16π 2 b g = 1 16π 2 b g = π 2 [ 11 4F 3 dgi 2 d ln Q = b ig 4 2 }{{} i ] 1 loop F =3,n =1 [ F 3 n ] 6 [ + 20F 9 + n ] π 2 ( 7) F =3,n =1 F =3,n =1 1 16π 2 ( 1 19 ) 6 ( + 41 ) 6 16π 2 P529 Spring,

11 Quartic coupling λ and top-yukawa h t also run dλ(q 2 ) d ln Q 2 = 1 32π 2 [ 24λ λh 2 t 24h4 t 3λ ( 3g 2 + g 2) (2g 4 + (g 2 + g 2 ) 2 )] dh t (Q 2 ) d ln Q = 1 [ 9h π 2 t h t (8g 2s g )] 12 g 2 t t t λ(ν 2 ) G F M 2 2 (> 1 for M 350 GeV) t h t (ν 2 ) m t /ν 0.7 P529 Spring,

12 λ 2 dominates for large M λ(q 2 ) = λ(ν 2 ) 1 3λ(ν2 ) 4π 2 ln Q2 ν 2 Diverges at Landau pole Q LP = νe 2π2 /3λ(ν 2 ) Require Q LP > Λ = new physics scale (triviality limit) M < ( 2 2π 2 3G F ln(λ/ν) ) 1/2 { O(140) GeV, Λ MP O(650) GeV, Λ 1500 GeV (Planck scale: M P = G 1/2 N GeV) Lattice: M < GeV Tree unitarity: M < 700 GeV (or else strong coupling) P529 Spring,

13 Lower limit from loop corrections to vacuum stability h 4 t dominates for small λ λ(q 2 ) λ(ν 2 ) 3h4 t Q2 ln 4π2 ν 2 λ(q 2 ) < 0 for Q 2 > Q 2, with M 2 = 3h4 t 2π 2 GF ln Q ν Vacuum unstable unless Q > Λ lower bound on M Weaker for metastable Doesn t apply in MSSM P529 Spring,

14 iggs Production and Decays Production: LEP: iggstrahlung (e + e Z Z) Tevatron, LC: GG-fusion (GG via top loop), vector boson fusion (W W or ZZ ), or associated production ( qq W, Z, GG t t) W, Z t t G t G q W, Z q q W, Z q G t t G P529 Spring,

15 10 3 SM iggs production gg h TeV II 10 5 σ [fb] SM iggs production LC σ [fb] 10 2 qq Wh 10 4 qq qqh gg h qq qqh 10 3 bb h qq Wh 10 qq Zh 10 2 bb h gg,qq tth gg,qq tth TeV4LC iggs working group m h [GeV] qb qth TeV4LC iggs working group qq Zh m h [GeV] P529 Spring,

16 Decays: bb dominates for M 2M W Γ( f f) = C f G F m 2 f 4 2π β3 f M (β f = (1 4m 2 f /M 2 )1/2 ; C f = 1 (leptons) or 3 (quarks)) W + W, ZZ dominate when allowed because of larger gauge coupling Γ( V V ) = δ V (δ W = 2, δ Z = 1; x V = 4M 2 V /M 2 ) ( G F 16 2π (1 x V ) 1/2 1 x V x2 V Virtual ( V V ) important below 2M V ) M 3 Loop-induced: γγ, Zγ, GG; 2γ best for low mass at LC P529 Spring,

17 P529 Spring,

18 Discovery at the LC: CMS, ATLAS: around 25 fb 1 each at (7) 8 TeV Summer 2012: 5σ observation of narrow resonance around GeV Strongest signals in 2γ and ZZ 4l Mainly GG fusion and VBF; some associated production J P = 0 + (probably not 0, spin-1 (Landau-Yang), spin-2)) 2γ rate somewhat large (2σ) (not new CMS) Discrepancy in ATLAS 2γ and ZZ masses (probably not significant) P529 Spring,

19 ZZ 4l: Mass spectrum CMS-IG Z 4l peak well visible Good description of ZZ continuum σ(pp ZZ, 8TeV) = 8.4±1.0 (stat.) ± 0.7 (syst.) ± 0.4(lum.) pb Clean signal peak at ~126 GeV P529 Spring,

20 ode and decay through loops sensitive to t / W couplings and to ction ecomposition Invariant m Stability of EM vs time γ ~ 75% didates per tus Simple topology: two high-e T (>40,30 GeV) isolated photons events in 100<m γγ P529 Spring, γγ [GeV]<160 γγ Mass reso

21 rength V tt σ/ σ SM = / P529 Spring,

22 clusion P529 Spring,

23 Consistent with SM iggs (metastable vacuum for Λ > GeV) Consistent with MSSM lightest iggs scalar, though on border of parameter space ints (2σ) Example: of discrepancies Prediction for will M W inbe thetested SM and the at MSSM LC, : ILC, etc [S.., W. ollik, D. Stockinger, G. Weiglein, L. Zeune 12] experimental errors 68% CL: M W [GeV] LEP2/Tevatron: today LC: future M = 123 GeV M h = GeV MSSM MSSM band: scan over SUSY masses overlap: SM is MSSM-like MSSM is SM-like SM M = 127 GeV MSSM, M h = GeV SM, MSSM einemeyer, ollik, Stockinger, Weiglein, Zeune 12 SM band: variation of M SM m t [GeV] Sven einemeyer Snowmass preparation workshop, BNL, 04/05/ 13 3 P529 Spring,

24 Standard model iggs summary LEP 2: M > GeV Precision + LEP 2: M < 150 GeV LC, Tevatron (CMS, ATLAS, CDF, D0): iggs-like state at GeV; consistent with SM but hints of discrepancies Additional iggs particles in MSSM; lightest (M < GeV) usually acts like SM iggs M 125 is near bottom (top) of likely SM (MSSM) range P529 Spring,