Basics of Higgs Physics

Transcription

1 Basics of iggs Physics Sven einemeyer, IFCA (Santander) Karlsruhe, 07/ The iggs Boson in the SM 2. The iggs Boson in the MSSM Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/1

2 Basics of iggs Physics (I) Sven einemeyer, IFCA (Santander) Karlsruhe, 07/ The iggs Boson in the SM (2/3) + (1/3) 2. The iggs Boson in the MSSM Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/1

3 The iggs Boson in the SM Sven einemeyer, IFCA (Santander) Karlsruhe, 07/ iggs Theory 2. Electroweak Precision Observables 3. Properties of the SM iggs boson 4. SM iggs boson Searches at LEP 5. SM iggs boson Searches at the Tevatron 6. SM iggs boson Searches at the LC 7. SM iggs boson precision physics at the ILC Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/1

4 The iggs Boson in the SM Sven einemeyer, IFCA (Santander) Karlsruhe, 07/ iggs Theory 2. Electroweak Precision Observables 3. Properties of the SM iggs boson 4. SM iggs boson Searches at LEP 5. SM iggs boson Searches at the Tevatron 6. SM iggs boson Searches at the LC 7. SM iggs boson precision physics at the ILC Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/1

5 1. iggs Theory Standard Model (SM) of the electroweak and strong interaction SM: Quantum field theory interaction: exchange of field quanta Construction principle of the SM: gauge invariance Example: Quantum electro-dynamics (QED) field quanta: photon A µ e e γ nucleus L QED invariant under gauge transformation: Ψ e i e λ(x) Ψ, A µ A µ + µ λ(x) mass term for photon: m 2 A µ A µ not gauge invariant A µ is massless gauge field Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/2

6 Problem: Gauge fields Z, W +, W are massive explicite mass terms in the Lagrangian breaking of gauge invariance Solution: iggs mechanism scalar field postulated, mass terms from coupling to iggs field iggs sector in the Standard Model: Scalar SU(2) doublet: Φ = iggs potential: φ+ φ 0 ) V( Φ + 0, Φ µ 2>0 V (φ) = µ 2 Φ Φ + λ Φ Φ 2, λ > 0 µ 2 < 0: Spontaneous symmetry breaking µ 2 minimum of potential at Φ 0 = 2 λ v 2 v/ 2 Φ + 2 µ<0 Φ 0 Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/3

7 Φ = v + (unitary gauge) : elementary scalar field, iggs boson Lagrange density: L iggs = (D µ Φ) (D µ Φ) g d Q L Φd R g u Q L Φ c u R V (Φ) with id µ = i g 2 I W g1 Y B Φ c = iσ 2 Φ Q L u L d L, Φ 0 v, Φ c v 0 Gauge invariant coupling to gauge fields mass terms for gauge bosons and fermions Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/4

8 1.) V V ΦΦ coupling: V + v q 2 1 q 2 + j 1 q 2 ( ) 2 gv 1 2 q 2 j = 1 q 2 M 2 : M2 = g 2v2 2 2.) fermion mass terms: Yukawa couplings: f + v q 1 q + j 1 q [ ] gf v j 1 = 2 q 1 q m f : m f = g f v 2 Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/5

9 1.) V V ΦΦ coupling: v x x v V V VV mass terms: g 2 2 v2 /2 M 2 W, (g2 1 + g2 2 )v2 /2 M 2 Z v x V V V V triple/quartic couplings to gauge bosons coupling masses Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/6

10 2.) fermion mass terms: Yukawa couplings f f v x f f m f = v g f coupling masses 3.) mass of the iggs boson: self coupling v x λ... λ = M 2 /v M = v λ free parameter v x last unknown parameter of the SM establish iggs mechanism find the iggs measure its couplings Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/7

11 Another effect of the iggs field: Scattering of longitudinal W bosons: W L W L W L W L W M V = γ, Z W violation of unitarity W W + γ, Z + = g 2 E 2 M 2 W + O(1) for E Contribution of a scalar particle with couplings prop. to the mass: W W M S = W W + = gww 2 E2 MW 4 + O(1) for E M tot = M V + M S = E2 ( g 2 MW 4 WW g 2 MW 2 ) +... compensation of terms with bad high-energy behavior for g WW = g M W Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/8

12 What else do we know about the iggs boson? Running of iggs self-interaction: λ t Renormalization group equation: d λ d t = 3 8 π 2 [ λ 2 + λg 2 t g 4 t ( 2g (g g2 1 )2)], t = log ( Q 2 v 2 ) Two conditions: 1.) avoid Landau pole (for large λ M 2 ) 2.) avoid vacuum instability (for small/negative λ) Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/9

13 1.) avoid Landau pole (for large λ M 2 ) d λ d t λ(q 2 ) = = 3 8 π 2 [ λ 2 ] λ(v 2 ) ( 1 3λ(v2 ) 8 π 2 log Q 2 v 2 ) λ(λ) < M 2 8 π2 v 2 3log ( Λ 2 ) v 2 : upper bound on M 2.) avoid vacuum instability (for small/negative λ): V (v) < V (0) λ(λ) > 0 d λ = 3 [ d t 8 π 2 gt ( 2g (g2 2 + g2 1 )2)] λ(q 2 ) = λ(v 2 ) 3 8 π 2 λ(λ) > 0 M 2 > v2 4 π 2 [ g 4 t [ g 4 t ( 2g (g g2 1 )2)] log ( 2g (g g2 1 )2)] log ( Λ 2 v 2 ) ( ) Q 2 v 2 : lower bound Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/10

14 Both limits combined: m t = 174 GeV M (GeV) Landau pole Potential bounded from below Λ (GeV) Λ: scale up to which the SM is valid Λ = M GUT 130 GeV < M < 180 GeV Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/11

15 2. Electroweak Precision Observables (EWPO): Comparison of electro-weak precision observables with theory: EW Precision data: Theory: M W,sin 2 θ eff, a µ SM, MSSM,... Test of theory at quantum level: Sensitivity to loop corrections, e.g. SM: limits on M Very high accuracy of measurements and theoretical predictions needed Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/12

16 Example: prediction of M W Theoretical prediction for M W in terms of M Z, α, G µ, r: M 2 W ( 1 M2 W M 2 Z ) = π α 2 Gµ (1 + r) loop corrections Evaluate r from µ decay M W One-loop result for M W in the SM: [A. Sirlin 80], [W. Marciano, A. Sirlin 80] r 1 loop = α c2 W s 2 ρ + r rem (M ) W log M Z m f m 2 t log(m /M W ) 6% 3.3% 1% Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/13

17 Comparison of SM prediction of M W with direct measurements: r = 11g π 2 s 2 W c 2 W log ( M M W ) 80.5 LEP1 and SLD LEP2 and Tevatron (prel.) 68% CL general for EWPO: g 2 2 [ log ( M M W ) leading term: log(m ) + g 2 2 M 2 M 2 W first term M 2 with g4 2 light iggs boson preferred ] m W [GeV] α m [GeV] [LEPEWWG 07] m t [GeV] Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/14

18 Results for M from other EWPO: light iggs preferred by: M W, A LR l (SLD) heavier iggs preferred by: A FB b (LEP) keeps SM alive Γ Z σ 0 had R 0 l A 0,l fb A l (P τ ) R 0 b R 0 c A 0,b fb A 0,c fb A b A c A l (SLD) sin 2 θ lept eff (Q fb ) m W * Γ W * Q W (Cs) sin 2 θ (e e MS ) sin 2 θ W (νn) g 2 L (νn) g 2 R (νn) *preliminary M [GeV] light iggs boson preferred [LEPEWWG 07] Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/15

19 Global fit to all SM data: [LEPEWWG 07] M = GeV M < 144 GeV, 95% C.L Theory uncertainty α had = α (5) ± ± incl. low Q 2 data m Limit = 144 GeV χ 2 3 Assumption for the fit: SM incl. iggs boson no confirmation of iggs mechanism 2 1 Excluded Preliminary m [GeV] iggs boson seems to be light, M < 150 GeV Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/16

20 3. Properties of the SM iggs boson 1.) Decay to fermions: coupling: g f f = [ 2 Gµ ] 1/2 mf decay width: Γ( f f) = N c G µ M 4 2 π m2 f (M2 ) 1 4 m2 f M 2 3/2 with N c = number of colors Bulk of QCD corrections for decays to quarks are mapped into m 2 q (pole) m2 q (M2 ) Dominant decay process: b b Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/17

21 2.) Decay to heavy gauge bosons (V = W, Z): coupling: g V V = 2 [ 2 Gµ ] 1/2 M 2 V on-shell decay width (M > 2M V ): Γ( V V ) = δ V G µ M π with δ W,Z = 2,1 ( 1 4 M2 V M M4 ) ( V M M2 ) 1/2 V M 2 off-shell decay width (M < 2M V ): Γ( V V ) = δ V 3G 2 µ M 16 π 3 M4 V Integral Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/18

22 3.) Decay to massless gauge bosons (gg, γγ): t t via the top quark loop with huge QCD corrections t g g Γ( gg) = G µ α 2 s(m 2 ) M π 3 C = log ( µ 2 M 2 ) W W [ W 1 + C α s(µ) π + O(α s ) γ γ ] Γ( γγ) = G µ α 2 M π 3 via the top quark and W boson loop 4 3 e2 t 7 2 Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/19

23 Overview of the branching ratios: [taken from hep-ph/ ] Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/20

24 The total SM iggs boson width: [taken from hep-ph/ ] Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/21

25 Discovering the iggs boson What has to be done? 1. Find the new particle Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/22

26 Discovering the iggs boson What has to be done? 1. Find the new particle 2. measure its mass ( ok?) Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/22

27 Discovering the iggs boson What has to be done? 1. Find the new particle 2. measure its mass ( ok?) 3. measure coupling to gauge bosons 4. measure couplings to fermions Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/22

28 Discovering the iggs boson What has to be done? 1. Find the new particle 2. measure its mass ( ok?) 3. measure coupling to gauge bosons 4. measure couplings to fermions 5. measure self-couplings Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/22

29 Discovering the iggs boson What has to be done? 1. Find the new particle 2. measure its mass ( ok?) 3. measure coupling to gauge bosons 4. measure couplings to fermions 5. measure self-couplings 6. measure spin,... Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/22

30 Discovering the iggs boson What has to be done? 1. Find the new particle T 2. measure its mass ( ok?) T 3. measure coupling to gauge bosons 4. measure couplings to fermions 5. measure self-couplings 6. measure spin,... T = Tevatron, Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/22

31 Discovering the iggs boson What has to be done? 1. Find the new particle T L 2. measure its mass ( ok?) T L 3. measure coupling to gauge bosons L 4. measure couplings to fermions L 5. measure self-couplings 6. measure spin,... T = Tevatron, L = LC, Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/22

32 Discovering the iggs boson What has to be done? 1. Find the new particle T L I 2. measure its mass ( ok?) T L I 3. measure coupling to gauge bosons L I 4. measure couplings to fermions L I 5. measure self-couplings I 6. measure spin,... I T = Tevatron, L = LC, I = ILC (International Linear e + e collider) We need the LC and the ILC to find the iggs and to establish the iggs mechanism! The LC can do a crucial part... Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/22

33 4. SM iggs search at LEP: Dominant production process: e + e Z: e Z e + Z σ(e + e Z) = G2 µm 4 Z 96 π s [ v 2 e + a 2 e] β β M 2 Z /s (1 M 2 Z /s)2 with β 2 = (1 (M + M Z ) 2 /s)(1 (M M Z ) 2 /s) (1) Dominant decay process: b b b b Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/23

34 Search for the Standard Model iggs at LEP: [LEP iggs WG 03] Exclusion limit at the 95% C.L.: M > GeV expected: GeV (LEP has seen exactly as many iggs-like events as could be expected for M 116 GeV, not more, not less) -2 ln(q) Observed Expected for background Expected for signal plus background LEP m (GeV/c 2 ) Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/24

35 5. SM iggs search at the Tevatron Tevatron: p p accelerator: T Production processes as at LEP: q W q Z q W q Z Other important production channels: g t q t g t q Dominant decays: b, τ W W q q W b, τ + W Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/25

36 Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/26

37 Overview of production cross sections: [F. Maltoni et al. 05] SM iggs production σ [fb] qq Wh qq qqh gg h TeV II 10 bb h qq Zh gg,qq tth TeV4LC iggs working group m h [GeV] Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/27

38 Expectations for iggs discovery at the Tevatron: Unfortunately: luminosity problems in the start of RunII progress slower than anticipated For SM iggs boson with M 120 GeV: 2008/09: sensitivity for 95% C.L. exclusion 2009: sensitivity for 3σ evidence or exclude SM iggs with M < 130 GeV Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/28

39 Results for various search channels for SM iggs: [CDF, D0 06] 95% CL Limit/SM CDF 320 pb -1 tt D0 378 pb -1 W lνbb Can they close the gap? Tevatron Run 2 Preliminary CDF 289 pb -1 Z ννbb D0 261 pb -1 Z ννbb CDF 360 pb -1 W lνbb D0 325 pb -1 WW lνlν D0 950 pb -1 combined CDF 360 pb -1 WW lνlν April 20, m (GeV) Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/29

40 Current status (latest results) of SM iggs search: [CDF, D0 06] Can they close the gap? Sven einemeyer Basics of iggs Physics presusy07 (Karlsruhe) I/30