Oblique corrections from Light Composite Higgs

Transcription

1 Oblique corrections from Light Composite Higgs Slava Rychkov (ENS Paris & CERN) with Axel Orgogozo & work in progress

2 EWPT in Standard Model M H 0.0 M W -1.2 % W 0.2 M Z 0.2 % Z 0.1 0! had 0 Rlep 0,l A FB A l (LEP) A l (SLD) 2 lept sin $ eff (Q ) FB A c A b A l (LEP) A l (SLD) ,c A FB 0,b A FB 0 Rc 0 Rb m c m b ,b A FB M W Fit w/o M H LHC average M H [GeV] ± 0.4 (5) #" had (M m t 2 Z ) GFitter (O fit - O meas ) /! meas

3 EWPT in BSM - With light fermion universality, 3 most important observables:

4 EWPT in BSM - With light fermion universality, 3 most important observables: - Most often new effects only in gauge boson propagators (oblique):

5 ε 1 = ρ The epsilons ε 3 = c 2 ρ +(c 2 s 2 ) k Altarelli, Barbieri ε 2 = c 2 ρ 2s 2 k + s2 r W c 2 s 2

6 ε 1 = ρ The epsilons ε 3 = c 2 ρ +(c 2 s 2 ) k Altarelli, Barbieri ε 2 = c 2 ρ 2s 2 k + s2 r W c 2 s 2 Have simple parametrization in terms of self-energies:

7 ε 1 = ρ The epsilons ε 3 = c 2 ρ +(c 2 s 2 ) k Altarelli, Barbieri ε 2 = c 2 ρ 2s 2 k + s2 r W c 2 s 2 Have simple parametrization in terms of self-energies:

8 ε 1 = ρ The epsilons ε 3 = c 2 ρ +(c 2 s 2 ) k Altarelli, Barbieri ε 2 = c 2 ρ 2s 2 k + s2 r W c 2 s 2 Have simple parametrization in terms of self-energies:

9 ε 1 = ρ The epsilons ε 3 = c 2 ρ +(c 2 s 2 ) k Altarelli, Barbieri ε 2 = c 2 ρ 2s 2 k + s2 r W c 2 s 2 Have simple parametrization in terms of self-energies:

10 Dependence on Higgs mass m H

11 Experimental determination GFitter

12 Experimental determination GFitter Since ε2 insensitive to heavy NP, makes sense to condition on U=0: T %, 95%, 99% CL fit contours, U=0 (SM : M H =126 GeV, m =173 GeV) ref t M H SM Prediction M H = ± 0.4 GeV = ± 0.94 GeV m t SM Prediction with M H![100,1000] GeV S

13 Thus: better W measurements improve determination of ε1,ε3. Studying consistency directly in terms of mw seems rather awkward. [GeV] % and 95% CL fit contours w/o M W and m t measurements kin m t Tevatron average ± 1! M W % and 95% CL fit contours w/o M W, m and M H measurements t 80.4 M W world average ± 1! M H =50 GeV M H =125.7 M H =300 GeV M H =600 GeV m t [GeV] Figure 4: Contours of 68% and 95% CL obtained from scans of fixed M W and m t. The blue (grey) areas

14 EWPT in composite Higgs models EWSB sector E } } E>> TeV: CFT with global symmetry G f : G/H resonances m=0 goldstones

15 EWPT in composite Higgs models EWSB sector E } } E>> TeV: CFT with global symmetry G f : G/H resonances m=0 goldstones W,Z,h upon coupling to the SM gauge fields

16 Problem: Which CFT observable controls them?

17 Case study: Higgsless case Peskin, Takeuchi 1991 G=SU(2)LxSU(2)R H=SU(2)V strong sector heavy Higgs SM

18

19 μ independence:

20 μ independence: Relative accuracy:

21 - If spectral densities are known (like in scaled-up QCD), then S parameter can be computed reliably - If unknown, still allows modelization (Vector Meson Dominance, Weinberg sum rules, etc) s

22 For composite Higgs: Aim for rel. accuracy

23 For composite Higgs: From resonances & CFT, a la Peskin-Takeuchi Aim for rel. accuracy

24 For composite Higgs: From resonances & CFT, a la Peskin-Takeuchi From pseudo-goldstone Higgs (mh=125 GeV => must go beyond heavy Higgs approximation) Aim for rel. accuracy

25 For concreteness, consider Minimal Comp. Higgs Model, i.e. SO(5)/SO(4) SO(5) Current correlators:

26 For concreteness, consider Minimal Comp. Higgs Model, i.e. SO(5)/SO(4) SO(5) Current correlators: order parameter of SO(5)/SO(4) breaking

27 For concreteness, consider Minimal Comp. Higgs Model, i.e. SO(5)/SO(4) SO(5) Current correlators: order parameter of SO(5)/SO(4) breaking

28 For concreteness, consider Minimal Comp. Higgs Model, i.e. SO(5)/SO(4) SO(5) Current correlators: order parameter of SO(5)/SO(4) breaking parity breaking term

29 For concreteness, consider Minimal Comp. Higgs Model, i.e. SO(5)/SO(4) SO(5) Current correlators: order parameter of SO(5)/SO(4) breaking term responsible for S(UV)

30 OPE analysis in the UV 1 Jµ A (x)jν B (0) = (η µν 2 µ ν ) (x 2 ) + 2 O Γ AB C OC (0) (x 2 ) O/2

31 OPE analysis in the UV 1 Jµ A (x)jν B (0) = (η µν 2 µ ν ) (x 2 ) + 2 O Γ AB C OC (0) (x 2 ) O/2

32 OPE analysis in the UV 1 Jµ A (x)jν B (0) = (η µν 2 µ ν ) (x 2 ) + 2 O Γ AB C OC (0) (x 2 ) O/2 These operators control formfactor asymptotics: Π i (q 2 ) q 2 q 2 /m 2 ρ Oi /2, O0 1, O 1 14, O 2 4.

33 Focus on Π1 Spectral density dominated by two-goldstone state at small s: ρ(s) 1/(192π 2 ) (s m 2 ρ)

34 Digression about Weinberg sum rules 0 ds ρ(s) =f 2 0 ds s ρ(s) =0

35 Digression about Weinberg sum rules 0 ds ρ(s) =f 2 0 ds s ρ(s) =0

36 Digression about Weinberg sum rules 0 ds ρ(s) =f 2 0 ds s ρ(s) = Poland, Simmons-Duffin, Vichi excluded

37 Digression about Weinberg sum rules 0 ds ρ(s) =f 2 0 ds s ρ(s) = Poland, Simmons-Duffin, Vichi excluded

38 Digression about Weinberg sum rules 0 ds ρ(s) =f 2 0 ds s ρ(s) = Poland, Simmons-Duffin, Vichi excluded Conformal Technicolor range

39 Back to computing S Step 1. Match UV theory to m h µ m ρ,

40 Back to computing S Step 1. Match UV theory to m h µ m ρ, The natural observable to match is

41 Back to computing S Step 1. Match UV theory to m h µ m ρ, The natural observable to match is In UV theory: Agashe,Contino,Pomarol

42 Back to computing S Step 1. Match UV theory to m h µ m ρ, The natural observable to match is In UV theory: Agashe,Contino,Pomarol

43 In effective theory:

44 In effective theory:

45 In effective theory: Matching UV to effective determines:

46 Step 2. Compute S from effective theory Recall SM:

47 Step 2. Compute S from effective theory Recall SM:

48 Step 2. Compute S from effective theory Recall SM:

49 e.g. Novikov, Okun, Vysotski H A (h) = hc2 h c 2 log h c 2 H R (h) = h 18 + c2 1 c2 h 8h 4 9(h 1) log h h h2 F h (h) log h 4 c h h2 F h (h)+ h log h, 1 h h + h2 9 Fh(h) h 18 h F h (h) =1+ h h h 1 4h log h + log h 1+ h, h > 4, h 1arctan 4 1, h < 4, h h Fh(h) = 1+ h 1 h (3 h) h 4 log h + log h 1+ h, h > 4, h (3 h) arctan 4 1, h < 4. 4 h h To facilitate h = m 2 h /m2 Z

50 In composite Higgs: 3 3,W/Z 3,Higgs ε 3 (MCHM) = ε 3,W/Z + a 2 ε 3,Higgs + g 2 v2 f 2 c(µ2 )

51 In composite Higgs: 3 3,W/Z 3,Higgs ε 3 (MCHM) = ε 3,W/Z + a 2 ε 3,Higgs + g 2 v2 f 2 c(µ2 ) Loops of W/Z cancel in the S parameter: Ŝ = ε 3 (MCHM) ε 3 (SM) = v2 f 2 ε3,higgs + g 2 c(µ 2 )

52 In composite Higgs: 3 3,W/Z 3,Higgs ε 3 (MCHM) = ε 3,W/Z + a 2 ε 3,Higgs + g 2 v2 f 2 c(µ2 ) Loops of W/Z cancel in the S parameter: Ŝ = ε 3 (MCHM) ε 3 (SM) = v2 f 2 ε3,higgs + g 2 c(µ 2 )

53 In composite Higgs: 3 3,W/Z 3,Higgs ε 3 (MCHM) = ε 3,W/Z + a 2 ε 3,Higgs + g 2 v2 f 2 c(µ2 ) Loops of W/Z cancel in the S parameter: Ŝ = ε 3 (MCHM) ε 3 (SM) = v2 f 2 ε3,higgs + g 2 c(µ 2 )

54 Toy model spectral density ρ(s) = 1 192π 2 θ(s m2 ρ)+f 2 ρ δ(s m 2 ρ). s

55 Toy model spectral density ρ(s) = 1 192π 2 θ(s m2 ρ)+f 2 ρ δ(s m 2 ρ). Ŝ = g 2 v2 f 2 s 3 64π 2 [H A(h) H R (h)] π 2 (log m2 ρ m 2 Z 1) + F 2 ρ m 2 ρ

56 Toy model spectral density ρ(s) = 1 192π 2 θ(s m2 ρ)+f 2 ρ δ(s m 2 ρ). Ŝ = g 2 v2 f 2 s 3 64π 2 [H A(h) H R (h)] π 2 (log m2 ρ m 2 Z 1) + F 2 ρ m 2 ρ g 2 v2 f 2 1 log m ρ 11 96π 2 m h 12 + F ρ 2 m 2 ρ (m h m Z ).

57 Toy model spectral density ρ(s) = 1 192π 2 θ(s m2 ρ)+f 2 ρ δ(s m 2 ρ). Ŝ = g 2 v2 f 2 s 3 64π 2 [H A(h) H R (h)] π 2 (log m2 ρ m 2 Z 1) + F 2 ρ m 2 ρ g 2 v2 f 2 1 log m ρ 11 96π 2 m h 12 Barbieri,Bellazzini,S.R.,Varagnolo + F ρ 2 m 2 ρ (m h m Z ). same 11/12 as in Peskin-Takeuchi

58 Toy model spectral density ρ(s) = 1 192π 2 θ(s m2 ρ)+f 2 ρ δ(s m 2 ρ). Ŝ = g 2 v2 f 2 s 3 64π 2 [H A(h) H R (h)] π 2 (log m2 ρ m 2 Z 1) + F 2 ρ m 2 ρ g 2 v2 f 2 1 log m ρ 11 96π 2 m h 12 Barbieri,Bellazzini,S.R.,Varagnolo + F ρ 2 m 2 ρ (m h m Z ). same 11/12 as in Peskin-Takeuchi = g 2 v2 f π 2 log m ρ 125 GeV F ρ 2 m 2 ρ (m h = 125 GeV).

59 Toy model spectral density ρ(s) = 1 192π 2 θ(s m2 ρ)+f 2 ρ δ(s m 2 ρ). Ŝ = g 2 v2 f 2 s 3 64π 2 [H A(h) H R (h)] π 2 (log m2 ρ m 2 Z 1) + F 2 ρ m 2 ρ g 2 v2 f 2 1 log m ρ 11 96π 2 m h 12 Barbieri,Bellazzini,S.R.,Varagnolo + F ρ 2 m 2 ρ (m h m Z ). same 11/12 as in Peskin-Takeuchi = g 2 v2 f π 2 log m ρ 125 GeV F ρ 2 m 2 ρ (m h = 125 GeV).

60 Instead of conclusions, an open problem: can one do smth similar for the T parameter?

61 Instead of conclusions, an open problem: can one do smth similar for the T parameter?

62 Instead of conclusions, an open problem: can one do smth similar for the T parameter? due to suppressed Higgs couplings Barbieri,Bellazzini,S.R.,Varagnolo

63 Instead of conclusions, an open problem: can one do smth similar for the T parameter? due to suppressed Higgs couplings Barbieri,Bellazzini,S.R.,Varagnolo But which dispersion relation, if any, controls UV?

64