Beyond Higgs Couplings

Transcription

1 Probing the Higgs with Angular Observables at Future e + e Colliders Miniworkshop on MC for e + e colliders Oct 19, 2015 based on current work with Nathaniel Craig, Zhen Liu and Kechen Wang

2 Introduction Angular observables Higgs effective field theory Expected precision Constraints on new physics Conclusion

3 Introduction The precision Higgs data can provide strong constraint on new physics. So far most studies are based on rate measurements. Angular distribution of the events can provide additional information. Theoretical calculations have been done in e.g (Beneke, Boito, Wang) using Higgs effective field theory. No existing phenomenology study yet.

4 Introduction Angular observables Higgs effective field theory Expected precision Constraints on new physics Conclusion Angular observables in HZ production h θ2 e e + φ Z l + l θ1 z Three angles in each event. It is convenient to define asymmetry observables in the form A = N + N N + + N. Focusing on leptonic decay of Z (good resolution, small background).

5 Angular observables in HZ production A θ1 = 1 σ A (1) ϕ = 1 σ A (2) ϕ = 1 σ A (3) ϕ = 1 σ A (4) ϕ = 1 σ A cθ1,cθ 2 = 1 σ 1 1 2π 0 2π 0 2π 0 2π d cos θ 1 sgn(cos(2θ 1 )) dϕ sgn(sin ϕ) dσ dϕ, dϕ sgn(sin(2ϕ)) dσ dϕ, dϕ sgn(cos ϕ) dσ dϕ, dϕ sgn(cos(2ϕ)) dσ dϕ, d cos θ 1 sgn(cos θ 1 ) 1 1 dσ d cos θ 1, d 2 σ d cos θ 2 sgn(cos θ 2 ). d cos θ 1 d cos θ 2

6 Higgs effective field theory O Φ = (Φ Φ) (Φ Φ) O ΦW = (Φ Φ)W I µνw Iµν O ΦD = (Φ D µ Φ) (Φ D µ Φ) O ΦB = (Φ Φ)B µν B µν O (1) Φ l = (Φ i D µφ)( lγ µ l) O ΦWB = (Φ τ I Φ)W I µνb µν O (3) Φ l = (Φ i DµΦ)( lγ I µ τ I l) O Φ W = (Φ Φ) W I µνw Iµν O Φe = (Φ i D µφ)(ēγ µ e) O Φ B = (Φ Φ) B µνb µν O 4L = ( lγ µl)( lγ µ l) O Φ WB = (Φ τ I Φ) W I µνb µν Table: A complete basis of dimension-6 operators contributing to e + e Zh. Here the τ I are the Pauli matrices. Starting with dimension-6 operators, we can derive the Higgs effective Lagrangian L eff c (1) ZZ hz µz µ + c (2) ZZ h Z µνz µν + c Z Zh Z µν Zµν + c AZ h Z µν A µν + c A ZhZ µν Ã µν + hz µ lγ µ (c V + c A γ 5 ) l + Z µ lγ µ (g V g A γ 5 )l g em Q l A µ lγ µ l.

7 Angular observables in terms of Wilson coefficients Using the Higgs effective Lagrangian we can derive the cross section and angular observables as functions of the Wilson coefficients. Keeping the linear order terms of the Wilson coefficients (ˆα k = v2 α Λ 2 k, s = 240 GeV). σ[fb] ˆα Φ 5.3 ˆα ΦD + 69 ˆα ΦW + 17 ˆα ΦB + 27 ˆα ΦWB ˆα (1) Φ l + 79 ˆα(3) Φ l 115 ˆα Φ e + 26 ˆα 4L, A θ ˆα ΦW ˆα ΦB ˆα ΦWB, A (1) ϕ 0.17 ˆα Φ W 0.14 ˆα Φ B ˆα ΦW B, A (2) ϕ 0.46 ˆα Φ W ˆα Φ B ˆα ΦW B, A (3) ϕ ˆα ΦD ˆα ΦW 0.51 ˆα ΦB 1.33 ˆα ΦWB ˆα (1) Φ l ˆα(3) Φ l ˆαΦ e ˆα 4L, A (4) ϕ ˆα ΦW ˆα ΦB ˆα ΦWB, A cθ1,cθ ˆα ΦD 0.33 ˆα ΦW ˆα ΦB ˆα ΦWB 0.65 ˆα (1) Φ l 0.18 ˆα(3) Φ l 0.74 ˆα Φ e 0.24 ˆα 4L.

8 σ A θ1 A cθ1,cθ 2 α Φ α ΦD α ΦW α ΦB α ΦWB α ΦW α ΦB α ΦW B α (3) α Φe α 4L +3.4 α Φ α ΦD α ΦW α ΦB α ΦWB α ΦW α ΦB α ΦW B α (3) α Φe α 4L α Φ α ΦD α ΦW α ΦB α ΦWB α ΦW α ΦB α ΦW B α (3) α Φe α 4L A ϕ (1) σ α=0 σ α i A ϕ (2) A θ1 α i α=0 A ϕ (3) A cθ1,cθ 2 α=0 α i A ϕ (4) α Φ α ΦD α ΦW α ΦB α ΦWB α ΦW α ΦB α ΦW B α Φ α ΦD α ΦW α ΦB α ΦWB α ΦW α ΦB α ΦW B α Φ α ΦD α ΦW α ΦB α ΦWB α ΦW α ΦB α ΦW B α Φ α ΦD α ΦW α ΦB α ΦWB α ΦW α ΦB α ΦW B α (3) α (3) α (3) 32 α (3) α Φe α Φe α Φe α Φe α 4L α 4L α 4L 42 α 4L A ϕ (1) α i α=0 A ϕ (2) α i α=0 A ϕ (3) α i α=0 A ϕ (4) α i α=0

9 Expected precision and statistical uncertainty A N + N N + +N = 2N + 1, where N+ has a binomial distribution with N standard deviation σ N+ = N p(1 p), where p is the probability for a event to be counted into N +. 1σ uncertainty of A σ A = 1 Ā2 1. (1) N N With s = 240 GeV and 5 ab 1 data, for the channel e e + ZH l + l b b, there are events after cuts. observable SM expectation σ A for 5 ab 1 A θ A (1) ϕ A (2) ϕ A (3) ϕ A (4) ϕ A cθ1,cθ

10 Detector effects For SM, we used the events generated with Whizard by our experimental colleagues. (Thanks!) For new physics, we used Madgraph5 with dimenion-6 operator model file generated via FeynRules. For simulation, we focus on the process e e + ZH µ µ + b b. Resolution, ISR effects (turned out to be small). 10 < θ µ < 170, 81 GeV < m µ µ + < 101 GeV, 120 GeV < m recoil < 150 GeV, b-tagging.

11 Detector effects Aϕ (4) x x c ϕb (TeV -2 ) The effects are much smaller than the statistical uncertainties except for A (4) ϕ ( with the cut10 < θ µ < 170 ). It shifts the central value but has little effects on the sensitivities to new physics (need to be further verified). We have justified that statistical uncertainties dominate in our study.

12 Constraining Wilson Coefficients ZZ solid line: 68%CL dotted line: 95%CL total σ A ZZ solid line: 68%CL dotted line: 95%CL total σ A s = 240 GeV, 5 ab 1, e e + ZH l + l b b, events. ZZ α ZZ α AZ solid line: 68%CL dotted line: 95%CL total σ A ZZ α V δg V total σ A solid line: 68%CL dotted line: 95%CL More parameters than constraints... ˆα (1) ZZ vs. another coefficient, assuming all others are zero. Useful for probing HZγ anomalous coupling.

13 FCC-ee 68%CL 68%CL CEPC FCC-ee FCC-ee FS CEPC FCC-ee FCC-ee FS ZZ ZZ α V α AZ FCC-ee: 3 CEPC luminosity at each IP, twice IPs (4 vs. 2). In principle one could use the full statistics (including other decay channels of Z and H), which requires further study. Plots made by simply scaling the statistics of CEPC by 6 (for FCC-ee) and 60 (for FCC-ee FS).

14 A (bad) example on model implication... M 2 (GeV) CEPC σ σ+a solid line: 68%CL dotted line: 95%CL Not so useful for probing Stop! Loop suppressed. The Wilson coefficients can be more sensitive to non-perturbative models M 1 (GeV)

15 Conclusion The angular observables in the HZ production at CEPC contain useful information about possible new physics and should be measured and studied. There are a wide range of interesting future directions. Hadronic channel of Z, other decay channels of Higgs... ILC can study this process at higher s and also with polarized beams. Asymmetry observables distributions. We should try to extract as much information as we could from future colliders.