EFT analysis of the double Higgs production in gluon fusion - - PowerPoint PPT Presentation

EFT analysis of the double Higgs production in gluon fusion

Aleksandr Azatov

CERN

XSWG HH meeting 24-02-2015

AA, R.Contino, G.Panico, M.Son arXiv: 1502.00539

When can we use EFT analysis ?

If new physics states are heavier than the SM states as well as the typical mass scale of the process Λ > E. We can integrate these states out and parametrize their effects in terms of the higher dimensional operators. The effects of new physics will appear as a corrections in the E

Λ

• series.

SM NP EFT

Operators important for the Higgs pair production in gluon fusion

Assuming that the Higgs boson is neutral under U(1)em the most generic lagrangian parametrizing the Higgs pair production in gluon fusion is Ln.l. = −mt¯ tt

• ct h

v + c2t h2 v 2

• − c3

m2

h

2v h3 + g 2

s

4π2

• cg h

v + c2g h2 2v 2

• G 2

µν

where we have kept only the terms with up to two derivatives. Terms with the higher number of derivatives should appear as a corrections in E

Λ

• series.

Low et al; Goertz et al,1205.5444 ,1405.7040,1410.3471

Double Higgs production in gluon fusion

Ln.l. = −mt¯ tt

• ct h

v + c2t h2 v 2

• − c3

m2

h

2v h3 + g 2

s

4π2

• cg h

v + c2g h2 2v 2

• G 2

µν

g g h h t g g h h h g g h h g g h h t h g g h h t

ct, cg will be constrained also by the single Higgs measurements c2t, c2g, c3 can constrained only by the double Higgs measurements

Linear vs non-linear lagrangian

The constraints from EWPT from LEP and single Higgs measurements at LHC 7+8 TeV indicate strongly that the Higgs boson comes as a part of the electroweak doublet. Assuming the doublet structure and keeping only the dim 6

• perators the relevant lagrangian for the Higgs interactions becomes

∆Llin. =

¯ cu v 2 yt

• HH†¯

qLHctR + h.c.

• − ¯

c6 v 2 m2

h

2v 2

• H†H

3 + ¯ cg

g 2

s

m2

w H†HG 2

µν

Ln.l. = −mt¯ tt

• ct h

v + c2t h2 v 2

• − c3

m2

h

2v h3 + g 2

s

4π2

• cg h

v + c2g h2 2v 2

• G 2

µν

ct = 1 − ¯ cu, c2t = − 3

2 ¯

cu, cg = c2g = ¯ cg

• 4π

α2

• c3 = 1 − ¯

c6 The doublet structure of the Higgs interactions fixes the relations between tth(ggh) and tthh(gghh) interactions

EFT limitations

We must be in the regime when the effects of the dimension (> 6)

• perators are not important

Linear lagrangian shows what are the range of the Wilson coefficients Ly = yt¯ qLHctR

• 1 + ¯

cuH†H v 2 +

• n

cn,m ∂ v m H†H v 2 n we can estimate the size of cn ∼

• v 2g 2

∗

Λ2

n v

Λ

m Expansion is valid if only v 2g 2

∗

Λ2

≪ 1 where g∗ and Λ are the coupling constant and the mass scale of the new resonances.

Dimension-8 vs dimension-6 operators

O6 = ¯ cg

g 2

s

m2

w H†HG 2

µν,

O8 = ¯ cD0

g 2

s

m4

w G 2

µν|DσH|2

keeping only the largest terms growing with energy A ∼

α 4π

• y 2

t + g 2 6 (E) + g 2 8 (E) + ...

• g 2

6 (E) ∼ ¯

cg 4π

α2 E 2 v 2 ,

g 2

8 ∼ ¯

cD0 4π

α2 E 4 m2

W v 2

We can estimate this contributions to be g 2

6 (E) ∼ g 2

∗E 2

Λ2 ,

g 2

8 (E) ∼ g 2

∗E 4

Λ4

Dimension-8 vs dimension-6 operators

O6 = ¯ cg

g 2

s

m2

w H†HG 2

µν,

O8 = ¯ cD0

g 2

s

m4

w G 2

µν|DσH|2

keeping only the terms fastest growing with energy A ∼

α 4π

• y 2

t + g 2 6 (E) + g 2 8 (E) + ...

• g 2

6 (E) ∼ ¯

cg 4π

α2 E 2 v 2 ,

g 2

8 ∼ ¯

cD0 4π

α2 E 4 m2

W v 2

We can estimate this contributions to be g 2

6 (E) ∼ g 2

∗E 2

Λ2

• λ2

g 2

∗

• ,

g 2

8 (E) ∼ g 2

∗E 4

Λ4

In Composite PNGB higgs models dimension 6 operators have an additional suppression ⇒ thus there will be energy region where the contribution of the dim-8 will larger than dim 6, E Λ

• λ

g∗

• and

comparable to SM E Λ/√g∗ and at the same time within validity of EFT E < Λ

Choosing the better strategy in extracting the Higgs couplings

g g h h t

, A ∼ c2

t αs 4πy 2 t

g g h h h

, A3 ∼ cgc3 αs

4π m2

h

v 2

g g h h

, A4 ∼ c2g αs

4π ˆ s v 2

g g h h t h

, A△ ∼ ctc3

αs 4πy 2 t m2

h

ˆ s

• log m2

t

ˆ s + iπ

2

g g h h t

, A△nl ∼ ct2

αs 4πy 2 t

• log m2

t

ˆ s + iπ

2 Different contributions scale differently with the center of mass energy √s, exclusive measurements will have better sensitivities on the Higgs couplings

Angular distributions

A(g(pa)g(pb) → h(pc)h(pd)) = (Pµν

0 M0 + Pµν 2 M2) ǫµ(pa)ǫν(pb)

M0,2 are the contributions mediating JZ = 0,Jz = ±2 transitions In the SM we are dominated by the M0 contribution NP contributions coming from Dim-6

• perators contribute only to M0

Dim-8 operators can contribute to the M2 (ηµν∂ρh†∂ρh − 4 ∂µh∂νh

• G a

µαG a α ν

cdim−8 ∼ g 2

∗

Λ4

0.0001 0.001 0.01 0.1 0.5 0.9 500 1000 1500 2000 0.0 0.2 0.4 0.6 0.8 1.0

mhhGeV cosΘmin

Λ = 1.9TeV , g∗ = 3

Simulation details

Signal yield as a function of ci was simulated by the dedicated code, which was tested against hpair. We have decided to study only bbγγ final state due to cleaner signal and smaller background In order to take into account NLO and NNLO QCD corrections to the Higgs production we use the k-factor calculated in the infinite top mass limit k14 = 2.27 (1309.6594 ) We bin our events in center of mass energy √s And for every bin after application of the selection cuts we extract the Higgs pair production cross section as a polinomial in ci couplings. σ = σSM

• A1 c4

t + A2c2 2t + A3 c2 t c2 3 + A4 c2 gc2 3 + A5 c2 2g + A6 c2tc2 t

+A7 c3

t c3 + A8 c2tct c3 + A9 c2tcgc3 + A10 c2tc2g + A11 c2 t cgc3

+A12 c2

t c2g + A13 ctc2 3cg + A14 ctc3c2g + A15 cgc3c2g

Combining single and double Higgs measurements

The bounds from single and double Higgs measurements are correlated In order to estimate the strength of the combined constraints we have constructed the approximate ”likelihood” based on the ATLAS high luminosity studies of the Higgs interaction measurements

Simulation details, yields for 14 TeV LHC 3 ab−1

Most of the Higgses are produced at threshold. We use the traditional cut based analysis to differentiate the background from the signal.

Results

In order to understand the HL-LHC prospects on measuring the various Higgs couplings we wanted to combine the information from the double and single Higgs production measurements. In order to derive approximate the LHC sensibility on the Higgs couplings we have used the ATLAS projections for the HL-LHC.

1.0 0.5 0.0 0.5 1.0 10 5 5 10

c2 t c3

0.5 0.0 0.5 1.0 0.15 0.10 0.05 0.00 0.05 0.10

c2 t c2 g

Results: inclusive vs exclusive

Binnning in mhh improves the sensibility. However at 14 TeV we are dominated by the low energy bins, thus the improvement is not so big.

1.0 0.5 0.0 0.5 1.0 5 5 10

c2t c3 LHC s 14TeV L3ab1

Results: inclusive vs exclusive

Binnning in mhh improves the sensibility. However at 14 TeV we are dominated by the low energy bins, thus the improvement is not so big.

1.0 0.5 0.0 0.5 1.0 5 5 10

c2t c3 LHC s 14TeV L3ab1

1.0 0.5 0.0 0.5 1.0 4 2 2 4 6 8 10

c2 t c3 s 100TeV L3ab1

Results

5 5 10 0.00 0.05 0.10 0.15 0.20 0.25

c6

c3 = 1 − ¯ c6 68% credibility intervals are LHC HL-LHC FCC [−1.2, 6.1] [−1.0, 1.8] ∪ [3.5, 5.1] [−0.33, 0.29]

Interpreting LHC results

LHC HL-LHC [−1.2, 6.1] [−1.0, 1.8] ∪ [3.5, 5.1] LHC is sensitive to the order one deviations in the trilinear Higgs coupling In this regime the EFT is probably not valid, unless the BSM model has some strong dynamics coupled through the Higgs portal.

• 0.3

0.2 0.1 0.0 0.1 0.2 0.3 4 2 2 4 6 8

cu c6

Results

The single Higgs production in gluon fusion is proportional to −mtct h

v + g 2

s

4π2 cg h v ⇒

σ ∝ |ct + 12cg|2 σ ∝ |1 − ¯ cu + 12

• 4π

α2 ¯

cg

• |2

We have large degeneracy in the Higgs couplings in ¯ cu, ¯ cg space which is broken only by the tth and h → γγ measurements. The double Higgs production can break this degeneracy due to the different scaling of the cross section with ¯ cu, ¯ cg

• 0.4

0.2 0.0 0.2 0.4 0.10 0.05 0.00 0.05

cu cg 4ΠΑ2

LHC s 14TeV L3ab1

Summary

If there is a mass gap between the new physics and the SM states EFT presents a coherent framework for analysing the Higgs interactions. The double Higgs production in gluon fusion is sensitive to the HH†G 2

µν, ¯

ttH(H†H), (H†H)3 operators, which modify not only the trilinear coupling, but also the interactions between the Higgs boson and the top quark and gluons.

In order to extract the Wilson coefficients the combination with single Higgs production measurements is essential. Studying energy distributions is very important in constraining the EFT operators.

It looks like HL-LHC can determine the trilinear coupling with order

• ne uncertainty.

14 TeV selection cuts, double Higgs production

photon isolation: pT(γ) > 25GeV, |η(γ)| < 2.5, ǫγ = 0.8 2 b-taggged jets: pT(j) > 25 GeV |η(j)| < 2.5, ǫb = 0.7, ǫj→b = 0.01 ∆R(b, b) < 2, ∆R(γ, γ) < 2,∆R(b, γ) > 1.5 105 < mrec

bb < 145, 120 < mrec γγ < 130 GeV