Effective field theory for double Higgs production

Effective field theoryfor double Higgs production

Giuliano Panico

IFAE, Barcelona

‘Gearing up for LHC13’ workshop

GGI Firenze – 14 September 2015

Based on A. Azatov, R. Contino, G.P., M. Son, arXiv:1502.00539

Introduction

Why double Higgs production?

Obvious answer:

v measure the Higgs trilinear coupling!

h

h

h

c3

t

t

h

c2t

h

g

g

h

c2g

h

V

V

h

c2V

h

Less obvious answers:

v extract non-linear couplings not accessible in single-Higgsmeasurements (eg. hhtt, h2GµνG

µν and h2VµVµ)

v improve single-Higgs measurements (in particular tth)

v probe the strength of EWSB dynamics at scales E � mh

Interpretation strategy

Several new-physics effects can affect double Higgs production

• modifications of Higgs trilinear coupling

• modification of single Higgs couplings

• new non-linear interactions

v Corrections to all these couplings can arise simultaneously

v Assuming that only h3 is modified limits the validity of the fit

v Proper interpretation strategy needed

â identify a parametrization of NP effects

â perform a global analysis

Note: strategy similar to single Higgs measurements, where distortions

of all couplings are taken into account in the fits

The Effective Field Theory approach

v EFT is a perfect framework to analyze the new physics effects belowthe direct production thresholds of new states

v Useful to obtain a model-independent parametrization in terms of afew local operators

v Many new physics effects grow with energy

2→ 2 processesδAA∼

g2∗g2SM

E2

m2∗

m∗ scale of NP

g∗ coupling of new states

â extend the analysis to higher energies to increase the sensitivity

range of validity: mh � E � m∗

The effective Lagrangian for a Higgs doublet

Assumptions:

• Higgs is an SU(2)L doublet

• derivative expansion

• expansion in Higgs powers

L = LSM + ∆L6 + ∆L8 + · · · [Buchmuller and Wyler; . . .

Giudice at al.; Grzadkowski et al.]

∆L6 ⊃cH

2v2[∂µ(H†H)]2+

cu

v2yuH

†HqLHcuR−

c6

v2m2h

2v2(H†H)3+

cg

m2w

g2sH†HGµνGµν

cV ≃ 1 − cH

2

cg = c2g = cg

(4π

α2

)

c2V ≃ 1 − 2cH ct ≃ 1 − cH

2− cu

c3 ≃ 1 − 3

2cH + c6

c2t ≃ −1

2(cH + 3cu)

Only four independent dim.-6 operators

à correlations among vertices

eg. cH determines cV and c2V

The effective Lagrangian for a Higgs doublet

The effective vertices correspond to the interactions in the unitary gauge

L ⊃(m2WW

2µ +

m2Z

2Z2µ

)(1 + 2cV

h

v+ c2V

h2

v2

)−mttt

(1 + ct

h

v+ c2t

h2

2v2

)−c3

m2h

2vh3 +

g2s4π2

(cgh

v+ c2g

h2

2v2

)GaµνG

aµν

This parametrization is more general than the previous one

I valid for a generic Higgs (even not part of a doublet)

I resums the expansion in Higgs powers (if Higgs is a doublet)

Main production channels at hadron colliders

Gluon Fusion

g

g

h

h

t

Vector Boson Fusion

q

q

h

h

Double Higgs production via Gluon Fusion

results from Azatov, Contino, G.P., Son, arXiv:1502.00539

Double Higgs production via gluon fusion

g

g h

h

t

g

g h

h

th

g

g h

h

t

∼ c2t × const. ∼ ctc3 ×m2

h

slog

2

(m2

t

s

)∼ c2t × log

2

(m2

t

s

)

g

g h

h

h

g

g h

h

∼ cgc3αs

4π× const. ∼ c2g

αs

4π

s

v2

v Different behaviour at high energy√s = mhh � 2mh

v Dependence on Higgs trilinear suppressed at high energy

I Events at threshold more sensitive to Higgs trilinear, events at largemhh more important to determine the other operators

Sensitivity to the Higgs trilinear

Dependence on Higgs trilinear c3much smaller than on ct and c2t

[Dib, Rosenfeld, Zerwekh;

Grober and Muhlleitner]

c2 t=D

c3=1+D

ct=1+DLHC 14 TeV

SM

-1.0 -0.5 0.0 0.5 1.0

0.10.2

0.51.02.0

5.010.020.0

D

ΣHp

p®hh

L�ΣHp

p®hh

L SM [Contino, Ghezzi, Moretti,

GP, Piccinini, Wulzer]

â Using the mhh distribution (shape analysis) is essential todisentangle the different new physics effects and maximize sensitivity

The angular distribution

The signal is also characterized by the anglebetween the Higgs pair and the beam axisin the c.o.m. frame

h

h

g gθ

The scattering is mainly due to two partial waves Jz = 0 and Jz = ±2

dσ

d cos θ∼ const. (Jz = 0)

dσ

d cos θ∼ sin2 θ (Jz = ±2)

I In the SM the Jz = ±2 amplitude comes only from the box diagramand is extremely suppressed

0 0.2 0.4 0.6 0.8 1

1

cosθ

(dσ/

dcosθ)

/σ

10-1

10

10

-2

-3

10-4

√s = 400GeV

0 0.2 0.4 0.6 0.8 1

1

cosθ

(dσ/

dcosθ)

/σ

10-1

10-2

√s = 700GeV

I The BSM diagrams (from dim.-6 operators) only generatecontributions with Jz = 0

â the angular analysis is not useful to disentangle NP effects

[possible exception: effects from dim.-8 operators (only at 100 TeV)]

The total cross section

Small total production cross section

â at LO for the SM

σ(pp→ hh)SM = 16.2 fb (14 TeV)

= 874 fb (100 TeV)

â beyond LO computed mainly in the mt →∞ approximation

NNLO k-factors: k14 TeV = 2.27

k100 TeV = 1.75

[De Florian and Mazzitelli]

σ(pp→ hh+X)SM = 36.8 fb (14 TeV)

= 1.53 pb (100 TeV)

I The mt →∞ limit severely distorts the mhh distribution.Conservative estimate of error ∼ 10%, can limit ultimate precision.

(complete mt dependence at NLO known only for real emission)

Final states

Final statesstudies so farin the literature:

• hh→ bbγγ: cleanest channel but small cross sectionBaur, Plehn, Rainwater PRD 69 (2004) 053004

Baglio et al. JHEP 1304 (2013) 151

Yao arXiv:1308.6302

Barger et al. PLB 728 (2014) 433

ATLAS, ATL-PHYS-PUB-2014-019

Barr et al. arXiv:1412.7154

• hh→ bbττ : sizable cross section, promising in theboosted regimeBaur, Plehn, Rainwater PRD 68 (2003) 033001

Dolan, Englert, Spannowsky JHEP 1210 (2012) 112


Barr, Dolan, Englert, Spannowsky PLB 728 (2014) 308

Goertz, Papaefstathiou, Yang, Zurita arXiv:1410.3471

• hh→ bbWW : large tt background, maybe observablein the boosted regimeDolan, Englert, Spannowsky JHEP 1210 (2012) 112


Papaefstathiou, Yang, Zurita PRD 87 (2013) 011301

• hh→ bbbb: very difficult, maybe observables in theboosted regimede Lima, Papaefstathiou, Spannowsky arXiv:1404.7139

The bbγγ channel

• Analysis at the 14 TeV LHC

Highlights of the analysis

Simulations: Parton level + Showering + Hadronization

• Signal at LO rescaled by NNLO k-factor

• Background with MadGraph5

Backgrounds included: bbγγ , jjγγ (non resonant)

bbh , Zh , tth (resonant)

bbγγ has a large NLO k-factor: k ∼ 2

Mainly due to real emissionsSelection tags: 2 b-tagged jets + 2 photons

efficiencies: εb = 0.7 , εj→b = 0.01 , εγ = 0.8

Highlights of the analysis

Simulations: Parton level + Showering + Hadronization

• Signal at LO rescaled by NNLO k-factor

• Background with MadGraph5

Backgrounds included: bbγγ , jjγγ (non resonant)

bbh , Zh , tth (resonant)

bbγγ has a large NLO k-factor: k ∼ 2

Mainly due to real emissions

Selection tags: 2 b-tagged jets + 2 photons

efficiencies: εb = 0.7 , εj→b = 0.01 , εγ = 0.8

Kinematic selection for the 14 TeV LHC

objects reconstruction: pT (j, γ) > 25 GeV, |η(j, γ)| < 2.5

veto isolated leptons: pT (l) > 20 GeV, |η(l)| < 2.5

first selection: pT>(b, γ) > 50 GeV

pT<(b, γ) > 30 GeV

angular cuts: ∆R(b, b) < 2, ∆R(γ, γ) < 2, ∆R(b, γ) > 1.5

0

20

40

60

80

100

120

R(b,b)0 0.5 1 1.5 2 2.5 3 3.5 4

) R

(b,

0

0.5

1

1.5

2

2.5

3

3.5

4

Signal (SM), 14 TeV

0

100

200

300

400

500

600

700

800

900

R(b,b)0 0.5 1 1.5 2 2.5 3 3.5 4

) R

(b,

0

0.5

1

1.5

2

2.5

3

3.5

4, 14 TeVb b

0

100

200

300

400

500

600

R(b,b)0 0.5 1 1.5 2 2.5 3 3.5 4

) R

(b,

0

0.5

1

1.5

2

2.5

3

3.5

4h, 14 TeVtt

Higgs reconstruction: 105 GeV < mrecobb < 145 GeV

120 GeV < mrecoγγ < 130 GeV

Backgrounds and shape analysis

Events in SM signal and backgrounds with L = 3 ab−1

hh bbγγ γγjj tth bbh Zh

After first selection 28.5 6919 684 130 7.2 24.5

After angular cuts 17.8 1274 104 29 1.2 15.8

After Higgs reco. 12.8 24.2 2.21 9.9 0.40 0.41

â dominant background: irreducible bbγγ

Simple shape analysis by binning the mhh distribution (in 6 categories)

mrecohh [GeV] 250−400 400−550 550−700 700−850 850−1000 1000−

hh 2.14 6.34 2.86 0.99 0.33 0.17

γγbb 7.69 10.1 3.35 1.38 1.18 0.59

γγjj 0.66 0.95 0.31 0.16 0.08 0.045

tth 3.33 4.53 1.41 0.41 0.16 0.043

bbh 0.20 0.16 0.03 0.0054 0.0022 0.00054

Zh 0.13 0.19 0.067 0.021 0.009 0.0009

Jet and W veto

Only marginal improvement from veto on extra hadronic activity

• Jet veto: N(jets) < 4 removes 80% of tth, keeps 70% of signal

• W veto: N(Whad) = 0 removes 50% of tth, keeps 90% of signal

N(jets) < 4 tth

N(Whad) = 0

Jet multiplicity2 3 4 5 6 7 8 9 10

Nor

mal

ized

rate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

14 TeV14 TeV

Hadronic W0 0.5 1 1.5 2 2.5 3

Nor

mal

ized

rate

0

0.2

0.4

0.6

0.8

1

14 TeV14 TeV

18

Only modest improvement of signal significance from veto on extra hadronic activity

Examples: removes 80% of keeping 70% of signal

tthremoves 50% of keeping 90% of signal

solid = signaldotted =dot-dashed =

bb��tth

solid = signaldotted =dot-dashed =

bb��tth

The bbγγ channel

• Prospects at a future 100 TeV hadronic collider

Kinematic selection at FCC100

The angular distributions at 100 TeV are similar to the ones at LHC14

I adopt the same angular cuts and Higgs reconstruction windows

∆R(b, b) < 2, ∆R(γ, γ) < 2, ∆R(b, γ) > 1.5

105 GeV < mrecobb < 145 GeV

120 GeV < mrecoγγ < 130 GeV

I slightly tighter pT cuts

pT>(b, γ) > 60 GeV , pT<(b, γ) > 40 GeV

Main features at 100 TeV: Backgrounds

Three main differences between 14 TeV and 100 TeV:

1. Change in the background composition

Number of eventswith L = 3 ab−1

hh bbγγ tth γγjj bbh Zh

14 TeV 12.8 24.2 9.9 2.21 0.40 0.41

100 TeV 303 137 303 18.2 6.2 3.2

• main background at LHC14: bbγγ

• main background at FCC100: tth

â Jet-veto or W-veto useful to reduce the tth background at FCC100

Jet multiplicity2 3 4 5 6 7 8 9 10

Nor

mal

ized

rate

0

0.1

0.2

0.3

0.4

0.5

0.6

100 TeV100 TeV

bbγγ

signal

tth

Hadronic W0 0.5 1 1.5 2 2.5 3

Nor

mal

ized

rate

0

0.2

0.4

0.6

0.8

1

100 TeV100 TeV

bbγγ

signal

tth

Main features at 100 TeV: Kinematics of the signal

2. Larger boost of the hh system à higher fraction of decay productsoutside the detector region

Fraction of Higgs decay products with :

(hh)z!2 4 6 8 10 12 14 16 18 20

Nor

mal

ized

rate

-610

-510

-410

-310

-210

-110

|max�b,

�|0 1 2 3 4 5 6

Nor

mal

ized

rate

0

0.05

0.1

0.15

0.2

0.25

Signal (SM) (14 TeV vs 100 TeV)Signal (SM) (14 TeV vs 100 TeV)

�(hh)

|�| > 2.5 13% 30%

9

Kinematics of the signal

Two main differences occur when going from 14TeV to 100TeV:

Larger boost of the (hh) system1. Higher fraction of Higgs decay products goes outside detector region

boost of hh system |⌘max� |max pseudorapidity of Higgs daughters

h ! ��

100TeV

14TeV

100TeV

14TeV

at LHC at 100TeVI Fraction of events with |η| > 2.5: 13% at LHC à 30% at 100 TeV

I Need to extend to |η| ≤ 3.3 to keep same fraction of events


3. Larger invariant mass of the hh system

Reach in mhh and pT : Boosted events

[GeV]min)hhm(

0 500 1000 1500 2000 2500 3000 3500 4000

) [fb

]hh

m/d

� (d×

hh d

m�

-210

-110

1

10

210

310

Signal (SM)Signal (SM)

dsigmadmhh.pdfdsigmadpTh.pdf

100 TeV

14 TeV

[GeV]min

(h))T

(p0 500 1000 1500 2000

(h) [

fb]

T/d

p�

d×

(h)

T d

p�

-210

-110

1

10

210

310


100 TeV

14 TeV

The highest accessible mhh and pT can be estimated by requiringat least 5 events beyond the threshold(we use L = 3 ab�1 and assume 10% e�ciency)

channel bbWW⇤ (24.9%) bb⌧+⌧� (7.35%) bb�� (0.264%)

Cross section > 0.067 fb > 0.227 fb > 6.31 fb

mhh [GeV] < 1280 (4170) < 1039 (3235) < 558 (1552)

pT [GeV] < 575 (2000) < 550 (1890) < 210 (664)

[numbers in parenthesis are for the 100 TeV collider]


[GeV]min)hhm(

0 500 1000 1500 2000 2500 3000 3500 4000

) [fb

]hh

m/d

� (d×

hh d

m�

-210

-110

1

10

210

310



100 TeV

14 TeV

[GeV]min

(h))T

(p0 500 1000 1500 2000

(h) [

fb]

T/d

p�

d×

(h)

T d

p�

-210

-110

1

10

210

310


100 TeV

14 TeV




mhh [GeV] < 1280 (4170) < 1039 (3235) < 558 (1552)

pT [GeV] < 575 (2000) < 550 (1890) < 210 (664)


Highest accessible mhh and pT estimated by requiring at least 5 eventsbeyond the threshold

channel bbbb (33.3%) bbWW∗ (24.9%) bbτ+τ− (7.35%) bbγγ (0.264%)

Cross section > 0.05 fb > 0.067 fb > 0.227 fb > 6.31 fb

mhh [GeV] < 1340(4290) < 1280 (4170) < 1039 (3235) < 558 (1552)

pT [GeV] < 575(2000) < 575 (2000) < 550 (1890) < 210 (664)

[We use L = 3/ab and assume 10% efficiency. Numbers in parenthesis for a 100 TeV collider]

Jet substructure techniques crucial at 100 TeV

∆R ∼ 2mhpT (h)

. 0.5 for pT (h) & 500 GeV


3. Larger invariant mass of the hh system


[GeV]min)hhm(

0 500 1000 1500 2000 2500 3000 3500 4000

) [fb

]hh

m/d

� (d×

hh d

m�

-210

-110

1

10

210

310



100 TeV

14 TeV

[GeV]min

(h))T

(p0 500 1000 1500 2000

(h) [

fb]

T/d

p�

d×

(h)

T d

p�

-210

-110

1

10

210

310


100 TeV

14 TeV




mhh [GeV] < 1280 (4170) < 1039 (3235) < 558 (1552)

pT [GeV] < 575 (2000) < 550 (1890) < 210 (664)



[GeV]min)hhm(

0 500 1000 1500 2000 2500 3000 3500 4000

) [fb

]hh

m/d

� (d×

hh d

m�

-210

-110

1

10

210

310



100 TeV

14 TeV

[GeV]min

(h))T

(p0 500 1000 1500 2000

(h) [

fb]

T/d

p�

d×

(h)

T d

p�

-210

-110

1

10

210

310


100 TeV

14 TeV




mhh [GeV] < 1280 (4170) < 1039 (3235) < 558 (1552)

pT [GeV] < 575 (2000) < 550 (1890) < 210 (664)


Boosted Higgses

Highest accessible mhh and pT estimated by requiring at least 5 eventsbeyond the threshold

channel bbbb (33.3%) bbWW∗ (24.9%) bbτ+τ− (7.35%) bbγγ (0.264%)

Cross section > 0.05 fb > 0.067 fb > 0.227 fb > 6.31 fb

mhh [GeV] < 1340(4290) < 1280 (4170) < 1039 (3235) < 558 (1552)

pT [GeV] < 575(2000) < 575 (2000) < 550 (1890) < 210 (664)

[We use L = 3/ab and assume 10% efficiency. Numbers in parenthesis for a 100 TeV collider]

Jet substructure techniques crucial at 100 TeV

∆R ∼ 2mhpT (h)

. 0.5 for pT (h) & 500 GeV

The bbγγ channel

• Sensitivity on the EFT coefficients

Sensitivity on the EFT coefficients

We consider three benchmark scenarios

LHC14 HL-LHC FCC100√s 14 TeV 14 TeV 100 TeV

Luminosity L = 300 fb−1 L = 3 ab−1 L = 3 ab−1

• Bayesian analysis for parameters of interest, marginalizing or fixingthe others

• Flat prior for unconstrained EFT coefficients

• Gaussian constraints from single-Higgs data(we use ATLAS projections [ATL-PHYS-PUB-2013-014])

• No theoretical uncertainties or systematic error included

Sensitivity on the EFT coefficients

Precision on single-Higgs observables from ATLAS projection[ATL-PHYS-PUB-2013-014]

300 fb−1 3 ab−1

σ(cH) 7.9% 5.4%

σ(cu) 5.9% (w/tth) 5.4% (w/tth)

20% (tth) 7.7% (tth)

σ(cd) 6.3% 4.4%

µ/µ!0 0.2 0.4

(comb.)

(incl.)

(comb.)

(comb.)

(VBF-like)

(comb.)

ATLAS Simulation Preliminary = 14 TeV:s -1Ldt=300 fb" ; -1Ldt=3000 fb"

µµ#H

$$#H

ZZ#H

WW#H

% Z#H

%%#H

µµ#H

$$#H

ZZ#H

WW#H

% Z#H

%%#H

1.5#

µ/µ!0 0.2 0.4

(+0j)(+1j)

(VBF-like)(ttH-like)(VH-like)(comb.)

(incl.)(+0j)(+1j)

(VBF-like)(comb.)

(ggF-like)(VBF-like)

(ttH-like)(VH-like)(comb.)

(VBF-like)(ttH-like)

(incl.)(comb.)

ATLAS Simulation Preliminary = 14 TeV:s -1Ldt=300 fb" ; -1Ldt=3000 fb"

µµ#H

$$#HZZ#H

WW#H

%Z#H%%#H

µµ#H

$$#HZZ#H

WW#H

%Z#H%%#H

0.7#

1.5#

0.8#

Figure 21: Relative uncertainty on the total signal strength µ for all Higgs final states in the di⇥erentexperimental categories used in the combination, assuming a SM Higgs Boson with a mass of 125 GeVand LHC at 14 TeV, 300 fb�1 and 3000 fb�1. The hashed areas indicate the increase of the estimated errordue to current theory systematic uncertainties. The abbreviation “(comb.)” indicates that the precision onµ is obtained from the combination of the measurements from the di⇥erent experimental sub-categoriesfor the same final state, while “(incl.)” indicates that the measurement from the inclusive analysis wasused. The left side shows only the combined signal strength in the considered final states, while the rightside also shows the signal strength in the main experimental sub-categories within each final state.

• The signals observed in the di⇥erent search channels originate from a single resonance. A mass of125 GeV is assumed here.

• The width of the Higgs boson is narrow, justifying the use of the zero-width approximation (thiscan be verified using a measurement as discussed in Section 5). Hence the predicted rate for agiven channel can be decomposed in the following way:

� · B (i⇥ H ⇥ f ) =�i · � f

�H(1)

where �i is the production cross section through the initial state i, B and � f are the branching ratioand partial decay width into the final state f , respectively, and �H the total width of the Higgs

31

�µ/µ 300 fb�1

All unc. No theory unc.H ⇥ µµ (comb.) 0.39 0.38

(incl.) 0.47 0.45(ttH-like) 0.73 0.72

H ⇥ ⇥⇥ (VBF-like) 0.22 0.16H ⇥ ZZ (comb.) 0.12 0.06

(VH-like) 0.32 0.31(ttH-like) 0.46 0.44

(VBF-like) 0.34 0.31(ggF-like) 0.13 0.06

H ⇥ WW (comb.) 0.13 0.08(VBF-like) 0.21 0.20

(+1j) 0.36 0.17(+0j) 0.20 0.08

H ⇥ Z� (incl.) 1.47 1.45H ⇥ �� (comb.) 0.14 0.09

(VH-like) 0.77 0.77(ttH-like) 0.55 0.54

(VBF-like) 0.47 0.43(+1j) 0.37 0.14(+0j) 0.22 0.12

3000 fb�1

All unc. No theory unc.0.15 0.120.19 0.150.26 0.230.19 0.120.10 0.040.13 0.120.20 0.160.21 0.160.12 0.040.09 0.050.12 0.090.33 0.100.19 0.050.57 0.540.10 0.040.26 0.250.21 0.170.21 0.150.37 0.050.20 0.05

Table 17: Relative uncertainty on the signal strength µ for the combination of Higgs analysis at 14 TeV,300 fb�1 (left) and 3000 fb�1 (right), assuming a SM Higgs Boson with a mass of 125 GeV. For both300 and 3000 fb�1 the first column shows the results including current theory systematic uncertainties,while the second column shows the uncertainties obtained using only the statistical and experimentalsystematic uncertainties. The abbreviation “(comb.)” indicates that the precision on µ is obtained fromthe combination of the measurements from the di⇥erent experimental sub-categories for the same finalstate, while “(incl.)” indicates that the measurement from the inclusive analysis was used.

30

20

ATLAS projections at high luminosity (ATL-PHYS-PUB-2013-014)

Precision on c3, c2t and c2g

The non-linear Higgs couplings c3, c2t, c2g can only be directly accessedin double Higgs production

-1.0 -0.5 0.0 0.5 1.0-10

-5

0

5

10

c2 t

c3

LHC

HL-LHC

FCC

14

100

-0.5 0.0 0.5 1.0-0.15

-0.10

-0.05

0.00

0.05

0.10

c2 t

c2 g

LHC

HL-LHC

FCC100

14

• Higgs trilinear c3 can only be extracted at FCC (at LHC only O(1)determination)

• good precision on c2t and c2g

Exclusive vs inclusive analysis

v Modest improvement from exclusive analysis at the LHC(small number of signal events hinders shape analysis)

-1.0 -0.5 0.0 0.5 1.0

-5

0

5

10

c2t

c3

LHC s =14TeV L=3ab-1

inclusive

exclusive (all cat.)

¯

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-10

-5

0

5

10

15

c2t

c3


cat. 3,4

cat. 1,2

cat. 5,6

category 1 2 3 4 5 6

mhh [GeV] 250−400 400−550 550−700 700−850 850−1000 1000−

Exclusive vs inclusive analysis

v Exclusive analysis is crucial at FCC100!

-1.0 -0.5 0.0 0.5 1.0

-4

-2

0

2

4

6

8

10

c2 t

c3

s =100TeV L=3ab-1

exclusive

inclusive

¯

-0.4 -0.2 0.0 0.2 0.4

-2

0

2

4

c2 t

c3

s =100TeV L=3ab-1

cat. 5,6

cat. 3,4

cat. 1,2

category 1 2 3 4 5 6

mhh [GeV] 250−400 400−550 550−700 700−850 850−1000 1000−

Improvement from jet substructure

Jet substructure key to extract but not crucial to determine and

�0.10 �0.05 0.00 0.05 0.10

�0.025

�0.020

�0.015

�0.010

�0.005

0.000

0.005

0.010

c2 t

c2 g

s ⇥100TeV L⇥3ab�1

category mrecohh [TeV]

Traditional Boosted

1 0.25 � 0.40 1.0 � 1.2

2 0.40 � 0.55 1.2 � 1.4

3 0.55 � 0.70 1.4 � 1.6

4 0.70 � 0.85 1.6 � 1.8

5 0.85 � 1.00 1.8 �

c3

c2g

14

• Improvement from jet substructure

�0.10 �0.05 0.00 0.05 0.100.0

0.5

1.0

1.5

2.0

c2 t

c3


with jet substructure

traditional


traditional

c2t

Jet substructure key to extract but not crucial to determine and

�0.10 �0.05 0.00 0.05 0.10

�0.025

�0.020

�0.015

�0.010

�0.005

0.000

0.005

0.010

c2 t

c2 g


category mrecohh [TeV]

Traditional Boosted

1 0.25 � 0.40 1.0 � 1.2

2 0.40 � 0.55 1.2 � 1.4

3 0.55 � 0.70 1.4 � 1.6

4 0.70 � 0.85 1.6 � 1.8

5 0.85 � 1.00 1.8 �

c3

c2g

14

• Improvement from jet substructure

�0.10 �0.05 0.00 0.05 0.100.0

0.5

1.0

1.5

2.0

c2 t

c3



traditional


traditional

c2t

Jet substructure techniques efficiently improve the sensitivity to boostedevents at FCC100

• important to extract c2g (effects in the tail of the distribution)

• not crucial to determine c3 and c2t (effects close to threshold)

Constraining the dim.-6 operators: cu and cg

¯

-0.5 0.0 0.5-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

cu

c gâH4pêa 2L


double Higgs

single Higgs(excl. tth)

only tth

¯

-0.4 -0.2 0.0 0.2 0.4

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

cu

c gâH4pêa 2L

s =100TeV L=3ab-1

â double Higgs can resolve the degeneracy in cg

â at FCC100 it can be competitive with tth for the determination ofthe top Yukawa cu (if precision from single Higgs similar to the LHC one)

Orange region: single Higgs incl. tth

Blue region: single + double Higgs

Constraining the dim.-6 operators: cu and c6

¯

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

-4

-2

0

2

4

6

8

cu

c6

LHC

HL-LHC

FCC

14

100

-5 0 5 100.00

0.05

0.10

0.15

0.20

0.25

c6

100

14LHC

HL-LHC

FCC

68% probability intervals on c6

LHC14 HL-LHC FCC100

[−1.2, 6.1] [−1.0, 1.8] ∪ [3.5, 5.1] [−0.33, 0.29]

The statistical treatment

Marginalization over has significant impact on the precision on

Example: uncertainty on from

Precision on at FCC100 :

0.02 0.05 0.10 0.20

⇥0.4

⇥0.2

0.0

0.2

0.4

⌅ �cu⇥

68�probabilityintervalon

c 6

s ⇤100TeV L⇤3ab⇥1

cH , cu, cd, cg

c6[�0.33, 0.29] [�0.18, 0.18]

cu for �(cu)=0.05

16

• Impact of the statistical treatment (marginalization)

�1.0 �0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

2.0

2.5

c6


without marginalization

with marginalization

Prob

abilit

y de

nsity



c6

Notice: for a Higgs doublet the uncertainty on the top Yukawa coupling (ttH) reflects on an uncertainty on ttHH

c6

c62 [�0.31, 0.27]

Marginalization has a significantimpact on the precision on c6

withmarginalization

withoutmarginalization

precisionat FCC100

[−0.33, 0.29] [−0.18, 0.18]

e.g. uncertainty on cuincreases uncertainty on c6

Marginalization over has significant impact on the precision on

Example: uncertainty on from

Precision on at FCC100 :

0.02 0.05 0.10 0.20

⇥0.4

⇥0.2

0.0

0.2

0.4

⌅ �cu⇥

68�probabilityintervalon

c 6

s ⇤100TeV L⇤3ab⇥1

cH , cu, cd, cg

c6[�0.33, 0.29] [�0.18, 0.18]

cu for �(cu)=0.05

16

• Impact of the statistical treatment (marginalization)

�1.0 �0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

2.0

2.5

c6




Prob

abilit

y de

nsity



c6

Notice: for a Higgs doublet the uncertainty on the top Yukawa coupling (ttH) reflects on an uncertainty on ttHH

c6

c62 [�0.31, 0.27]

Projections by the experimental collaborations

Figure 1 – Stacked histograms for the Higgs pair production signal and all of the background processes showthe expected distributions for the diphoton mass (left) and the dijet mass (right) for 3000 fb�1 of integratedluminosity.

Figure 2 – The expected uncertainty on the Higgs pair production cross section measurement is shown as afunction of the integrated luminosity (left) and the hypothetical improvement to the photon selection e�ciency(right).

[CMS CR -2015/044]

[GeV]bb

m

50 100 150 200 250

Eve

nts

/10 G

eV

0

2

4

6

8

10

12

14

16

18

20

22ATLAS Simulation Preliminary

-1=14 TeV, 3000 fbs

)γγ)H(bH(b

Othersγγbb

Xtt)γγH(tt

)γγ)H(bZ(b)γγH(bb

(a) mbb

[GeV]γγm

50 100 150 200 250

Eve

nts

/2.5

GeV

0

5

10

15

20

25 ATLAS Simulation Preliminary-1=14 TeV, 3000 fbs

)γγ)H(bH(b

Othersγγbb

Xtt)γγH(tt

)γγ)H(bZ(b)γγH(bb

(b) mγγ

Figure 7: The distributions of mbb (a) and mγγ (b) for 3000 fb−1 after applying all the selection criteria

except the mbb (a) and mγγ (b) mass cuts. The individual shapes of the contributions are obtained

using the events surviving the event selection before the mass criteria and angular cuts are applied,

but normalized to the number of expected events after the full event selection. The ttX contribution

includes tt(≥ 1 lepton) and ttγ, while ‘Others’ includes ccγγ, bbγ j, bb j j and j jγγ.

SMλ / λ

-2 0 2 4 6 8 10Pro

ject

ed

lim

it o

n t

he

to

tal H

H y

ield

(e

ven

ts)

0

5

10

15

20

25

30

35

40

Exp. 95% CLsσ1 ±σ2 ±

-1 = 14 TeV: 3000 fbs

ATLAS Simulation Preliminary

Figure 8: 95% CLs limit (dashed line) on the size of an additional HH contribution summed with the

expected Standard Model HH yield, as well as the ±1/2σ uncertainty bands, overlaid on the number

of predicted total (box + self-coupling) HH events as a function of the λ/λS M ratio after application of

the analysis cuts (solid line).

12

λ [-1.3,8.7] at 95% CL⊂

[ATL-PHYS-PUB-2014-019]

⊂λ [-1.3, 8.7] at 95% CL

The projections from the experimental collaborations confirm that theHiggs trilinear coupling can only be measured at O(1) at the LHC

Double Higgs via Vector Boson Fusion

results from Contino, Rojo, work in progress (courtesy of R. Contino)

Double Higgs production via vector boson fusion

+ ∼s

v2(c2V − c2V ) ∼

m2h

v2c3cV

I Sensitivity on c3 mainly from events at threshold

I Events with large mhh more important to extract c2V

Study of double Higgs in VBFat 100 TeV requires a detector

in the very forward region

∼ 67% of signal events has |η(j)max| > 4.5

⇠ s

v2

�c2V � c2V

�⇠ m2

h

v2c3cV

c3

c2Vmhh

22

Double Higgs production via Vector Boson Fusion

+

• Sensitivity on mainly from events at threshold. Events with large crucial to extract

0 2 4 6 80

0.01

0.02

0.03

0.04

0.05

0.06

|η(j)max|

100TeV

40TeV

14TeV

parton level

Study of double Higgs via VBF at 100TeV requires a dedicated

detector in the very forward region

Results from: R.C. and J. Rojo, work in progress(see also: Bondu et al. proceeding of Les Houches 2013)

Higgs couplings from the hh→ 4b channel

�15 �10 �5 0 5 10 150.00

0.02

0.04

0.06

0.08

0.10

c3�1�0.6 �0.4 �0.2 0.0 0.2 0.4 0.60

1

2

3

4

c2 V�1

68% probability intervals on :

m(hh) [GeV]

14 TeV 250 � 500 500 � 750 750 � 1000 1000 � 1500 > 1500

hh!4b [SM] 6.6 4.1 1.6 0.68 0.18

4b2j 9.8⇥103 557 203 101 15

m(hh) [GeV]

100 TeV 250 � 1000 1000 � 2500 2500 � 3500 3500 � 5000 > 5000

hh!4b [SM] 413 144 10 2.1 1.1

4b2j 5.9⇥105 3.4⇥104 6.2⇥103 2.3⇥103 2.3⇥103

c3 =1cV =1

c2V =1

�c2V ⌘ c2V �1 LHC14 HL-LHC FCC100

[�0.18, 0.22] [�0.08, 0.12] [�0.01, 0.03]

23

Number of events with 3ab-1 after cuts

Prob

abilit

y de

nsity

Prob

abilit

y de

nsity

FCC100

HL-LHC

LHC14

FCC100

HL-LHC

LHC14

cV =1

(uncertainties included: 50% systematic on background, 10% on )BR(hh ! 4b)

PRELIMINARY

�15 �10 �5 0 5 10 150.00

0.02

0.04

0.06

0.08

0.10

c3�1�0.6 �0.4 �0.2 0.0 0.2 0.4 0.60

1

2

3

4

c2 V�1

68% probability intervals on :

m(hh) [GeV]

14 TeV 250 � 500 500 � 750 750 � 1000 1000 � 1500 > 1500

hh!4b [SM] 6.6 4.1 1.6 0.68 0.18

4b2j 9.8⇥103 557 203 101 15

m(hh) [GeV]

100 TeV 250 � 1000 1000 � 2500 2500 � 3500 3500 � 5000 > 5000

hh!4b [SM] 413 144 10 2.1 1.1

4b2j 5.9⇥105 3.4⇥104 6.2⇥103 2.3⇥103 2.3⇥103

c3 =1cV =1

c2V =1

�c2V ⌘ c2V �1 LHC14 HL-LHC FCC100

[�0.18, 0.22] [�0.08, 0.12] [�0.01, 0.03]

23

Number of events with 3ab-1 after cuts

Prob

abilit

y de

nsity

Prob

abilit

y de

nsity

FCC100

HL-LHC

LHC14

FCC100

HL-LHC

LHC14

cV =1

(uncertainties included: 50% systematic on background, 10% on )BR(hh ! 4b)

PRELIMINARY

Huge background, sensitive only if deviations much larger than the SM

• Poor precision on Higgs trilinear (not competitive with gluon fusion)

• FCC100 can provide good bounds on ∆c2V ≡ c2V − 1

68% probability intervalson ∆c2V

LHC14 HL-LHC FCC100

[−0.18, 0.22] [−0.08, 0.12] [−0.01, 0.03]

Conclusions

Conclusions

v Double Higgs production is an essential channel to extract informationon the Higgs non-linear couplings

• Measure te Higgs trilinear coupling c3

• Access new couplings to top and vector bosons: c2t, c2g, c2V .

• Global analysis needed to get a model-independent fit

v Main processes at hadronic colliders:

I. Gluon Fusion (in particular gg → hh→ bbγγ)

• Higgs trilinear coupling c3

δλ ∼ O(1) @ HL− LHC δλ ∼ 30% @ FCC

• coupling to tops c2t and gluons c2g

• at FCC100 possible relevance to measure top Yukawa

II. Vector Boson Fusion

• coupling to EW bosons c2V

Backup material

Leptonic machines: Main production channels

25

Measurement of Higgs couplings and self-coupling at the ILC Junping TIAN

Z

H

ZH

He+

e�Z

H

ZH

e+

e�Z

H

ZH

e+

e�Z

H

ZH

e+

e�+ + +

Background diagramsSignal diagram

(a)

+ + +


(b)

H

HH

�

��e+

e�

H

H�

��e+

e�

H

H�

��e+

e�

H

H�

e+

e�

��

Center of Mass Energy / GeV400 600 800 1000 1200 1400

Cro

ss S

ect

ion

/ f

b

0

0.1

0.2

0.3

0.4

0.5

0.6 ZHH→ - + e+e

HH (WW-fusion)νν → - + e+eHH (Combined)νν → - + e+e

) = (-0.8,+0.3)+,e-

M(H) = 125 GeV P(e

Figure 7: Diagrams of the double Higgs production processes, e+e� ⇥ ZHH (left a) and e+e� ⇥⇤⇤HH (left b), and their cross sections as function of

⌅s (right).

SMλ/λ0 0.5 1 1.5 2

SM

σ/σ

0.5

1

1.5

2w/o weight

w/ weight (Optimal)

Zhh @ 500 GeV→-+e+e

= 120 GeVhm

SMλ/λ0 0.5 1 1.5 2

SM

σ/σ

1

2

3

4

w/o weight

w/ weight (Optimal)

hh @ 1 TeVνν→-+e+e

= 120 GeVhm

Figure 8: Cross sections of e+e� ⇥ ZHH (left) and e+e� ⇥ ⇤⇤HH (right) as a function of Higgs self-coupling.

calculable factor corresponding to the search mode. In addition, the recoil mass measurementsprovide absolute cross section measurements of the e+e� ⇥ ZH, process, which can be predictedas Y ⇤

j = Fj · g2HZZ . To combine all of these measurements to exact the 9 couplings, HZZ, HWW ,

Hbb, Hcc, Hgg, H⌅⌅ , Hµµ , Htt, and H⇥⇥ , and the Higgs total width, GH , a method of modelindependent global fit is applied by constructing a �2 which is defined as following:

�2 =i=N

Âi=1

(Yi �Y ⇤

i

DYi)2,

where Yi is the measured value, DYi is the error on Yi, N is the total number of measurements and Y ⇤i

is the predicted value which can always be parameterized by couplings and Higgs total width. Nextstep is to minimize this �2 and get the fitted values of the 10 parameters and their errors. Here weassume all the 9 couplings and the Higgs total width are free parameters without any correlation.The result of our global fit is given in Table 1, at different energies and for both baseline andluminosity upgraded scenarios. The systematic errors and theoretical errors are not consideredhere, which however will be well controlled to below sub-percent level at the ILC.

8. Summary and Acknowlegement

The physics case at the ILC has a solid base complementary to the LHC, and provides a com-

7

Double Higgs-strahlung (DHS) vs VBF

from arXiv:1311.6528

Double Higgs-strahlung (DHS)

dominant below 1 TeV

e+

e−

e+

e−

Z

h

h

+

++c2V c3

Vector Boson Fusion (VBF)

dominant above 1 TeV

c2V c3

Leptonic machines: Main production channels

25

Measurement of Higgs couplings and self-coupling at the ILC Junping TIAN

Z

H

ZH

He+

e�Z

H

ZH

e+

e�Z

H

ZH

e+

e�Z

H

ZH

e+

e�+ + +


(a)

+ + +


(b)

H

HH

�

��e+

e�

H

H�

��e+

e�

H

H�

��e+

e�

H

H�

e+

e�

��

Center of Mass Energy / GeV400 600 800 1000 1200 1400

Cro

ss S

ect

ion / fb

0

0.1

0.2

0.3

0.4

0.5

0.6 ZHH→ - + e+e

HH (WW-fusion)νν → - + e+eHH (Combined)νν → - + e+e

) = (-0.8,+0.3)+,e-

M(H) = 125 GeV P(e

Figure 7: Diagrams of the double Higgs production processes, e+e� ⇥ ZHH (left a) and e+e� ⇥⇤⇤HH (left b), and their cross sections as function of

⌅s (right).

SMλ/λ0 0.5 1 1.5 2

SM

σ/σ

0.5

1

1.5

2w/o weight

w/ weight (Optimal)

Zhh @ 500 GeV→-+e+e

= 120 GeVhm

SMλ/λ0 0.5 1 1.5 2

SM

σ/σ

1

2

3

4

w/o weight

w/ weight (Optimal)

hh @ 1 TeVνν→-+e+e

= 120 GeVhm

Figure 8: Cross sections of e+e� ⇥ ZHH (left) and e+e� ⇥ ⇤⇤HH (right) as a function of Higgs self-coupling.

calculable factor corresponding to the search mode. In addition, the recoil mass measurementsprovide absolute cross section measurements of the e+e� ⇥ ZH, process, which can be predictedas Y ⇤

j = Fj · g2HZZ . To combine all of these measurements to exact the 9 couplings, HZZ, HWW ,

Hbb, Hcc, Hgg, H⌅⌅ , Hµµ , Htt, and H⇥⇥ , and the Higgs total width, GH , a method of modelindependent global fit is applied by constructing a �2 which is defined as following:

�2 =i=N

Âi=1

(Yi �Y ⇤

i

DYi)2,

where Yi is the measured value, DYi is the error on Yi, N is the total number of measurements and Y ⇤i

is the predicted value which can always be parameterized by couplings and Higgs total width. Nextstep is to minimize this �2 and get the fitted values of the 10 parameters and their errors. Here weassume all the 9 couplings and the Higgs total width are free parameters without any correlation.The result of our global fit is given in Table 1, at different energies and for both baseline andluminosity upgraded scenarios. The systematic errors and theoretical errors are not consideredhere, which however will be well controlled to below sub-percent level at the ILC.

8. Summary and Acknowlegement

The physics case at the ILC has a solid base complementary to the LHC, and provides a com-

7

Double Higgs-strahlung (DHS) vs VBF

from arXiv:1311.6528

Double Higgs-strahlung (DHS)

dominant below 1 TeV

e+

e−

e+

e−

Z

h

h

+

++c2V c3

Vector Boson Fusion (VBF)

dominant above 1 TeV

c2V c3

Leptonic machines: Expected precision on c3 and c2V

COM Energy Precision Process Reference

ILC

500 GeV[L = 500 fb−1]

∆c3 ∼ 104% DHS ILC TDR, Volume 2, arXiv:1306.6352

1 TeV[L = 1 ab−1]

∆c3 ∼ 28% VBF ILC TDR, Volume 2, arXiv:1306.6352

∆c2V ∼ 20% DHS Contino et al., JHEP 1402 (2014) 006

CLIC

1.4 TeV[L = 1.5 ab−1]

∆c3 ∼ 24%

VBF Roloff (CLICdp Coll.), talk at LCWS14

∆c2V ∼ 7%

3 TeV[L = 2 ab−1]

∆c3 ∼ 12%

∆c2V ∼ 3%

Precision on Higgs trilinear

slightly better than FCC100

(effects at threshold)

Precision on c2V worse

than FCC100

(effects grow with energy)

Effective field theory for double Higgs production

Documents

Transcript of Effective field theory for double Higgs production