higgs boson physics

Higgs Boson Physics

Ambresh Shivaji

IISER Mohali, Punjab, INDIA

Madgraph School 2019IMSc Chennai, November 18-22, 2019

The only fundamental scalar particle known to us

Neutral under SU(3)c⇑

Q = 0⇐ Higgs Boson (H) ⇒ JCP = 0+

⇓

mH = 125.10 ± 0.14 GeVΓH < 0.013 GeV (95% CL)

Its discovery at the LHC (pp collider,√

s = 7 + 8 TeV) was announcedin 2012 by the ATLAS and CMS collaborations.

Standard Model and Electroweak Symmetry Breaking

In the Standard Model (SM), the electroweak (EW) interactions are described bySU(2)L × U(1)Y gauge symmetry group.

Existance of massive gauge bosons of EW interactions =⇒ EW symmetry is broken.

The EWSB is realized with the help of a complex scalar SU(2)L doublet Φ =(φ+

φ0

).

LHiggs = |DµΦ|2 −∑fyf L̄fΦRf − V(Φ)

V(Φ) = −µ2(Φ†Φ) + λ(Φ†Φ)2

〈Φ〉 =1√

2

(0v

)⇒ mW ,mZ ,mf (v ∼ 246 GeV)

Φ =1√

2

(0

v + H

)⇒ Higgs mass and Higgs couplings

Couplings of the Higgs Boson

LHiggs = |DµΦ|2 −∑fyf L̄fΦRf − V(Φ)

V (Z,W )

H

f

κV κF κλ

Couplings are proportional to the masses. Notice the mass dependence.

I Higgs couplings with gaugebosons (κV) and with heavyfermions (κF) are know withan accuracy of 10-20%.

I Higgs-self couplings arepractically unconstrained.More about them later...

Single Higgs Production

State-of-the-art calculations and MC tools

Single Higgs Production: ggFDominant production channel, it’s a loop-induced process. Indirectly sensitive totop-Yukawa coupling.

Mµν = B00 gµν + B11 pνqµ (1)

Gauge invariance (Mµνpµ =Mµνqν = 0) and on-shell conditions⇒ B11 = −B00/p.q, where p.q = m2

H/2.

B00 =Mµν 1

2

(gµν −

pνqµ

p.q

)(2)

At LO, B00 ≡ m2q[(16m2

q − 8p.q)C0 + 8], where,

C0 =

∫d4`

1

(`2 −m2q)((` + p)2 −m2

q)((` − q)2 −m2q)

(3)

Single Higgs Production: ggF

The LO result depends on mq and mH .

In mq →∞ limit, the amplitude becomes independent of the quark mass in the loop.Note that the amplitude does not vanish⇒ violation of Decoupling theorem.

Mµν →αs3πv(p.q gµν − pνqµ) (4)

We get and effective ggH vertex.

This feature can be utilized to probe the existence of heavy up or down type quarksbeyond SM.


The effective ggH vertex can be obtained from an effective Lagrangian (HEFT),

Leff = −14(1 −

αs3π

Hv)GµνGµν (5)

Exercise: Derive the Feynman Rules.

The effective Lagrangian is useful in calculating higher order corrections to gg → H.For example, at NLO

Single Higgs Production: ggFExact vs HEFT

Scale dependence and pT (H) distribution

More on NLO in Huasheng Shao’s Talk...


The most updated result for 13 TeV LHC, mH = 125 GeV and µF = µR = mH/2:

σggH = 48.58 pb+4.56%−6.72%

(Theory)

Single Higgs Production: VBF

Characteristic features:two hard jets in the forward and backward regions of the detector.no gluon radiation from central-rapidity region

These features allow to distinguish themfrom gg → H + 2j andqq′ → VH → H + 2j

Sensitive to VVH couplings. Results known at NNLO (QCD) and NLO(EW).

Single Higgs Production: VH

Drell-Yan like production, sensitive to VVH couplings.

Channel through which H → bb̄ isdetected in the boosted regime.

Results known at NNLO (QCD) (including NLO correction to loop-inducedgg → ZH) and NLO(EW).

Single Higgs Production: ttHDirectly sensitive to the top-Yukawa coupling. Has been observed recently.

NLO QCD corrections increase the cross section by 20%. NLO EW are also known.

Single Higgs ProductionPDG2017

Signal strength for production, µi =σExp.(i → H)σSM(i → H)

. Assuming SM Higgs BRs,

Higgs Boson Decay

Computation of decay width is required to interpret the experimentaldata.

mH = 125 GeV

Higgs Boson Decay to Fermions

H → bb̄ is the dominant decay mode among all, followed byH → τ+τ− and H → cc̄ .Known up to N4LO (QCD) and NLO (EW).

Higgs Boson Decay to Gauge Bosons

For mH = 125 GeV, one of the two vector bosons is always off-shell.

Invisible decay mode: H → ZZ ∗ → 4ν.

WW ∗ and ZZ ∗ interfere in 2`2ν final state.


H → 4` (2e2µ) (4e) (4µ) is very clean, allows reconstruction of theHiggs mass.

Has been the discovery mode.

Higgs Boson Decay to Gauge BosonsH → ZZ ∗ → 4` decay mode can be utilized to fix the spin and CP-properties of theHiggs boson.

CP-even (red) vs CP-odd (blue)


Loop-induced decay to di-photon.

Dominated by W-loop contribution.Destructive intereference between t-loop and W-loop contributions.No decoupling for large loop masses.


Another Higgs discovery mode.

H → Zγ is also loop-induced decay but it’s very rare.

Higgs Boson Decay

Signal strength for decay, µf =BRExp.

H→f

BRSMH→f

. Assuming SM production

rates,

Higgs Boson Mass

ATLAS and CMS collaborations rely on the two high mass resolutionand sensitive channels, H → γγ and H → ZZ ∗ → 4`.

Higgs Boson WidthΓSMH = 4.07 MeV+4.0%

−3.9%for mH = 125 GeV

Sensitivity to Higgs decay width via intereference effect. For example, theinterference effect between the signal: gg → h→ γγ and background: gg → γγ

1704.08259

Double Higgs ProductionCan provide information on Higgs-self coupling parameter (λ).

Double Higgs Production

10-1

100

101

102

-4 -3 -2 -1 0 1 2 3 4

σ(N

)LO

[fb]

λ/λSM

pp→HH (EFT loop-improved)pp→HHjj (VBF)

pp→ttHH

pp→WHH

pp→ZHH pp→tjHH

HH production at 14 TeV LHC at (N)LO in QCDMH=125 GeV, MSTW2008 (N)LO pdf (68%cl)

MadGraph5_aMC@NLO

Figure 3: Total cross sections at the LO and NLO in QCD for HH production channels, at the√s =14 TeV LHC as a function of the

self-interaction coupling λ. The dashed (solid) lines and light- (dark-)colour bands correspond to the LO (NLO) results and to the scale andPDF uncertainties added linearly. The SM values of the cross sections are obtained at λ/λSM = 1.

Grant Agreement numbers PITN-GA-2010-264564 (LHCPhe-noNet) and PITN-GA-2012-315877 (MCNet). The work ofFM and OM is supported by the IISN “MadGraph” con-vention 4.4511.10, by the IISN “Fundamental interactions”convention 4.4517.08, and in part by the Belgian FederalScience Policy Office through the Interuniversity Attrac-tion Pole P7/37. OM is "Chercheur scientifique logistiquepostdoctoral F.R.S.-FNRS".

References

[1] F. Englert and R. Brout, Phys.Rev.Lett. 13, 321 (1964).[2] P. W. Higgs, Phys.Rev.Lett. 13, 508 (1964).[3] CMS-HIG-13-003. CMS-HIG-13-004. CMS-HIG-13-006. CMS-

HIG-13-009. (2013).[4] ATLAS-CONF-2013-009. ATLAS-CONF-2013-010. ATLAS-

CONF-2013-012. ATLAS- CONF-2013-013. (2013).[5] E. Asakawa, D. Harada, S. Kanemura, Y. Okada, and

K. Tsumura, Phys.Rev. D82, 115002 (2010), arXiv:1009.4670[hep-ph] .

[6] S. Dawson, E. Furlan, and I. Lewis, Phys.Rev. D87, 014007(2013), arXiv:1210.6663 [hep-ph] .

[7] R. Contino, M. Ghezzi, M. Moretti, G. Panico, F. Piccinini,et al., JHEP 1208, 154 (2012), arXiv:1205.5444 [hep-ph] .

[8] G. D. Kribs and A. Martin, Phys.Rev. D86, 095023 (2012),arXiv:1207.4496 [hep-ph] .

[9] M. J. Dolan, C. Englert, and M. Spannowsky, Phys.Rev. D87,055002 (2013), arXiv:1210.8166 [hep-ph] .

[10] M. J. Dolan, C. Englert, and M. Spannowsky, JHEP 1210, 112(2012), arXiv:1206.5001 [hep-ph] .

[11] M. Gouzevitch, A. Oliveira, J. Rojo, R. Rosenfeld, G. P. Salam,et al., JHEP 1307, 148 (2013), arXiv:1303.6636 [hep-ph] .

[12] T. Plehn, M. Spira, and P. Zerwas, Nucl.Phys. B479, 46 (1996),arXiv:hep-ph/9603205 [hep-ph] .

[13] S. Dawson, S. Dittmaier, and M. Spira, Phys.Rev. D58, 115012(1998), arXiv:hep-ph/9805244 [hep-ph] .

[14] T. Binoth, S. Karg, N. Kauer, and R. Ruckl, Phys.Rev. D74,113008 (2006), arXiv:hep-ph/0608057 [hep-ph] .

[15] J. Baglio, A. Djouadi, R. Gröber, M. Mühlleitner, J. Quevillon,et al., JHEP 1304, 151 (2013), arXiv:1212.5581 [hep-ph] .

[16] R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer,H.-S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, to appear .

[17] The code can be downloaded at:https://launchpad.net/madgraph5,http://amcatnlo.cern.ch.

[18] U. Baur, T. Plehn, and D. L. Rainwater, Phys.Rev.Lett. 89,151801 (2002), arXiv:hep-ph/0206024 [hep-ph] .

[19] V. Hirschi et al., JHEP 05, 044 (2011), arXiv:1103.0621 [hep-ph].

[20] A. Denner, S. Dittmaier, M. Roth, and D. Wackeroth,Nucl.Phys. B560, 33 (1999), arXiv:hep-ph/9904472 [hep-ph] .

[21] A. Denner, S. Dittmaier, M. Roth, and L. Wieders, Nucl.Phys.B724, 247 (2005), arXiv:hep-ph/0505042 [hep-ph] .

[22] Q. Li, Q.-S. Yan, and X. Zhao, (2013), arXiv:1312.3830 [hep--ph] .

[23] P. Maierhöfer and A. Papaefstathiou, (2013), arXiv:1401.0007[hep-ph] .

[24] J. Grigo, J. Hoff, K. Melnikov, and M. Steinhauser, Nucl.Phys.B875, 1 (2013), arXiv:1305.7340 [hep-ph] .

[25] D. de Florian and J. Mazzitelli, Phys. Rev. Lett. 111, 201801(2013), 10.1103/PhysRevLett.111.201801, arXiv:1309.6594[hep-ph] .

[26] D. Y. Shao, C. S. Li, H. T. Li, and J. Wang, JHEP07, 169(2013), arXiv:1301.1245 [hep-ph] .

6

Dominant production mode is via gluon fusion.

The two diagrams interefere destructively.

Double Higgs Production

[1608.04798]

Summary

Being the only fundamental scalar, Higgs has every special place inthe particle spectrum of the SM.

We now know its mass (∼ 125 GeV) and its couplings with heavyfermions and gauge bosons are determined with an accuracy of10-20%.

It has a very narrow width (∼ 4 MeV).

The information on Higgs self-couplings is not available.

Higgs self-couplings

VSM(Φ) = −µ2(Φ†Φ) + λ(Φ†Φ)2

EWSB⇒ V(H) =12m2HH

2 + λ3vH3 +14λ4H4.

λ3 λ4

H

H

H

The mass and the self-couplings of the Higgs boson depend only on λ andv = (

√2Gµ)−1/2,

m2H = 2λv2; λSM3 = λSM4 = λ.

mH = 125 GeV and v ∼ 246 GeV,⇒ λ ' 0.13 .

Presence of new physics at higher energy scales can contribute to the Higgs potentialand modify the Higgs self-couplings.

Independent measurements of λ3 and λ4 are crucial.

Direct determination of Higgs self-couplings

Information on λ3 and λ4 can be extracted by studying multi-Higgs productionprocesses.

H

H

H

H

H

λ3 λ4

t

10-1

100

101

102

-4 -3 -2 -1 0 1 2 3 4

σ(N

)LO

[fb]

λ/λSM

pp→HH (EFT loop-improved)pp→HHjj (VBF)

pp→ttHH

pp→WHH

pp→ZHH pp→tjHH

HH production at 14 TeV LHC at (N)LO in QCDMH=125 GeV, MSTW2008 (N)LO pdf (68%cl)

MadGraph5_aMC@NLO

Figure 3: Total cross sections at the LO and NLO in QCD for HH production channels, at the√s =14 TeV LHC as a function of the

self-interaction coupling λ. The dashed (solid) lines and light- (dark-)colour bands correspond to the LO (NLO) results and to the scale andPDF uncertainties added linearly. The SM values of the cross sections are obtained at λ/λSM = 1.

Grant Agreement numbers PITN-GA-2010-264564 (LHCPhe-noNet) and PITN-GA-2012-315877 (MCNet). The work ofFM and OM is supported by the IISN “MadGraph” con-vention 4.4511.10, by the IISN “Fundamental interactions”convention 4.4517.08, and in part by the Belgian FederalScience Policy Office through the Interuniversity Attrac-tion Pole P7/37. OM is "Chercheur scientifique logistiquepostdoctoral F.R.S.-FNRS".

References

[1] F. Englert and R. Brout, Phys.Rev.Lett. 13, 321 (1964).[2] P. W. Higgs, Phys.Rev.Lett. 13, 508 (1964).[3] CMS-HIG-13-003. CMS-HIG-13-004. CMS-HIG-13-006. CMS-

HIG-13-009. (2013).[4] ATLAS-CONF-2013-009. ATLAS-CONF-2013-010. ATLAS-

CONF-2013-012. ATLAS- CONF-2013-013. (2013).[5] E. Asakawa, D. Harada, S. Kanemura, Y. Okada, and

K. Tsumura, Phys.Rev. D82, 115002 (2010), arXiv:1009.4670[hep-ph] .

[6] S. Dawson, E. Furlan, and I. Lewis, Phys.Rev. D87, 014007(2013), arXiv:1210.6663 [hep-ph] .

[7] R. Contino, M. Ghezzi, M. Moretti, G. Panico, F. Piccinini,et al., JHEP 1208, 154 (2012), arXiv:1205.5444 [hep-ph] .

[8] G. D. Kribs and A. Martin, Phys.Rev. D86, 095023 (2012),arXiv:1207.4496 [hep-ph] .

[9] M. J. Dolan, C. Englert, and M. Spannowsky, Phys.Rev. D87,055002 (2013), arXiv:1210.8166 [hep-ph] .

[10] M. J. Dolan, C. Englert, and M. Spannowsky, JHEP 1210, 112(2012), arXiv:1206.5001 [hep-ph] .

[11] M. Gouzevitch, A. Oliveira, J. Rojo, R. Rosenfeld, G. P. Salam,et al., JHEP 1307, 148 (2013), arXiv:1303.6636 [hep-ph] .

[12] T. Plehn, M. Spira, and P. Zerwas, Nucl.Phys. B479, 46 (1996),arXiv:hep-ph/9603205 [hep-ph] .

[13] S. Dawson, S. Dittmaier, and M. Spira, Phys.Rev. D58, 115012(1998), arXiv:hep-ph/9805244 [hep-ph] .

[14] T. Binoth, S. Karg, N. Kauer, and R. Ruckl, Phys.Rev. D74,113008 (2006), arXiv:hep-ph/0608057 [hep-ph] .

[15] J. Baglio, A. Djouadi, R. Gröber, M. Mühlleitner, J. Quevillon,et al., JHEP 1304, 151 (2013), arXiv:1212.5581 [hep-ph] .

[16] R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer,H.-S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, to appear .

[17] The code can be downloaded at:https://launchpad.net/madgraph5,http://amcatnlo.cern.ch.

[18] U. Baur, T. Plehn, and D. L. Rainwater, Phys.Rev.Lett. 89,151801 (2002), arXiv:hep-ph/0206024 [hep-ph] .

[19] V. Hirschi et al., JHEP 05, 044 (2011), arXiv:1103.0621 [hep-ph].

[20] A. Denner, S. Dittmaier, M. Roth, and D. Wackeroth,Nucl.Phys. B560, 33 (1999), arXiv:hep-ph/9904472 [hep-ph] .

[21] A. Denner, S. Dittmaier, M. Roth, and L. Wieders, Nucl.Phys.B724, 247 (2005), arXiv:hep-ph/0505042 [hep-ph] .

[22] Q. Li, Q.-S. Yan, and X. Zhao, (2013), arXiv:1312.3830 [hep--ph] .

[23] P. Maierhöfer and A. Papaefstathiou, (2013), arXiv:1401.0007[hep-ph] .

[24] J. Grigo, J. Hoff, K. Melnikov, and M. Steinhauser, Nucl.Phys.B875, 1 (2013), arXiv:1305.7340 [hep-ph] .

[25] D. de Florian and J. Mazzitelli, Phys. Rev. Lett. 111, 201801(2013), 10.1103/PhysRevLett.111.201801, arXiv:1309.6594[hep-ph] .

[26] D. Y. Shao, C. S. Li, H. T. Li, and J. Wang, JHEP07, 169(2013), arXiv:1301.1245 [hep-ph] .

6

100755033251413

100

10−1

pp→HH

HLO

FT

pp→HH

HNL

OFT

approx

Mad

Graph5aM

C@NLO

MH=125 GeV, MSTW2008 (N)LO pdf (68%cl)

HHH production at pp colliders

. .

-

√s[TeV]

σ(N

)LO[fb]

[Frederix et al. ‘14, 1408.6542]Very challenging due to small cross sections: ∼33 fb (HH), ∼ 0.1 fb (HHH)Compare it with the single Higgs production (gg → H) cross section: ∼ 50 pb

Current and future experimental sensitivity (κλ = λ3/λSM3 )

ATLAS (HL-LHC, 2b2γ): [ATL-PHYS-PUB-2017-001],

κλ < −0.8 and κλ >∼ 7.7

Bounds are sensitive to κt value.

Indirect determination of λ3 in single Higgs

g

g

tH

HH

H

W

γ

γ

Gorbahn, Haisch: 1607.03773; Degrassi, Giardino, Maltoni, Pagani: 1607.04251;Bizon, Gorbahn, Haisch, Zanderighi: 1610.05771; Di Vita, Grojean, Panico,Riembau, Vantalon: 1704.01953; Maltoni, Pagani, AS, Zhao: 1709.08649

Master formula: Anomalous trilinear coupling (κ3 = λ3/λSM3 )

ΣBSMNLO = ZBSM

H [ΣLO(1 + κ3C1 + δZH ) + ∆SMNLO]

ZBSMH =

11 − (κ2

3 − 1)δZH, δZH = −1.536 × 10−3

Current and future reach at the LHC

0

1

2

3

4

5

−4.7 −1.3 1 2.9 7.9 12.6

1σ

2σ

χ2min/d.o.f. = 1.3

∆χ2

κ3

13TeV data

0

2

4

6

8

10

−9 −7 −5 −3 −1 1 3 5 7 9 11 13 15

1σ

2σ

S2

−2∆

lnL

κ3

ggFVBF

tt̄H,tottt̄H,difVH,totVH,dif

Plot by Xiaoran 1709.08649

13 TeV:−4.7 < κ3 < 12.6

HL-LHC:

−2 . κ3 . 8

CMS Projections: HL-LHCtH + ttH: using the calculation of Maltoni, Pagani, AS, Zhao:1709.08649

λκ10− 5− 0 5 10 15 20

ln L

∆-2

0

1

2

3

4

5

6Simulation Preliminary CMS Phase-2 TeV) (14-13 ab

= 1tκ

68% CL

95% CL

w/ YR18 syst. uncert.

Stat. uncert. only

Hadronic categories only

Leptonic categories only

λκ10− 5− 0 5 10 15

Hµ

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

ln L

∆-2

2

4

6

8

10

12

14

Simulation Preliminary CMS Phase-2 TeV) (14-13 ab

SM

68% CL

95% CL

[CMS-PAS-FTR-18-020]

−3 . κλ . 13

Question: Can we extend this strategy to double Higgs production ?Maltoni, Pagani, Zhao: 1802.07616; Bizon, Haisch, Rottoli: 1810.04665; Borowka,Duhr, Maltoni, Pagani, AS, Zhao: 1811.12366

Indirect determination of λ4 in double Higgs

At LO, the gg → HH amplitude is sensitive to only λ3.

λ4 affects gg → HH amplitude at two-loop level via NLO EW corrections.

EFT framework is necessary in order to vary cubic and quartic couplingsindependently in a consistent way.

V NP(Φ) ≡

∞∑n=3

c2n

Λ2n−4

(Φ†Φ −

12v2

)n

.

This also ensures gauge invariance and UV finiteness in our calculation.

NP Paramterization

V (H) =12m2

HH2 + λ3vH3 +14λ4H4 + λ5

H5

v+O(H6) ,

κ3 ≡λ3

λSM3

= 1 +c6v2

λΛ2 ≡ 1 + c̄6,

κ4 ≡λ4

λSM4

= 1 +6c6v2

λΛ2 +4c8v4

λΛ4 ≡ 1 + 6c̄6 + c̄8 .

We can trade κ3 and κ4 with parameters c̄6 and c̄8.

c̄6 ≡c6v2

λΛ2 = κ3 − 1 ,

c̄8 ≡4c8v4

λΛ4 = κ4 − 1 − 6(κ3 − 1) .

The Phenomenological quantity of interestInclusive/differential cross section

σphenoNLO = σLO + ∆σc̄6 + ∆σc̄8 ,

EFT insertion at one-loop :

σLO = σ0 + σ1c̄6 + σ2c̄26 ,

EFT insertions at two-loop :

∆σc̄6 = c̄26

[σ30c̄6 + σ40c̄2

6

]+ σ̃20c̄2

6 ,

∆σc̄8 = c̄8

[σ01 + σ11c̄6 + σ21c̄2

6

],

Taking an agnostic view on possible values of κ3 and κ4, we haveignored the SM EW corrections, and have kept highest powers of c̄6 in∆σc̄6 .The quantity ∆σc̄8 is the most relevant part of our computation and itsolely induces the sensitivity on c̄8.We assume that higher order QCD corrections factorize fromtwo-loop EW effects.

Relevant two-loop topologies

Non-factorizable, factorizable and counterterms:

(b)

(d)

(f)(e)

(j)

(k) (ℓ)

(c)

(a)

g

g

t

H

H

(i)

(g) (h)

G0

Effect on inclusive cross sectionFor αs , µR = µF =

12m(HH) while µEFT = 2mH .

One-loop:√

s [TeV] σ0 [fb] σ1 [fb] σ2 [fb]14 19.49 -15.59 5.414

- (-80.0%) (27.8%)100 790.8 -556.8 170.8

- (-70.5%) (21.6%)

Two-loop:√

s [TeV] σ̃20 [fb] σ30 [fb] σ40 [fb] σ01 [fb] σ11 [fb] σ21 [fb]14 0.7112 -0.5427 0.0620 0.3514 -0.0464 -0.1433

(3.6%) (-2.8%) (0.3%) (1.8%) (-0.2%) (-0.7%)100 24.55 -16.53 1.663 12.932 -0.88 -4.411

(3.1%) (-2.1%) (0.2%) (1.6%) (-0.1%) (-0.6%)

Cross sections grow considerably with energy. The contributions(numbers in brackets) from c̄6 and c̄8 slowly decrease wrt the SM LOprediction.

Effect on differential cross sectionOne-loop

0.0001

0.001

0.01

0.1

1

10

300 400 500 600 700 800 900 1000

σ[fb]

m(HH) [GeV]

σ0

σ1

σ2

Two-loop

1× 10−8

1× 10−7

1× 10−6

1× 10−5

0.0001

0.001

0.01

0.1

1

300 400 500 600 700 800 900 1000

σ[fb]

m(HH) [GeV]

σ̃20

σ30

σ40

1× 10−6

1× 10−5

0.0001

0.001

0.01

0.1

300 400 500 600 700 800 900 1000

σ[fb]

m(HH) [GeV]

σ01

σ11

σ21

The dashed lines show absolute values of -ve contributions.

Projections for 100 TeV pp collider

−30

−20

−10

0

10

20

30

−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

c̄ 8

c̄6

68% CL (flat µ-bin)68% CL

95% CL (flat µ-bin)95% CL

100 TeV30 ab−1

−30

−20

−10

0

10

20

30

−5 −4 −3 −2 −1 0 1 2 3 4 5

c̄ 8

c̄6

HHH(εb = 60%)HHH(εb = 80%)

HH

100 TeV30 ab−1

95% CL

For κ3 = 1, at 95% CL

−6 . κ4 . 18 [Direct from HHH(4b2γ)]

−4.2 . κ4 . 6.7 [Indirect from HH(2b2γ)]

At 100 TeV pp collider, the HH channel would be more sensitive toindependent variation in self-couplings than HHH channel.

higgs boson physics

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