EFT analysis of the off-shell Higgs data Aleksandr Azatov CERN - - PowerPoint PPT Presentation

EFT analysis of the off-shell Higgs data

Aleksandr Azatov

CERN

HXSWG meeting 24 Oct. 2014

work with C.Grojean,A.Paul, E.Salvioni arXiv:1406.6338

Recent Constraints on the Higgs width

Recently both CMS and ATLAS collaborations presented the studies

• f the off-shell Higgs production by studying

gg → h → ZZ → 4l, 2l2ν processes (CMS-PAS-HIG-14-000, CMS-HIG-14-002, ATLAS-CONF-2014-042) One can interpret these measurements to constrain the total width

• f the Higgs boson (Caola,Melnikov)

Off-Shell Higgs production

• n-shell cross secyion

σ ∼ g 2 prod.g 2 decay Γ

• ff-shell cross section:

σ ∼ g 2 prod.g 2 decayS + gprod.gdecayI + B Assuming the on-shell cross section is exactly as in the SM σOff −shell ∼ Γ ΓSM S +

• Γ

ΓSM I + B Γ < 5.4 × ΓSM

Flat direction in the Higgs couplings space

What kind of flat direction in the Higgs coupling space are we exploring ? to keep the on-shell rate the same g 2

gg→hg 2 h→ZZ

Γ =

• g 2

gg→hg 2 h→ZZ

Γ

• SM

To keep SM like yields in the other channels we need as well gi gj = gi gj

• SM

The flat direction is along gi = g SM

i

µ, Γ = ΓSMµ4 However Γvisible ∝ g 2

i ∝ µ2 thus we need an invisible decay width

Γinvisible = ΓSM(µ4 − µ2) The same flat direction is constrained also by the invisible Higgs decay searches Γ 3ΓSM

What else can we learn from the off-shell Higgs production measurements?

If there is a mass gap between the new physics states and the SM

• nes we can parametrize its effects by the higher dimensional
• perators.

Generically the effects of the higher dimensional operators are becoming larger at higher energies ⇒ the far off-shell region is becoming very important.

Operators effecting the Higgs decay

Let us look at the modifications of the hZZ vertex (see also 1403.4951,1410.5440) c0 m2

Z

v hZµZ µ + c1 v hZµνZ µν + c2 v hZµ∂νZ µν + c v hZ µZµ

c0 is constrained strongly by the on-shell Higgs measurements. The terms c1

v hZµνZ µν + c2 v hZµ∂νZ µν contribute only to the

transverse polarizations of the Z boson so the overall growth of the cross section with energy is SM like. The contribution

c v hZ µZµ growth as ∼ s relative to the SM.

68% : c ∈ [−0.7, −0.17] ∪ [0.42, 0.84] ,

Operators effecting the Higgs decay

Electroweak precision measurements and on-shell Higgs measurements favour the assumption that the Higgs boson is part of the electoweak

• doublet. hZZ interactions can be modified by the following dimension 6
• perators

(DµH)† σaDνHW µν,a, (DµH)† DνHBµν, H†HBµνBµν,

• H†σa ←

→

D ν H

• (DµWµν)a,
• H† ←

→

D ν H

• (DµBµν)

⇒ hZµνZ µν, h∂µZνZ µν ⇒ weak constraints on the Wilson coefficients. (∂µ(H†H))2,

• H† ←

→

D µ H 2 ⇒ hZµZ µ are strongly constrained by the

• n shell measurements

hZµZ µ appears only at dim 8 level (DµH)2(H†H)

Λ4

which leads to the irrelevant constraints on the scale Λ.

Operators effecting the Higgs production

At dimension-6 level there are two operators modifying the Higgs production in gluon fusion (see also 1406.1757) Ldim-6 = cy

yt|H|2 v 2

¯ QL HtR + h.c. +

cgg 2

s

48π2v 2 |H|2GµνG µν

L = −ct mt

v ¯

tth +

g 2

s

48π2 cg h v GµνG µν,

ct = 1 − Re(cy)

SM

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 ct cg ATLAS CMS 68,95

Current measurements have a strong degeneracy along ct + cg = 1 line. The degeneracy becomes even stronger if the

• perators are generated by the top-like states.

−ct mt

v ¯

tth +

g 2

s

48π2 cg h v GµνG µν + e2 18π2 cg h v γµνγµν

gg → h → ZZ matrix element behavior

g g Z Z c t g g Z Z g g Z Z c g

• n shell σ ∼ |ct + cg|2
• ff shell

Mgg→ZZ = Mbcg + ctMct + cgMcg M++00

bcg

∼ M++00

ct

∼ log2 ˆ s m2

t

, M++00

cg

∼ ˆ s In the SM there in order to preserve unitarity there is a cancellation between the triangle diagram which is logarithmically divergent and the box diagrams. New physics contribution grows with ˆ s - high energy bins become very important.

First bounds from CMS-PAS-HIG-14-002

imposing the condition ct + cg = 1 we find 68% : ct ∈ [−4, −1.5] ∪ [2.9, 6.1] 95% : ct ∈ [−4.7, 0.5] ∪ [1, 6.7]

10 5 5 10 10 5 5 10 ct cg 15 10 5 5 10 15 0.00 0.05 0.10 0.15 ct P

Validity of the EFT analysis

Effective couplings ct, cg can appear as a result of the dimension six

• perator.

Ldim-6 = cy yt|H|2 v 2 ¯ QL HtR + h.c. + cgg 2

s

48π2v 2 |H|2GµνG µν Our analysis is valid only in the range where the effects of the dimension-8

• perators can be ignored

O8 =

c8g 2

s

16π2v 4 GµνG µν (DλH)† DλH

√ ˆ s cg, cy c8 v Square of the dimension 6 operators act effectively as the dimension-8

• perators. So we can keep O(c2

g) in

the analysis only if c8 ≪ c2

g,y

High Luminosity 3 ab−1 14 TeV LHC prospects

We simulate the signal and the background with the MCFM 6.8 code, and bin the events in six categories √ ˆ s = (250, 400, 600, 800, 1100, 1500) GeV K- factors: we assume the same K-factor for the signal and the interfering background and calculate them using the ggHiggs code.

nonlinear analysis 68% ct ∈ [0.74, 1.28] linear analysis 68% ct ∈ [0.36, 1.66] keeping √s < 600GeV 68% ct ∈ [0.1, 1.25]

1.0 0.5 0.0 0.5 1.0 1.5 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 ct cg

1 1 2 3 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ct P

Recent progress in gg → h → ZZ (1410.5806)

Looking at angular distributions can suppress the q¯ q → ZZ background and improve the sensitivity on the coupling measurements the direct t¯ th provides stronger constraints on the top Yukawa couplings

Summary

On-shell Higg couplings measurements so far did not observe any significant deviations from the SM. Off-shell Higgs production is very sensitive to the higher dimensional

• perators in production/decay.

Studies of the off-shell Higgs production can be used as an additional independent constraint on the top Yukawa coupling.

Models with (ct, cg) degeneracy

Simple addition of one vector-like fermion L = −y ¯ QLtRH − M∗ ¯ TT − Y∗ ¯ QLTRH m = yv Y∗v M∗

• ⇒

cg(mH) ≈ ∂ log Detm

∂ log v

= 1 Higgs coupling to the gluons is exactly the same as in the SM, however Higgs couplings to the top quarks is modified

Q L Q L T

yt ∼ y SM

t

• 1 − Y 2

∗v 2

M2

∗

• L = −ct mt

v ¯

tth +

g 2

s

48π2 cg h v GµνG µν

ct = 1 − Y 2

∗v 2

M2

∗

cg = Y 2

∗v 2

M2

∗

Similar effect occurs in the composite Higgs models

Bounds on top partners

L = −y ¯ QLtRH − M∗ ¯ TT − Y∗ ¯ QLTRH cg = cy ∼ Y 2

∗v 2

M2

∗ ,

c8 ∼ Y 2

∗v 4

M4

∗

analysis ignoring the dimension eight

• perator is valid up to the energies

√ ˆ s M∗

0.1 0.3 0.4 0.5

1000 1500 2000 2 4 6 8 MT GeV Y

Figure: 95% exclusion in Y∗/top partner mass plane.

Recent progress

Higgs plus jet: Schlaffer, Spannowsky,Takeuchi,Weiler,Wymant arxiv: 1405.4295, h → ττ, WW ∗ ct ∈ [0.71, 1.24] at 95% Higgs plus two jets: Buschmann, Englert , Goncalves ,Plehn Spannowsky arXiv:1405.7651 h → ττ, WW ∗ ct ∈ [0.7, 1.3] at 95%