Higgs Physics - Theory Lecture 3

(1)

Higgs Physics - Theory

Lecture 3

From Higgs-boson properties to new physics

Laura Reina

(2)

• Lecture 1: the Standard-Model Higgs boson.

,→

EW gauge symmetry, Higgs mechanism.

,→

Higgs-boson interactions.

,→

Quantum constraints.

• Lecture 2: Higgs-boson physics at the LHC.

,→

Production and decay modes, what do they probe.

,→

Theoretical predictions and their accuracy.

• Lecture 3: from Higgs-boson properties to new physics.

,→

Probing specific extensions of the SM.

(3)

EW+Higgs precision physics in the LHC era:

What does it imply for theory?

Q1

:

How accurate?

,

_{→ See yesterday’s lecture.}

Q2:

How to interpret deviations from SM prediction?

• NP

can just rescale the Higgs-boson couplings: κ

_i

= g

_Hi

/g

_HiSM

:

only limited scope.

• NP

can introduce new structures in Higgs couplings: how to

explore?

,→

Model-specific

approach: more stringent, yet arbitrary.

,→

Effective Field Theory

approach: less arbitrary, systematic, but less

prone to simple prescriptions.

(4)

Constraining NP via deviations from SM Higgs-boson couplings:

rescaling factors (

κ

_i

)

V κ 0.5 1 1.5 2 F κ 0.5 1 1.5 2 bb → H H→ττ ZZ → H H→γγ WW → H Combined region σ 1 region σ 2 Best fit SM expected (13 TeV) -1 35.9 fb CMS V κ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 F κ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ATLAS Preliminary 1 − = 13 TeV, 24.5 - 79.8 fb s | < 2.5 H y = 125.09 GeV, | H m = 41% SM p Best fit 68% CL 95% CL SM Combined H→γγ ZZ → H H→WW bb → H H→ττ

κ

i

= g

Hi

/g

_HiSM

κ

V

→ all g

HV

κ

f

→ all g

Hf γ κ 0.7 0.8 0.9 1 1.1 1.2 1.3 g κ 1 1.2 1.4 region σ

1 2σ region Best fit SM expected (13 TeV) -1 35.9 fb CMS g κ 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 γ κ 0.8 0.9 1 1.1 1.2 1.3 ATLAS Preliminary −1 = 13 TeV, 24.5 - 79.8 fb s | < 2.5 H y = 125.09 GeV, | H m = 88% SM p Best fit 68% CL 95% CL SM

(5)

Constraining

κ

_i

from Higgs data+EWPO

Example:

κ

_V

_{→ all g}

_HV

κ

_f

_{→ all g}

_Hf

Higgs only

68% 95% correlation V 1.02± 0.03 [0.97, 1.08] 1.00 f 0.98± 0.07 [0.84, 1.12] 0.24 1.00 1

Higgs+EWPO

68% 95% correlation V 1.02± 0.02 [0.99, 1.06] 1.00 f 1.00± 0.06 [0.88, 1.12] 0.14 1.00 1

−→

Main effect on κ

V 0.8 0.9 1 1.1 1.2 V κ 0.6 0.8 1 1.2 1.4 f κ _EW+Higgs EW Higgs HEP_fit

σ

i

= σ

_iSM

+ δσ

i

Γ

j

= Γ

SM_j

+ δΓ

j

σ

_iSM

, Γ

SM_j

→ from

Higgs XS WG

(CERN Yellow Report, arXiv:1610.07922)

δσ

i

→ using

Madgraph

+K-factors (from

Higgs XS WG

)

(6)

Constraining NP via SM Effective Field Theory

Extension of the SM Lagrangian by d > 4 operators

L

eff_SM

= L

SM

+

X

d>4

1 Λ

d−4

L

d

= L

SM

+

1 Λ

L

5

+

1 Λ

2

L

6

+ · · ·

where

L

_d

=

X

i

C

i

O

i

,

[O

i

] = d ,

considering:

→

one Higgs doublet of SU (2)

L

, linearly realized SSB

→

no L

5

(only one operator affecting neutrino masses)

→

d = 6 operators only, obeying SM gauge symmetry, L and B conservation

,→

expansion in (p, v)/Λ

,→

truncation at linear order →

O((p, v)

2

/Λ

2

) to be verified a posteriori.

and requiring:

→

flavour universality:

59 operators

[basis by

Grzadkowski et al.

, JHEP 1010 (2010) 085 →

Warsaw basis

]

→

CP even operators only, with at least one Higgs:

27 operators

(7)

O

φG

= (φ

†

φ) G

A_µν

G

Aµν

O

φW

= (φ

†

φ) W

_µνI

W

Iµν

O

φB

= (φ

†

φ) B

µν

B

µν

O

φW B

= (φ

†

τ

I

φ) W

_µνI

B

µν

O

φD

= (φ

†

D

µ

φ)

∗

(φ

†

D

µ

φ)

O

φ

= (φ

†

φ)

∗

(φ

†

φ)

bosonic operators

−→

corrections to:

• oblique parameters (

in red

)

• HV V

−→ κ

V

• W W Z and W W γ

O

_φL(1)

= (φ

†

i

←

D

→

_µ

φ)(Lγ

µ

L)

O

_φL(3)

= (φ

†

i

←

D

→

I_µ

φ)(L τ

I

γ

µ

L)

O

φe

= (φ

†

i

←

D

→

µ

φ)(e

R

γ

µ

e

R

)

O

_φQ(1)

= (φ

†

i

←

D

→

_µ

φ)(Qγ

µ

Q)

O

_φQ(3)

= (φ

†

i

←

D

→

I_µ

φ)(Q τ

I

γ

µ

Q)

O

φu

= (φ

†

i

←

D

→

µ

φ)(u

R

γ

µ

u

R

)

O

φd

= (φ

†

i

←

D

→

µ

φ)(d

R

γ

µ

d

R

)

single-fermionic-vector-current

operators

−→

corrections to:

• V f ¯

f (

in blue

)

• HV f ¯

f

(8)

O

eφ

= (φ

†

φ)( ¯

L e

R

φ)

O

uφ

= (φ

†

φ)( ¯

Q u

R

φ)

e

O

dφ

= (φ

†

φ)( ¯

Q d

R

φ)

single-fermionic-scalar-current

operators

−→

corrections to:

• Yukawa couplings

• Hf ¯

f −→ κ

_f

O

LL

= ( ¯

Lγ

µ

L)( ¯

Lγ

µ

L)

four-fermion operator

−→

corrections to:

• G

F

extraction from µ decay

O

W

=

IJK

W

_µIν

W

_νJρ

W

_ρKµ

bosonic operator, no φ

−→

corrections to:

• gauge self-interactions

Notice:

Only highlighted operators (10) enters EWPO, and only 8 combinations

can be constrained

_{−→ “flat directions”}

(9)

Where effective operators matter . . .

They shift masses and couplings in

_L

SM

and introduce new

interactions.

Example: Consider

O

φD

and

O

φ

. Upon SSB (unitary gauge):

O

φD

= (φ

†

D

µ

φ)

∗

(φ

†

D

µ

φ) =

v

2

4 1 +

eH

v

+

H

2

v

2

(∂

µ

H)(∂

µ

H) +

g

2

v

4

16c

2_W

Z

µ

Z

µ

1 +

4H

v

+

6H

2

v

2

+

4H

3

v

3

+

H

4

v

4

O

_φ

= (φ

†

φ)

∗

_(φ

†

φ) = −(v

2

+ 4vH + 4H

2

)(∂

µ

H)(∂

µ

H)

New interactions

: H(∂

µ

H)(∂

µ

H), H

2

(∂

µ

H)(∂

µ

H), . . . (notice: → p-dependence)

and they both affect the H kinetic term → normalize it by shifting the H field:

H = H

0

1 −

1

4 ˆ

C

HD

+ ˆ

C

H

where ˆ

C

i

= C

i

v

2

/Λ

2

. This

shift affects the HV V and Hf ¯

f vertices

,

and the Higgs mass

, now be given by:

M

_H2

= 2λv

2

1 −

3 2λ

ˆ

C

H

−

1

2 C

HD

+ 2 ˆ

C

H

Notice: O

H

= (φ

†

φ)

3

affects V (φ) (→ M

_H2

). Not among the listed operators

(10)

Towards Global Fits of d=6 interactions

→

Combined global EW fit

of 8 combinations of dim=6 operators.

Jorge de Blas

INFN - University of Padova

29th International Symposium on Lepton Photon Interactions at High Energies Toronto, August 6, 2019

Constraints on the dimension-6 SMEFT

26

Global fit to EW data (2019)

_{J. B. et al., In preparation}

See also:

J. Ellis et al. ,JHEP 1806 (2018) 146,

A. Biekötter et al. arXiv:1812.07587 [hep-ph],

E. da Silva Almeida et al., Phys.Rev. D99 (2019) no.3, 033001 (1) l φ O O_φ(3)_l O(1)_φ_e O(1)_φ_q O(3)_φ_q O(1)_φ_u O(1)_φ_d Oll ] -2 [TeV 68%,95% ⏐ 2 Λ/ i c 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0 0.2 0.4 0.6 0.8 1 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0 0.2 0.4 0.6 0.8 1 -2 0.012 TeV ± 0.013 -2 0.017 TeV ± -0.027 -2 0.009 TeV ± -0.003 -2 0.044 TeV ± -0.027 -2 0.039 TeV ± -0.077 -2 0.14 TeV ± 0.04 -2 0.24 TeV ± -0.63 -2 0.028 TeV ± -0.029 -2 0.004 TeV ± 0.003 -2 0.004 TeV ± -0.005 -2 0.005 TeV ± -0.003 -2 0.018 TeV ± 0.009 -2 0.006 TeV ± 0.002 -2 0.039 TeV ± 0.008 -2 0.053 TeV ± -0.046 -2 0.007 TeV ± 0.009 Global fit 1 Op. at a time HEP fit

The Wilson coefficients for the operators O W B and O D contribute to the EWPO via

their corrections to the well known Peskin-Takeuchi parameters S and T [52], S = 4sWcW ↵em(MZ) v2 ⇤2C W B , (2.27) T = 1 2↵em(MZ) v2 ⇤2C D , (2.28)

where cW and sW are, respectively, the cosine and sine of the weak mixing angle ✓W, and

↵emis the electromagnetic fine-structure constant. Finally, some interactions enter in all

ob-servables in the EW sector indirectly, via their contributions to the physical processes used to extract the values of the SM input parameters. In this work we use{↵em(0), MZ, GF}

as input parameters in the EW sector. Hence, the four lepton operatorOll, which enters

in muon decay, has to be included among the list of dimension-six interactions entering in EWPO. (Note that apart from their direct e↵ects described before, the interactions O(3)L,O W BandO Dalso induce indirect corrections in EW observables.) As it is easy to

see, the EWPO (Z-pole observables and W mass) cannot constrain independently the 10 operators discussed above, but only a total of 8 combinations of dimension-6 interactions (assuming fermion universal modifications of the SM interactions). These are given by,

ˆ C(1)_l = C(1)_l +1 4C D (2.29) ˆ C(3)_l = C(3)_l + c 2 w 4s2 w C D+ cw swC W B (2.30) ˆ C(1)_q = C(1)_q 1 12C D (2.31) ˆ C(3)_q = C(3)_q + c 2 w 4s2 w C D+ cw swC W B (2.32) ˆ C e= C e+1 2C D (2.33) ˆ C u= C u 1 3C D (2.34) ˆ C d= C d+1 6C D (2.35) ˆ Cll= Cll (2.36)

which are the quantities that we will use in our global fit to electroweak precision observ-ables as described in Sections3and4.

All the interactions that enter in EWPO also enter, directly or indirectly, in Higgs observables. The latter are however a↵ected by interactions not correcting the EW mea-surements at the Z pole or the W mass. Any operator contributing to the Higgs kinetic term will be propagated to all SM Higgs couplings via its wavefunction renormalization. The SM-like single Higgs couplings to the electroweak bosons are also directly a↵ected by the operator O D, hence modifying the relation between the W and Z interactions with

the Higgs. Non-SM-like interactions, i.e. di↵erent tensor structures of the form hVµ⌫Vµ⌫,

are generated by the operators of formO V (V = G, W, B, W B). As mentioned above,

– 7 –

Flat directions in Warsaw basis

Combination with WW/Higgs lifts degeneracies in this basis

Sensitive to eight combinations of dimension-6 operators

Preliminary

New Physics assumptions: CP-even, U(3)5

For O(1) couplings, bound on New Physics scale ~1-10 TeV

Jorge de Blas

Constraints on the dimension-6 SMEFT

26

Global fit to EW data (2019)

_{J. B. et al., In preparation}

See also:

J. Ellis et al. ,JHEP 1806 (2018) 146,

E. da Silva Almeida et al., Phys.Rev. D99 (2019) no.3, 033001

(1) l φ

O

_φ(3)_l

O

(1)_φ_e

O

(1)_φ_q

O

(3)_φ_q

O

(1)_φ_u

O

(1)_φ_d

O

ll

]

-2

[TeV

68%,95%

⏐

2

Λ/

i

c

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0 0.2 0.4 0.6 0.8 1 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0 0.2 0.4 0.6 0.8 1 -2 0.012 TeV ± 0.013 -2 0.017 TeV ± -0.027 -2 0.009 TeV ± -0.003 -2 0.044 TeV ± -0.027 -2 0.039 TeV ± -0.077 -2 0.14 TeV ± 0.04 -2 0.24 TeV ± -0.63 -2 0.028 TeV ± -0.029 -2 0.004 TeV ± 0.003 -2 0.004 TeV ± -0.005 -2 0.005 TeV ± -0.003 -2 0.018 TeV ± 0.009 -2 0.006 TeV ± 0.002 -2 0.039 TeV ± 0.008 -2 0.053 TeV ± -0.046 -2 0.007 TeV ± 0.009 Global fit 1 Op. at a time HEP fit

The Wilson coefficients for the operators O W B and O D contribute to the EWPO via

their corrections to the well known Peskin-Takeuchi parameters S and T [52],

S = 4sWcW ↵em(MZ) v2 ⇤2C W B , (2.27) T = 1 2↵em(MZ) v2 ⇤2C D , (2.28)

where cW and sW are, respectively, the cosine and sine of the weak mixing angle ✓W, and

↵emis the electromagnetic fine-structure constant. Finally, some interactions enter in all

ob-servables in the EW sector indirectly, via their contributions to the physical processes used

to extract the values of the SM input parameters. In this work we use {↵em(0), MZ, GF}

as input parameters in the EW sector. Hence, the four lepton operator Oll, which enters

in muon decay, has to be included among the list of dimension-six interactions entering in EWPO. (Note that apart from their direct e↵ects described before, the interactions

O(3)L,O W B and O D also induce indirect corrections in EW observables.) As it is easy to

see, the EWPO (Z-pole observables and W mass) cannot constrain independently the 10 operators discussed above, but only a total of 8 combinations of dimension-6 interactions (assuming fermion universal modifications of the SM interactions). These are given by,

ˆ C(1)_l = C(1)_l + 1 4C D (2.29) ˆ C(3)_l = C(3)_l + c 2 w 4s2 w C D+ cw sw C W B (2.30) ˆ C(1)_q = C(1)_q 1 12C D (2.31) ˆ C(3)_q = C(3)_q + c 2 w 4s2 w C D+ cw sw C W B (2.32) ˆ C e= C e+ 1 2C D (2.33) ˆ C u = C u 1 3C D (2.34) ˆ C d = C d+ 1 6C D (2.35) ˆ Cll= Cll (2.36)

which are the quantities that we will use in our global fit to electroweak precision

observ-ables as described in Sections 3 and 4.

All the interactions that enter in EWPO also enter, directly or indirectly, in Higgs observables. The latter are however a↵ected by interactions not correcting the EW mea-surements at the Z pole or the W mass. Any operator contributing to the Higgs kinetic term will be propagated to all SM Higgs couplings via its wavefunction renormalization. The SM-like single Higgs couplings to the electroweak bosons are also directly a↵ected by

the operator O D, hence modifying the relation between the W and Z interactions with

the Higgs. Non-SM-like interactions, i.e. di↵erent tensor structures of the form hVµ⌫Vµ⌫,

are generated by the operators of form _O V (V = G, W, B, W B). As mentioned above,

– 7 –

Flat directions in Warsaw basis

Combination with WW/Higgs

lifts degeneracies in this basis

Sensitive to eight combinations of dimension-6 operators

Preliminary

New Physics assumptions: CP-even, U(3)

5

For O(1) couplings, bound on New Physics scale ~1-10 TeV

(Oi → ˆOi)

[

J. de Blas

, talk at Lepton-Photon 2019]

(11)

→

Combined global EW+Higgs fit

of extended set of operators

G φ O W φ O B φ O WB φ O D φ O φ O (1) l φ O (3) l φ O e φ O (1) q φ O (3) q φ O u φ O d φ O φ e O φ u O φ d O uG O ll O W O

]

-2

[TeV

68%,95%

⏐

2

Λ/

_i

c

1 − 0.5 − 0 0.5 1 1 − 0.5 − 0 0.5 1 -2 0.003 TeV ± 0.00 -2 0.22 TeV ± 0.10 -2 0.09 TeV ± 0.15 -2 0.23 TeV ± 0.35 -2 0.47 TeV ± -0.89 [x10] -2 1.2 TeV ± -1.0 [x10] -2 0.12 TeV ± 0.24 -2 0.09 TeV ± 0.13 -2 0.23 TeV ± 0.44 -2 0.06 TeV ± -0.10 -2 0.09 TeV ± 0.09 -2 0.20 TeV ± -0.27 -2 0.24 TeV ± -0.44 -2 1.1 TeV ± 0.05 [x10] -2 1.3 TeV ± -1.5 [x10] -2 1.6 TeV ± 1.9 [x10] -2 0.30 TeV ± -0.03 -2 0.03 TeV ± -0.03 -2 0.49 TeV ± 0.79 [x10]

Global fit (EW+Higgs+aTGC) 1 Op. at a time (EW+Higgs+aTGC)

Figure 6. Global fit to the EFT operators in the Lagrangian (

19 ). We show the marginalized 68% probability reach for each

Wilson coefficient c

_i

/

L

2 in Eq. (

19 ) from the global fit (solid bars). The reach of the vertical lines indicate the results assuming

only the corresponding operator is generated by the new physics.

fully developed program including such contributions in the SMEFT framework, we restrict the discussion in this section to SM

uncertainties only.

In the previous sections the results for future colliders after the HL/HE-LHC era were presented taking into account

parametric uncertainties only. This was done to illustrate the final sensitivity to BSM deformations in Higgs couplings, as

given directly by the experimental measurements of the different inputs (i.e. Higgs rates, diBoson measurements, EWPO or the

processes used to determine the values of the SM input parameters). On the other hand, for this scenario to be meaningful, it

is crucial to also study the effect in such results of the projections for the future intrinsic errors. This is needed to be able to

quantify how far we will be from the assumption that such intrinsic errors become subdominant and, therefore, which aspects

of theory calculations should the theory community focus on to make sure we reach the maximum experimental sensitivity at

future colliders.

In this section we discuss more in detail the impact of the two types of SM theory errors described above, from the point

of view of the calculations of the predictions for Higgs observables. This will be done both within the

k framework and also

in the context of the EFT results. For the results from the

k-framework we will use the most general scenario considered in

Section

3.1 , i.e. kappa-3, which allows non-SM decays. On the EFT side, we will use the scenario SMEFT

PEW

, where the

uncertainty associated to the precision of EWPO has already been “factorized”. In this scenario each fermion coupling is

also treated separately, thus being sensitive to the uncertainties in the different H ! f ¯f decay widths. Finally, we will also

restrict the study in this subsection to the case of future lepton colliders only (we always consider them in combination with the

HL-LHC projections. For the latter we keep the theory uncertainties as reported by the WG2 studies [

10 ]).

In Table

9 we show the results of the

k fit for the benchmark scenario kappa-3, indicating the results obtained

includ-ing/excluding the different sources of SM theory uncertainties. Similarly, Table

10 shows the results of the EFT fit for the

benchmark scenario SMEFT

PEW

. For the EFT results the impact of the different theory uncertainties is also illustrated in

Figure

8 . As can be seen, if the SM errors were reduced to a level where they become sub-dominant, the experimental precision

would allow to test deviations in some of the couplings at the one per-mille level, e.g. the coupling to vector bosons at CLIC

in the SMEFT framework (the presence of extra decays would however reduce the precision to the 0.4% level, as shown in

the kappa-3 results). The assumed precision of the SM theory calculations and inputs, however, prevents reaching this level

24/58

Jorge de Blas

Constraints on the dimension-6 SMEFT

28

Global fit to EW and Higgs data (2019)

J. B. et al., In preparation

Preliminary

See also:

J. Ellis et al. ,JHEP 1806 (2018) 146,

[

J. de Blas

, talk at Lepton-Photon 2019]

,→

Lifted degeneracy among EWPO operators.

,→

Large difference between global and individual bounds →Large correlations

,→

Studies should aim for global fit of all necessary operators.

(12)

Bounds on operators can be translated in bounds on Λ

_{N P}

→

Extended set of operators, switching on one operator at a time

Coefficient 95% prob. range 95% prob. lower bound Ci/⇤2[TeV 2] on ⇤ [TeV] (|Ci| = 1) C G [ 0.00029, 0.0059] 13.5 C W [ 0.019, 0.0040] 7.63 C B [ 0.0051, 0.0011] 14.7 C W B [ 0.0045, 0.0038] 15.7 C D [ 0.027, 0.00092] 6.38 C _⇤ [0.015, 1.4] 0.85 C(1)L [ 0.0052, 0.012] 9.81 C(3)L [ 0.013, 0.0030] 9.46 C(1)e [ 0.015, 0.0070] 9.14 C(1)_Q [ 0.027, 0.043] 5.13 C(3)_Q [ 0.0111, 0.015] 8.71 C u [ 0.072, 0.082] 3.59 C d [ 0.16, 0.050] 2.72 Ce [ 0.034, 0.015] 5.97 Cu [ 2.0, 0.050] 0.74 Cd [0.0031, 0.061] 4.18 CLL [ 0.0048, 0.022] 7.11 1 G φ O W φ O B φ O WB φ O D φ O φ O (1) l φ O (3) l φ O e φ O (1) q φ O (3) q φ O u φ O d φ O φ e O φ u O φ d O ll O [TeV] 95%  | _i |c / Λ 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 EW fit Higgs fit EW+Higgs fit HEPfit

• EWPO constraints still more stringent: Higgs bounds ≤ EWPO bounds

• Increasing precision in constraining the C

i

can greatly boost the reach in Λ!

,→

Need to incrementally move towards more global fits.

,→

Need to use more observables: Higgs kinematic distributions, EW

triple-gauge-coupling measurements, . . .

,→

incrementally release flavour universality → t-quark observables (b, τ ).

,→

Include NLO QCD/EW corrections and running of C

i

.

(13)

Projected bounds for Λ at future colliders

WB φ O D φ O (1) l φ O (3) l φ O (1) e φ O (1) q φ O (3) q φ O (1) u φ O (1) d φ O ll O [TeV] 95%  | _i |c / Λ 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Today HL-LHC ILC CepC FCCee WB φ O D φ O (1) l φ O (3) l φ O (1) e φ O (1) q φ O (3) q φ O (1) u φ O (1) d φ O ll O [TeV] 95%  | _i |c / Λ 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Today HL-LHC ILC CepC FCCee

with/without theoretical errors

with/without theoretical and

parametrical errors

,→ Most recent study:

J. de Blas et al.

,

Higgs boson studies at future particle colliders

, arxiv:1905.03764

prepared for the

“Symposium on the Update of the European Strategy for Particle Physics”,

Granada, May 13-16 2019.

(14)

Effect of new interactions: Higgs

p

_T

in

gg

_{→ H}

Not visible in the inclusive cross sections, but in the shape of distributions.

��_�� _�� _�� _�� _�� _��

[

Grazzini et al.

, arXiv:1612.00283]

O

φG

= (φ

†

φ)G

aµν

G

a.µν

−→

α_πvs

c

g

hG

aµν

G

a,µν

←

Top-Higgs interaction

12 E.Vryonidou

~20% accuracy

ttH

H

Observation of ttH

or

Heavy particles

in the loops?

O

uφ

= (φ

†

φ) ¯

Q

L

u

R

φ −→

˜

m_vt

c

t

ht¯

t

←

Top-Higgs interaction

12 E.Vryonidou

~20% accuracy

ttH

H

Observation of ttH

or

Heavy particles

in the loops?

Include O

_φG

and O

_uφ

in NLO+NLL computation: simultaneous effects

(15)

Probing the gluon-Higgs vs top-Higgs interactions

pp®ttH pp®H -0.04 -0.02 0.00 0.02 0.04 -20 -10 0 10 20 CΦGL2@TeV-2D CtΦ L 2 @TeV -2 D LHC current pp®ttH pp®H pp®Hj -0.04 -0.02 0.00 0.02 0.04 -20 -10 0 10 20 CΦGL2@TeV-2D CtΦ L 2 @TeV -2 D HL-LHC 3000 fb-1

[

Maltoni et al.

, arXiv:1607.05330]

-1.0 _-0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 cy cg HL_-LHC incl. off-shell hh tth boosted

Combining:

inclusive H

ttH

HH

boosted H

off-shell H

(16)

Effect of new interactions: Higgs

p

T

in VH and VBF

10−2 10−1 d σ dp H T [fb /GeV ] W+_{H: H→ b ¯b, W → l}+_ν LHC 13 TeV Higgs pT LO+PS NLO+PS SM ¯cHW= 0.03, ¯cW = ¯cB= 0. ¯cHW= −¯cW= 0.03, ¯cB= 0.015 LO+PS NLO+PS SM ¯cHW= 0.03, ¯cW = ¯cB= 0. ¯cHW= −¯cW= 0.03, ¯cB= 0.015 0 2 4 δA_SM -0.5 -0.25 0 δ_SMB 50 100 150 200 250 300 pH T[GeV ] 1 1.5 2 Kfact 10−3 10−2 d σ dp H T [fb /GeV ] VBF: H → γγ LHC 13 TeV Higgs pT LO+PS NLO+PS SM ¯cHW= 0.03, ¯cW= ¯cB= 0. ¯cHW= −¯cW= 0.03, ¯cB= 0.015 LO+PS NLO+PS SM ¯cHW= 0.03, ¯cW= ¯cB= 0. ¯cHW= −¯cW= 0.03, ¯cB= 0.015 -0.5 -0.25 0 0.25 δA_SM -0.25 0 0.25 δB_SM 0 50 100 150 200 250 pH T[GeV ] 0.75 1 1.25 1.5 1.75 Kfact

[

Degrande et al.

, arXiv:1612.00283]

,→

Includes NLO QCD matched to PS, validated with both MG5aMC@NLO

and POWHEG-BOX.

(17)

From SM-EFT to specific models

Specific model

_{→ {O}

_i

_{} −→ bounds on {C}

_i

_{} → bounds on the mode}

G φ O W φ O B φ O WB φ O D φ O φ O (1) l φ O (3) l φ O e φ O (1) q φ O (3) q φ O u φ O d φ O φ e O φ u O φ d O uG O ll O W O ] -2 [TeV 68%,95% ⏐ 2 Λ/i c 1 − 0.5 − 0 0.5 1 1 − 0.5 − 0 0.5 1 -2 0.003 TeV ± 0.00 -2 0.22 TeV ± 0.10 -2 0.09 TeV ± 0.15 -2 0.23 TeV ± 0.35 -2 0.47 TeV ± -0.89 [x10] -2 1.2 TeV ± -1.0 [x10] -2 0.12 TeV ± 0.24 -2 0.09 TeV ± 0.13 -2 0.23 TeV ± 0.44 -2 0.06 TeV ± -0.10 -2 0.09 TeV ± 0.09 -2 0.20 TeV ± -0.27 -2 0.24 TeV ± -0.44 -2 1.1 TeV ± 0.05 [x10] -2 1.3 TeV ± -1.5 [x10] -2 1.6 TeV ± 1.9 [x10] -2 0.30 TeV ± -0.03 -2 0.03 TeV ± -0.03 -2 0.49 TeV ± 0.79 [x10]

Global fit (EW+Higgs+aTGC) 1 Op. at a time (EW+Higgs+aTGC)

Figure 6. Global fit to the EFT operators in the Lagrangian (19). We show the marginalized 68% probability reach for each

Wilson coefficient ci/L2 in Eq. (19) from the global fit (solid bars). The reach of the vertical lines indicate the results assuming

only the corresponding operator is generated by the new physics.

fully developed program including such contributions in the SMEFT framework, we restrict the discussion in this section to SM uncertainties only.

In the previous sections the results for future colliders after the HL/HE-LHC era were presented taking into account parametric uncertainties only. This was done to illustrate the final sensitivity to BSM deformations in Higgs couplings, as given directly by the experimental measurements of the different inputs (i.e. Higgs rates, diBoson measurements, EWPO or the processes used to determine the values of the SM input parameters). On the other hand, for this scenario to be meaningful, it is crucial to also study the effect in such results of the projections for the future intrinsic errors. This is needed to be able to quantify how far we will be from the assumption that such intrinsic errors become subdominant and, therefore, which aspects of theory calculations should the theory community focus on to make sure we reach the maximum experimental sensitivity at future colliders.

In this section we discuss more in detail the impact of the two types of SM theory errors described above, from the point of view of the calculations of the predictions for Higgs observables. This will be done both within thek framework and also in the context of the EFT results. For the results from thek-framework we will use the most general scenario considered in Section 3.1, i.e. kappa-3, which allows non-SM decays. On the EFT side, we will use the scenario SMEFTPEW, where the

uncertainty associated to the precision of EWPO has already been “factorized”. In this scenario each fermion coupling is also treated separately, thus being sensitive to the uncertainties in the different H ! f ¯f decay widths. Finally, we will also restrict the study in this subsection to the case of future lepton colliders only (we always consider them in combination with the HL-LHC projections. For the latter we keep the theory uncertainties as reported by the WG2 studies [10]).

In Table 9 we show the results of the k fit for the benchmark scenario kappa-3, indicating the results obtained includ-ing/excluding the different sources of SM theory uncertainties. Similarly, Table 10 shows the results of the EFT fit for the benchmark scenario SMEFTPEW. For the EFT results the impact of the different theory uncertainties is also illustrated in

Figure8. As can be seen, if the SM errors were reduced to a level where they become sub-dominant, the experimental precision would allow to test deviations in some of the couplings at the one per-mille level, e.g. the coupling to vector bosons at CLIC in the SMEFT framework (the presence of extra decays would however reduce the precision to the 0.4% level, as shown in the kappa-3 results). The assumed precision of the SM theory calculations and inputs, however, prevents reaching this level

24/58

Jorge de Blas

INFN - University of Padova

Constraints on the dimension-6 SMEFT

28

Global fit to EW and Higgs data (2019) J. B. et al., In preparation

Preliminary

See also:

J. Ellis et al. ,JHEP 1806 (2018) 146, A. Biekötter et al. arXiv:1812.07587 [hep-ph],

[

J. de Blas

, talk at Lepton-Photon 2019]

−→

SMEFT EW/Higgs fit (Z') 2-σ region 1-σ region -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 gϕ/M2[TeV-2] gl /M 2[TeV -2]

SMEFT EW/Higgs fit (CH) 2-σ region 1-σ region 0 5 10 15 20 2 4 6 8 10 12 m*[TeV] g*

(18)

Broad spectrum of searches, old and new ideas

2HDM

: natural extension, MSSM motivated, FC scalar currents

[Eberhardt, Chowdhury, arXiv:1711.02095]

1 − −0.5 0 0.5 1 ) α -β cos( 1 − 10 1 10 β tan Preliminary ATLAS -1 = 13 TeV, 24.5 - 79.8 fb s | < 2.5 H y = 125.09 GeV, | H m 2HDM Type-I Obs. 95% CL Best Fit Obs. Exp. 95% CL SM 1 − −0.5 0 0.5 1 ) α -β cos( 1 − 10 1 10 β tan Preliminary ATLAS -1 = 13 TeV, 24.5 - 79.8 fb s | < 2.5 H y = 125.09 GeV, | H m 2HDM Type-II Obs. 95% CL Best Fit Obs. Exp. 95% CL SM ) α -β cos( 0.8 − −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 β tan 1 − 10 1 10 (13 TeV) -1 35.9 fb 2HDM Type III Observed 95% CL Expected 95% CL CMS ) α -β cos( 0.8 − −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 β tan 1 − 10 1 10 (13 TeV) -1 35.9 fb 2HDM Type IV Observed 95% CL Expected 95% CL CMS

Favor alignement scenario −→ consistent with SM-like couplings and EWPO

Towards a decoupling scenario: M

h

M

H

, M

A

, M

_H±

, i.e. spectrum of very

(19)

2HDM - Type II, MSSM-like, quick guide

Two complex SU (2)

L

doublets

, with hypercharge Y =

±1:

Φ

u

=





φ

+_u

φ

0_u





,

Φ

d

=





φ

0_d

φ

−_d





and (super)potential (Higgs part only):

V

_H

=

(

_|µ|

2

+ m

_u2

)

_|Φ

_u

_|

2

+ (

_|µ|

2

+ m

2_d

)

_|Φ

_d

_|

2

_{− µB}

_ij

(Φ

i_u

Φ

j_d

+ h.c.)

+

g

2

_{+ g}

₀₂

8 |Φ

u

|

2

− |Φ

d

|

2

+

g

2

2 |Φ

† u

Φ

d

|

2

The EW symmetry is spontaneously broken by choosing:

hΦ

u

i =

1 √

2 



0 v

u





,

hΦ

d

i =

1 √

2 



v

d

0 



(20)

Five physical scalar/pseudoscalar degrees of freedom

:

h

0

=

₋₍

√

2ReΦ

0_d

_{− v}

_d

) sin α + (

√

2ReΦ

0_u

_{− v}

_u

) cos α

H

0

=

(

√

2ReΦ

0_d

_{− v}

d

) cos α + (

√

2ReΦ

0_u

_{− v}

u

) sin α

A

0

=

√

2 ImΦ

0_d

sin β + ImΦ

0_u

cos β

H

±

= Φ

±_d

sin β + Φ

±_u

cos β

where

tan β = v

_u

/v

_d

.

All masses can be expressed (at tree level) in terms of

tan β

and

M

A

:

M

_H2 ±

= M

_A2

+ M

_W2

M

_H,h2

=

1

2 M

_A2

+ M

_Z2

_{± ((M}

_A2

+ M

_Z2

)

2

_{− 4M}

_Z2

M

_A2

cos

2

2β)

1/2

(21)

Higgs boson couplings to SM gauge bosons

:

Some phenomenologically important ones:

g

hV V

= g

V

M

V

sin(β

− α)g

µν

,

g

HV V

= g

V

M

V

cos(β

− α)g

µν

where g

V

= 2M

V

/v for V = W, Z

, and

g

_hAZ

=

g cos(β

− α)

2 cos θ

W

(p

_h

_{− p}

_A

)

µ

,

g

_HAZ

=

₋

g sin(β

− α)

2 cos θ

W

(p

_H

_{− p}

_A

)

µ

Notice

: g

_AZZ

= g

_{AW W}

= 0 , g

_H±_ZZ

= g

_H±_{W W}

= 0

Decoupling limit

: M

_A

_M

_Z

_−→







M

h

' M

hmax

M

H

' M

_H±

' M

_A

cos

2

(β − α) '

M

4 Z

sin

2

4β

M

_A4

−→







cos(β − α) → 0

sin(β − α) → 1

(22)

Higgs boson couplings to quarks and leptons

:

Yukawa type couplings, Φ

_u

to up-component and Φ

_d

to down-component of

SU (2)

_L

fermion doublets. Ex. (

3

rd

generation quarks

):

L

Y ukawa

= h

t

_¯

tP

_L

tΦ

0_u

_{− ¯tP}

_L

bΦ

+_u

+ h

_b

¯bP

_L

bΦ

0_d

_{− ¯bP}

_L

tΦ

−_d

+ h.c.

and similarly for leptons. The corresponding couplings can be expressed as

(

y

t

, y

b

→ SM

):

g

_ht¯_t

=

cos α

sin β

y

t

= [sin(β − α) + cot β cos(β − α)] y

t

g

_hb¯_b

= −

sin α

cos β

y

b

= [sin(β − α) − tan β cos(β − α)] y

b

g

_Ht¯_t

=

sin α

sin β

y

t

= [cos(β − α) − cot β sin(β − α)] y

t

g

_Hb¯_b

=

cos α

cos β

y

b

= [cos(β − α) + tan β sin(β − α)] y

b

g

_At¯_t

=

cot βy

t

, g

_Ab¯_b

= tan βy

b

g

_H±_t¯_b

=

g

2 √

2M

W

[m

t

cot β(1 + γ

5

) + m

b

tan β(1 − γ

5

)]

(23)

Heavy-scalar and charged-scalar searches further explore parameter space.

[GeV] A m 200 300 400 500 600 700 β tan 1 2 3 4 5 10 20 30 40 τ τ → H/A -1 = 13 TeV, 36.1 fb s JHEP 01 (2018) 055 ν τ → + H -1 = 13 TeV, 36.1 fb s JHEP 09 (2018) 139 tb → + H -1 = 13 TeV, 36.1 fb s arXiv:1808.03599 [hep-ex] ν ν 4l/ll → ZZ → H -1 = 13 TeV, 36.1 fb s Eur. Phys. J. C (2018) 78: 293 Zh → A → gg -1 = 13 TeV, 36.1 fb s JHEP 03 (2018) 174 ν l ν l → WW → H -1 = 13 TeV, 36.1 fb s Eur. Phys. J. C 78 (2018) 24 4b, → hh → H , τ τ / γ γ bb → γ γ WW → -1 = 8 TeV, 20.3 fb s Phys. Rev. D92, 092004 (2015) γ γ bb → hh → H -1 = 13 TeV, 3.2 fb s ATLAS-CONF-2016-004 ] d κ , u κ , V κ h couplings [ -1 = 13 TeV, 36.1 - 79.8 fb s ATLAS-CONF-2018-031 ATLAS Preliminary hMSSM, 95% CL limits October 2018 Observed Expected 200 240 280 320 360 400 440 480 520 560 600 (GeV) τ τ ll c m 0 0.51 1.5 2 2.5 3 Obs./Bkg. 0 5 10 15 20 25 30 Events / 20 GeV Observed

Production of a 125 GeV h boson 4l) → ZZ → 4l (excl. h → ZZ Other Reducible Uncertainty = 20 fb Β σ = 300 GeV, A AZh m (13 TeV) -1 35.9 fb CMS Preliminary h τ τ ll+

More exotic scenarios

• Higgs FCNC decays (H → eτ , H → µτ , t → Hc, . . .)

• Higgs decays to BSM gauge bosons (U (1)

dark

)

(24)

Axion-like particles (ALP)

|Cahe↵|/⇤2 [TeV 2] ��-� ��-� ��-� ��-� � �� -� ��-� ��-� ��-� � �� -� ��-� ��-� ��-� � �� -� ��-� ��-� ��-� � �� -� ��-� ��-� ��-� � �� -� ��-� ��-� ��-� � �� ma = 1 GeV ma = 10 GeV ma = 100 MeV LHC LHC27 FCC-hh 1% 0.1% 10% 1% 0.1% 10% 1% 0.1% 10%

[Bauer et al., arXiv:1808.10323]

ALP

: pseudo-Goldstone bosons of SB global symmetry (NP at scale Λ)

,→

light

pseudoscalar messangers of NP

L

eff

= L

SM

+L

a

+· · ·+

C

γγ

Λ

aF

µν

_F

_˜

µν

+· · ·+

C

ah

Λ

2

(∂

µ

_a)(∂

µ

a)φ

†

φ+

C

aZ

Λ

3

(∂

µ

_a)(φ

†

_iD

µ

φ)φ

†

φ+· · ·

LHC gives access in particular to:

H → Za → l

+

l

−

2γ

and

H → aa → 4γ

,→

models with

extra singlet-scalar

very important templates for future collider studies!

(25)

Could new physics be beyond reach?

102 ₁₀4 ₁₀6 ₁₀8 ₁₀10 ₁₀12 ₁₀14 ₁₀16 ₁₀18 ₁₀20 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

RGE scale Μ in GeV

Higgs quartic coupling Λ 3Σ bands in Mt= 173.3 ± 0.8 GeV HgrayL Α₃HMZL = 0.1184 ± 0.0007HredL Mh= 125.1 ± 0.2 GeV HblueL Mt= 171.1 GeV ΑsHMZL = 0.1163 ΑsHMZL = 0.1205 Mt= 175.6 GeV 107 108 109 1010 1011 1012 1013 1014 1016 120 122 124 126 128 130 132 168 170 172 174 176 178 180

Higgs pole mass Mhin GeV

Top pole mass Mt in GeV 1017 1018 1019 1,2,3 Σ Instability Stability Meta-stability

Buttazzo et al.

, arXiv:1307.3536

Including quantum effects in the study of the Higgs potential, for

M

h

≈ 125 GeV, a condition of criticality (λ → 0) is reached for

Λ

_{≈ 10}

10

_{− 10}

12

GeV

.

(26)