shape of higgs potential at future colliders

C.-P. Yuan

Tyler Corbett, Aniket Joglekar, Hao-Lin Li, Jiang-Hao Yu, JHEP 1805 (2018) 061

Hao-Lin Li, Ling-Xiao Xu, Jiang-Hao Yu, Shouhua Zhu, 1904.05359

Pankaj Agrawal, Debashis Saha, Ling-Xiao Xu, Jiang-Hao Yu, C.-P. Yuan, 1905.xxxxx

C.-P. YuanMichigan State University

Wu-Ki Tung Endowed Professor

May 11, 2019

NHWG Regular Meeting @ Osaka University

Shape of Higgs Potentialat Future Colliders

1

C.-P. Yuan

Higgs BosonHiggs discovery completes the standard model spectrum

Given Higgs mass, all parameters in Higgs sector are predicted!

2

For the theoretical discovery of the Brout-Englert-Higgs mechanism

The Standard Model of Particle Physics

Gauge Symmetry ( Gravity is not included )

Color Left Hyper charge

UnificationWeak Ele

of a ctromagnetnd c i

( IntStrong eraction)

QCD W

(3) (2) (

EAK QE

)

D

1SU SU U

Spontaneously Broken(Higgs Mechanism)

E.M.(1)U

QED(Electromagnetic Interaction)

Higgs Mechanism in the SM

To generate MW and MZ

22

2vL D D

To generate

L RfF fy

v

2f f

vm y

fm

v

1

2WM gv

v

f fWW

A fundamental (complex) scalar doublet:

†

0

The cause of Electroweak Symmetry Breaking

The origin of Flavor Symmetry Breaking(MW = 80.42 GeV, MZ = 91.187 GeV)

(Quarks and Leptons have diverse masses.)

C.-P. Yuan 8

define and *

2i

†† †,

The Higgs-sector Lagrangian becomes:

2† † 21 ( )

2 4H Tr D D Tr v

3'D ig W ig B

The Higgs vacuum expectation value breaks the global symmetry

give rise to 3 Goldstone bosons, which form a triplet of SU(2)V

(2) (2) (2)L R VSUSU SU

Custodial symmetry

Global symmetry (2) (2)L RSU SUIn the limit g’ →0

+

0=

，

“custodial symmetry”

(2) (2) (2)L R VSU SU SU

Custodial Symmetry is an important part of any theory of EWSB!

Due to residual SU(2)V “custodial symmetry”, for g’ →0, the SU(2)V gauge boson are degenerate

This, plus , tell us 0m

2

222

2 '

' '2

2

g

gvM

g gg

gg g

and hence2

2 2 1cos

W

Z W

M

M

(at tree level)

Global symmetry: SU(2)V

It is broken in the SM by hypercharge and Yukawa couplings.

• At tree level, in the SM,

• Considering higher order corrections

• Related to Higgs-boson mass

• Related to top-quark mass

Custodial symmetry

2

2 2 1cos

W

Z W

M

M

2 2

2 2

0 01 WW ZZ

W Z

p p

M M

22

2 ln ( )16 H

gm

2

2 2

116

tm

v

Veltman’s screening theorem

The electroweak precision data (EWPD)

( MZ is one of the input parameters )

0.00030.0004

0.00200.0011

1.0004

1.00

(Fit Higgs search)

with

witho (Fit Higgs seat08 u rch)PDG 2013

Is the new boson an elementary particle?

• SM Higgs boson is an elementary particle.

• SM predicts a definite ratio between

HVV and HHVV couplings.

(at tree level)

• For a strongly interacting Higgs-like particle, this relation may not hold.

HHVV needs to be measured.

2

2 VMi g

v

2

22 VMi g

v

Higgs self couplings(probe Higgs potential)

C.-P. Yuan 13

2 2 3 4 2 2 3 41 1 1 4 2 2 4H H HH vH H M H M H H

The scalar sector Lagrangian:

Higgs self-couplings:2

3

6

HMi

v

i v

2

23

6

HMi

v

i

Higgs boson mass: 2 2 22 2HM v

C.-P. Yuan

Known Known

Higgs couplings to gauge boson and fermion are measured

Any deviation from the SM in the Higgs sector is new physics!

3

Use running quark mass to minimize higher order corrections

• Beyond leading order, large logs can be absorbed into running quark mass

resum large logs

•

• For example, naively, we expect

But,

4.18, 1.275, 1.777 (GeV)

2.79, 0.621, 1.744 (GeV)b b c c

b H c H H

m m m m m m

m m m m m m

2

c c2

(H cc) N ~ (N 3)(H )

1.5cmBr

Br m

2 2

2 2

3 (m )(H cc) 3 (0.621)(H ) (m ) (1.7 4

0)

.44

c H

H

mBr

Br m

2

2lnq

Q

m

PDG 2013

arXiv: 1112.3112

Running Quark Mass

In the on-shell scheme, the quark mass counterterm

2

2

13 ln 4 3ln 44

SF

m mC

m

1bare ren

mm m

m

2

21 3 ln 4 finite number4

pole S Fm C m

v Q

①

whereren polem m

and

With one-loop QCD correction, the effective Yukawa coupling is

43FC

Running Quark Mass

2ren pole

21 3 ln finite number4S F

m m C m

v Q

②

ren pole pole 1 SFm m m C

③

We can rewrite the effective Yukawa coupling in as

where the renormalized mass, evaluated at pole mass scale, is

Introduce the running mass (in the scheme) MS

2

ren pole 2

31 ln4

S FC mm Q m m

1 finite number

4S F

m Q C

v

MS

② =① =

①

Running Quark Mass

1

20

( ) ( )( ) ( )ln

i

q SS q i q

i

d mm m

d

2

2 10

( ) ( )( )d ln

i

S SS i i

i

d

The evolution of quark mass mq(μ)

The running of strong coupling ( )s

Resum large logs to all orders in Yukawa coupling using running quark mass.

Testing Yukawa couplingusing running quark mass

2.79 (GeV)

0.621

1.744

b H

c H

H

m m

m m

m m

C.-P. Yuan

Known UnknownHiggs self coupling is not yet determined.

Shape of Higgs potential could be different from the SM!

ATL-PHYS-PUB-2018-053

4

C.-P. Yuan

Higgs Portal to New Physics

Top-down approach: new physics models

Bottom-up approach: Higgs effective field theory (HEFT)

5

C.-P. Yuan

SMEFT Framework

SM effective field theory

Higgs effective field theory

6

C.-P. Yuan

Fundamental Higgs

Higgs potential in SM Higgs potential in SMEFT

7

C.-P. Yuan

UV Models

Scalar Extension

Fermion Extension Gauge Extension

Higgs Singlet

Higgs Doublet

Higgs Triplet

Minimal Dark Matter

Type-II seesaw

Type-I seesaw

Vectorlike fermion

Singlet-doublet dark matter

Heavy 4th gen.

U(1) extensions

SU(2) extensions

G331

Pati-Salam

GUT

Vectorlike top

… … …

8

C.-P. Yuan

New Physics ModelsScalar Extension

Tree level generate?

Scalar singlet

Group theory?

2HDM Triplet/Seesaw Quadruplet

Scalar Extension

Gauge ExtensionFermion Extension

[Corbett, Joglekar, Li, Yu, 2018]

9

C.-P. Yuan

Fundamental HiggsScalar singlet 2HDM Triplet/Seesaw Quadruplet

Integrate out heavy scalars

Constrained by EWPT and Single Higgs data

[Corbett, Joglekar, Li, Yu, 2018]

10

C.-P. Yuan

Fundamental HiggsEWPT and Single Higgs data put constraints on di-Higgs cross section

[Corbett, Joglekar, Li, Yu, 2018] 11

C.-P. Yuan

Pseudo Nambu-Goldstone Higgs

Higgs as pseudo Nambu-Goldstone Boson (PNGB)

Pseudo Nambu-Goldstone HiggsPion potential

The top partner triggers EWSB!

13

C.-P. Yuan

Top Partner

The top partner also protects the Higgs mass

Usually need to introduce symmetry with composite states

Solving hierarchy problem and realize EWSB

C.-P. Yuan

PNGB Higgs Models

Minimal Composite Higgs (MCH) Left-Right Z2

Composite Twin Higgs (CTH) Minimal Neutral Naturalness

[Xu, Yu, Zhu, 2018] [Chacko, Goh, Harnik 2006]

[Agashe, Contino, Pomarol 2004] [Li, Xu, Yu, Zhu, 2019]

Neutral naturalness = QCD neutral top partner: mirror Z2 symmetry

Composite Higgs framework: collective symmetry

15

C.-P. Yuan

PNGB Chiral LagrangianHiggs nonlinearity effect is not included in SMEFT

16

C.-P. Yuan

Electroweak Chiral Lagrangian

Composite Higgs Left-Right Z2 Twin Higgs Minimal NN

[Li, Xu, Yu, Zhu, 2019]

[Agrawal, Saha, Xu, Yu, Yuan, 2019]

17

C.-P. Yuan

Pseudo Nambu-Goldstone Higgs

Similar to 2HDM, di-Higgs cross section is larger than SM one[Agrawal, Saha, Xu, Yu, Yuan, 2019]

18

C.-P. Yuan

Shape of Higgs Potential

Coleman Weinberg HiggsPseudo Nambu-Goldstone Higgs Tadpole-induced Higgs

Very different analytic Higgs behavior from SMLandau-Ginzburg Higgs

19

C.-P. Yuan

Coleman Weinberg Higgs

Radiative correction triggers EWSB!

Coleman Weinberg HiggsTree-level potential[Coleman, Weinberg 73], [Gildner, Weinberg 76] ,

…

Self-coupling runs to negative

Classically scale invariant theory

20

C.-P. Yuan

Coleman Weinberg HiggsDimensional transmutation: quartic coupling induces minmum

21

C.-P. Yuan

Technicolor

Tadpole Induced HiggsTechnicolor vs Higgs discovery

[Simmons 1989], [Carone, Georgi 1994] , [Galloway, etc, 2013]

…

Long-live technicolor: Bosonic technicolor

Violate unitary in WL-WL scattering

Predict no Higgs …

Elementary Higgs22

C.-P. Yuan

Tadpole Induced HiggsBosonic technicolor (Induced EWSB)

Higgs self couplings are induced by integrating out heavy states

[Galloway, etc, 2013]

23

C.-P. Yuan

How to Distinguish Them?

SMEFT PNGB Higgs CW Higgs Tadpole Higgs


24

C.-P. Yuan

Theoretical Constraints

Perturbative tree-level unitarity constraint

(s-wave partial wave)25

C.-P. Yuan

Higgs Self Coupling

SM

Tadpole HiggsMCHM

CTHM

Coleman-Weinberg

Models

Di-Higgs production

Make use of large difference in Higgs self coupling

26

C.-P. Yuan

Di-Higgs Production

[Many references here … ]

27

C.-P. Yuan

Di-Higgs Production

including tthh interference terms

Take LO cross sectionNLO K factor = 1.6

[Dawson, Dittmaier, Spira, 1998] 28

C.-P. Yuan

Discriminating Models via HH Production


14% accuracy (1 sigma CL) for SM xsec at 27 TeV[Goncalves, Han, Kling, Plehn, Takeuchi, 2018]

29

C.-P. Yuan

Discriminating Models via HH Production

5% accuracy (1 sigma CL) for SM xsec at 100 TeV[Goncalves, Han, Kling, Plehn, Takeuchi, 2018]


30

C.-P. Yuan

Confirm quartic coupling

Quartic Higgs Coupling

SMTadpole Higgs

MCHM

CTHM

Coleman-Weinberg

Models

tri-Higgs production

To further determine the shape of Higgs potential

31

C.-P. Yuan

Quartic Higgs CouplingThree Higgs production at 100 TeV collider

Indirect search via HH @ two-loop

[Chen,Yan, Zhao, Zhong, Zhao, 2016][Papaefstathiou, Sakurai, 2016]

…

[Borowka, Duhr, Maltoni, Pagani, Shivaji, Zhao, 2018]Di-Higgs at HL-LHC and 100 TeV collider

[Borowka, Duhr, Maltoni, Pagani, Shivaji, Zhao, 2018]

32

C.-P. Yuan

Tri-Higgs Production


LO cross section

33

C.-P. Yuan


LO cross section, NLO K factor ~ 2.


[Maltoni, Vryonidou, Zaro, 2014]34

C.-P. Yuan


20% accuracy (1 sigma CL) for SM xsec at 100 TeV


[Chen,Yan, Zhao, Zhong, Zhao, 2016]35

C.-P. Yuan

Determine Quartic Coupling

SM

MCHMColeman-Weinberg

36

C.-P. Yuan

SummaryExplore Higgs potential beyond Landau-Ginzburg Higgs potential

SMEFT cannot be utilized due to non-decoupling of new particles.

Coleman Weinberg Higgs

Pseudo Nambu-Goldstone Higgs Tadpole-induced Higgs

Discriminate shape of Higgs potential via di/tri-Higgs production

SMTadpole Higgs

MCHM

CHTM

Coleman-Weinberg

Landau-Ginzburg Higgs

37

C.-P. Yuan

Backup Slides

38

C.-P. Yuan

Top Quark Form Factor Approach


Heavy composite states

[Li, Xu, Yu, Zhu, 2019]

Generalized top-Higgs Lagrangian

arXiv:1904.05359

39

C.-P. Yuan

Low Energy Theorem

[Li, Xu, Yu, Zhu, 2019]

Top quark couplings to gluon gluon

Top-Higgs couplings

40

C.-P. Yuan

Radiative Higgs Potential

Coleman-Weinberg effective potential [Li, Xu, Yu, Zhu, 2019]

41

C.-P. Yuan

Higgs Couplings


Form factor method

Low energy theorem

[Li, Xu, Yu, Zhu, 2019]

Radiative Higgs potential

42

C.-P. Yuan

Tree-level Vacuum Stability

45

shape of higgs potential at future colliders

Documents