Hong-Jian HeTsinghua University

Higgs Boson: from Weak Interaction to Gravitation

PKU, Beijing, December 5, 2015

LHC Discovery @ 2012Higgs Boson (125GeV) － God

Particle??High Energy Physics comes to

a New Historical Turning Point, posing :

─ New Opportunities ─ New Questions ─ New Challenges

& Interface with Cosmology & Quantum Gravity

Making of the Standard Model

SM Structure seems complete, but ....Recall: situation around 1900 ─

People mis-claimed: Newton Mechanics was complete!so physics reached “the End”. → wrong !

But, it was just at the Start of series of New Revolutions, in 1905 and afterwards ─ SR, GR, QM, QFT ....

Spin-0 Higgs Boson Itself is

New Physics !!!

Representation of Lorentz Group Equivalent Lorentz Group Group Generators of :

Lorentz Algebra:

Irreducible Representation (j) of SU(2) (j=0, ½, 1, 3/2…) can be used to construct representations of Lorentz Group: ( j, j’ ).

The Simplest Lorentz representation is Scalar Representation:

(0, 0)Special Relativity predicted possible Scalar Particle (Higgs Boson) !!!

Spin-0 Higgs Boson Itself is New Physics:

EWSB – W,Z MassesFermion Masses – Quark/Lepton/neutrino

Higgs Boson Mass: NaturalnessHiggs Self-interactions

Vacuum Structure (Stability…)Vaccum Energy (Dark Energy…)

Higgs boson as Inflaton Scalar Dark Matter from Higgs sector ?

CP Violation: Baryogenesis, Leptogenesis…

New Physics = New Particles

New Physics = New Phenomena !

New Physics = New Principles !!

─ Nima Arkani-Hamed

?

Fundamental Forces vs Higgs Boson

5th and 6th Forces ？ ?— Yukawa Force— Higgs Self-Interaction

3 Types of Fundamental Forces in SM Itself

1. Gauge Forces ： mediated by Spin-1 Vector Boson.

2. Yukawa Forces ： mediated by Spin-0 Higgs Boson.

3. Higgs Self-Interaction Force ： h3 & h4 forces,(concerns spontaneous EWSB and generating Higgs mass itself).

Type-2 & Type-3 are two New Fundamental Forces, Solely due to Spin-0 Higgs, which were never directly probed before, despite they already exist in SM !!!

3 Types of Fundamental Forces in SM Itself

1. Gauge Forces ： mediated by Spin-1 Vector Boson.

2. Yukawa Forces ： mediated by Spin-0 Higgs Boson.

3. Higgs Self-Interaction Force ： h3 & h4 forces,(concerns spontaneous EWSB and generating Higgs mass itself).

In SM, Only Higgs can have Self-Interactions (involving exactly the same particle, h3 & h4 ), but not all other fundamental particles (as forbidden by their spin & charge) !

Spin-0 Higgs Boson is Unique in many ways, but all its associated forces are not yet directly tested, especially, the New Type-2 and Type-3 forces mediated by Higgs Itself !

3 Fundamental Forces in SM Itself: Status

LHC Run.1+2 only give some good tests on Gauge Forces . Higgs Yukawa Force is Flavor-dependent, with Large Hierarchy ! LHC only has weak sensitivity to Yukawa couplings of h-τ-τ, h-b-b, h-t-t at order of 10-15% . LHC cannot probe Most Other Yukawa Couplings ! LHC can hardly probe Higgs Self-Interaction ! LHC cannot establish h(125GeV) as God Particle !

M. E. Peskin, Snowmass Study, arxiv:1312.4974

3 Types of Fundamental Forces in SM Itself

Conclusion-1:

Even within SM Forces, we are strongly motivated to quantitatively test Type-2 + Type-3 New Forces (Higgs Yukawa Forces and Self-Interaction-Forces)

mediated by Higgs Boson.

This requires to Go Beyond the CERN LHC!

High Energy Circular Colliders: CEPC (ee, 240-250 GeV) + SPPC (pp, 50-100TeV) & CERN FCC-ee(250-350GeV) +pp(80-100TeV)

A rather Unique Opportunity: Timing + Physics

E.g.

From the Great Wall to

the Great Collider ,

by Steve Nadis and S. T. Yau

International Press of Boston 出版。翻译本 :

《从万里长城到巨型对撞机》

(translation by Z.Z.Xianyu & HJH)

即将出版。13

Higgs Factory: CEPC (240-250GeV)

LHC-8 tells us: h(125) is SM-like. Precision Test is Crucial !

CEPC produces h(125) mainly via ee hZ and ee ννh .

CEPC makes indirect probe to New Physics !

CEPC designed: 5/ab for 2 detectors in 10y. 106 Higgs Bosons !!

CEPC: Summary of Detector Simulations

─ CEPC Detector WG Rept

Effective Higgs Couplings: Gauge & Yukawa

Effective Operators & Sizes of New Physics

─ Higgs WG Report

( M = Λ )

CEPC Sensitivity to Higgs Coupling

─ CEPC Higgs WG Report, Ge and He

Testing Higgs Coupling: CEPC vs LHC

─ CEPC Higgs WG Report, Ge and He

Dimension-6 Effective Operators

( M = Λ )

Example: CEPC Reach of New Physics Scale

Craig, Farina, McCullough, Perelstein, arXiv:1411.0676

Probing New Physics Scale associated with dim-6 Operators.

For ee hZ at CEPC(5/ab), including current precision data.

SM is Incomplete: Mass Puzzle

－ Yukawa Force is Flavor-dependent & Unnatural ！ － Why Quark/Lepton Masses differ so much at Tree level?

－ What are underlying Scales of Fermion Mass generations ？－ Why is Higgs Mass itself Unnatural under radiative corrections?

h

SM is Incomplete: Mass Puzzle

Only (t, W, Z, h) stand out at Weak Scale!

－ holds within 2% accuracy!

SM: (Un)Naturalness of Matter Masses

Only Top & Neutrino masses are Natural (adding Right-handed Neutrinos for Seesaw):

Why All Other Yukawa’s so tiny ?? e.g.,

Note: in actual case, the New Physics unitaritizing the theory needs not to saturate unitarity bound! e.g., Mh=125GeV << 1.2TeV .

Probing Higgs Self-Interactions

and Heavier Higgs Boson

CEPC Probe of h3 Coupling

Recall: HL-LHC probes h3 to 50%. ILC500 probes h3 to 83%.

M. Mcullough, 1312.3322

Sensitivity to Higgs Self-Coupling h3

Comparison: h3 at CEPC(1, 3, 5/ab) and SPPC(3/ab), vs HL-LHC (3/ab):

-- Higgs WG Rept

Probing Higgs Self-Interactions

SM:

New Physics could modify h3 & h4 couplings only via dim-6 operators!

Under SU(2)c and using EOM, only 2 modify h3/h4 vertex:

Probing Higgs Self-Interaction h3

He, Ren, Yao, arXiv:1506.03302, PRD(2015)

pp(100TeV) with (3, 30)/ab:pp hh bbγγ

Probing Higgs Self-Interaction h3

He, Ren, Yao, arXiv:1506.03302, PRD(2015)

With 3/ab (30/ab) Luminosity:probe r to 13% (4.2%) precision .probe x to 5% (1.6%) precision.

Probing Higgs Self-Interaction Hhh

Lv, Du, Fang, He, Zhang, arXiv:1507.02644, PLB(2015)

（ ， ）

Probing Higgs Self-Interaction Hhh

Lv, Du, Fang, He, Zhang, arXiv:1507.02644, PLB(2015)

（ ， ）

Natural EWSB from Scale Symmetry

Natural EWSB vs Scale Symmetry

Farzinnia, HJH, Ren, PLB(2013), arXiv:1308.0295

Farzinnia, HJH, Ren, PLB(2013), arXiv:1308.0295

Higgs Inflation

God Particle as Origin of Inflation:

A Fundamental Scalar may do one of 2 possible jobs:

1. Serves as Higgs Boson for symmetry breaking to

generate Inertial Masses for elementary particles.

2. Serves as Inflaton to drive Inflation of the Universe.

So far, SM Higgs Boson only generates masses for

all particle masses.

Can Higgs Boson drive Inflation as well to become

the True God Particle of the Universe ?!!

44

Higgs Boson vs Inflation

What drives the Inflation?

E.g., ρ ≈ Λ = (1016 GeV) 4, H ≈ 1014 GeV, Ne = HΔt = 50-60.

Picture of Inflation

Inflation Observables

Planck: arXiv: 1502.02114 Joint: arXiv:1502.00612

SM Higgs Potential

Effective Theory: SM + GR

Jordan Frame Lagrangian

into Einstein Frame:

Higgs Potential at Weak Scale:

Conventional SM Higgs Inflation

Conventional SM Higgs Inflation

Bezrukov & Shaposhnikov, PLB 659(2008)703

?

Dimension-6 interactions in Einstein frame:

ξ Coupling induced corrections to Gauge-Higgs vertex:

Nonminimal Coupling in EF: New Interactions

Xianyu, Ren, HJH, PRD 88 (2013) 096013

Unitarity Analysis for Weak Boson Scattering

Unitarity Bound on Higgs-Gravity Coupling:

Ren, Xianyu, HJH, JCAP 06 (2014) 032

ξ

Unitarity bound on the Higgs-Gravity coupling |ξ| :

Unitarity of Higgs Inflation

Ren, Xianyu, HJH, JCAP 06 (2014) 032

Conventional Higgs inflation with large ξ = 104 :

Unitarity of Higgs Inflation

Ren, Xianyu, HJH, JCAP 06 (2014) 032

Higgs inflation near critical point with small ξ = 10-102 :

Unitarity of Higgs Inflation

Ren, Xianyu, HJH, JCAP 06 (2014) 032

Collider Probe of Higgs-Gravity Coupling

W + W+ W + W+

Ren, Xianyu, HJH, JCAP 06 (2014) 032

at LHC (14TeV): at pp(100TeV):

( Λ = MP /ξ )

So, Unitarity of Higgs Inflation is OK .

But, Instability Problem occurs at Loop Level:

Origin of Instability in SM Higgs Potential

Instability of Higgs Potential in SM

Spencer-Smith: arXiv:1405.1975

Higgs Inflation with TeV New Physics

Higgs Instability ~ 1011 GeV

New Physics ! Inflation Scale ~ 1016 GeV

Adding Minimal New Physics: an additional pair of singlet scalar and fermion at TeV scale:

HJH & Xianyu, JCAP 1410 (2014) 019

Running of scalar interactions:

Higgs Inflation with TeV New Physics

HJH, Xianyu, JCAP 1410 (2014) 019

Higgs Inflation with TeV New Physics

Modified beta-function:

Four Samples:

HJH, Xianyu, JCAP 1410 (2014) 019

New Particles at O(TeV) can be tested at LHC(14TeV) and future pp(50-100TeV) collider.

Higgs Inflation with TeV New Physics

Inflation potential in h-direction:

HJH, Xianyu, JCAP 1410 (2014) 019

Higgs Inflation with TeV New Physics

Inflation Potential in (h,S)-plane:

HJH, Xianyu, JCAP 1410 (2014) 019

Higgs inflation with TeV New Physics

Predictions for inflation observables:

HJH, Xianyu, JCAP 1410 (2014) 019

Critical Region

Large ξ Region

Higgs Inflation in No-Scale SUSY GUT

SUSY: a natural solution to Higgs instability

Inflation Scale ~ GUT Scale GUT Inflation

No-Scale SUGRA: simple string compactification

A viable realization in no-scale SU(5) GUT

Ellis, He, Xianyu, PRD.91(2015)021302 (R) [arXiv:1411.5537]

Higgs Inflation in No-Scale SUSY GUTEllis, He, Xianyu, arXiv:1411.5537

No-Scale Kahler Potential:

Superpotential up to dim-4:

GUT breaking:

Doublet-triplet splitting:

Higgs Inflation in No-Scale SUSY GUTEllis, He, Xianyu, arXiv:1411.5537

Inflation Potential and Inflaton as EW Higgs Boson:

Higgs Inflation in No-Scale SUSY GUTEllis, He, Xianyu, arXiv:1411.5537

Higgs Inflation potential:

Kinetic term of inflaton:

Derive normalized inflaton:

Higgs Inflation in No-Scale SUSY GUTEllis, He, Xianyu, arXiv:1411.5537

Two limits:

Starobinsky-like potential

Quadratic potential

Higgs Inflation in No-Scale SUSY GUTEllis, He, Xianyu, arXiv:1411.5537

Higgs Inflation in No-Scale SUSY GUT

Predictions for inflation observables:

Ellis, He, Xianyu, arXiv:1411.5537

ζ =1: quadratical inflation. With small deviation δ : ζ =0: Starobinsky-like inflation

Beyond Higgs Boson(125) ??!!

All Particle Masses & Inflation of Universe ?! ….. Connections to SUSY, DM, CPV, Baryogenesis? …..

h(125) is just the Tip of a giant Iceberg ! To open a Door to New Phys beneath water ?

Is Higgs Boson New Physics by Itself