Hong-Jian He Tsinghua University Higgs Boson: from Weak Interaction to Gravitation PKU, Beijing, December 5, 2015

LHC 2012 Higgs 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 Masses  Fermion Masses – Quark/Lepton/neutrino  Higgs Boson Mass: Naturalness  Higgs 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 Particles New Physics = New Phenomena ! New Physics = New Phenomena ! New Physics = New Principles !! New Physics = New Principles !! ─ Nima Arkani-Hamed ─ Nima Arkani-Hamed ?

Fundamental Forces vs Higgs Boson 5 th and 6 th 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 ： h 3 & h 4 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 ： h 3 & h 4 forces, ( concerns spontaneous EWSB and generating Higgs mass itself ).  In SM, Only Higgs can have Self-Interactions (involving exactly the same particle, h 3 & h 4 ), 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 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:

3 Types of Fundamental Forces in 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, GeV) + SPPC (pp, TeV) & CERN FCC-ee( GeV) +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 ( GeV)   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 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: 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 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 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., M h =125GeV << 1.2TeV.

Probing Higgs Self-Interactions and Heavier Higgs Boson

CEPC Probe of h 3 Coupling  Recall: HL-LHC probes h 3 to 50%. ILC500 probes h 3 to 83%. M. Mcullough,

Sensitivity to Higgs Self-Coupling h 3  Comparison: h 3 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 h 3 & h 4 couplings only via dim-6 operators! Under SU(2) c and using EOM, only 2 modify h 3 / h 4 vertex:

Probing Higgs Self-Interaction h 3 He, Ren, Yao, arXiv: , PRD(2015) pp(100TeV) with (3, 30)/ab: pp hh bbγγ

Probing Higgs Self-Interaction h 3 He, Ren, Yao, arXiv: , 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: , PLB(2015) （ ， ）

Probing Higgs Self-Interaction Hhh Lv, Du, Fang, He, Zhang, arXiv: , PLB(2015) （ ， ）

Natural EWSB from Scale Symmetry

Natural EWSB vs Scale Symmetry Farzinnia, HJH, Ren, PLB(2013), arXiv:

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 1. Serves as Higgs Boson for symmetry breaking to generate Inertial Masses for elementary particles. generate Inertial Masses for elementary particles. 2. Serves as Inflaton to drive Inflation of the Universe. 2. Serves as Inflaton to drive Inflation of the Universe.  So far, SM Higgs Boson only generates masses for all particle masses. all particle masses.  Can Higgs Boson drive Inflation as well to become the True God Particle of the Universe ?!! the True God Particle of the Universe ?!! 44 Higgs Boson vs Inflation

What drives the Inflation? E.g., ρ ≈ Λ = (10 16 GeV) 4, H ≈ GeV, N e = HΔt =

Picture of Inflation

Inflation Observables Planck: arXiv: Joint: arXiv:

SM Higgs Potential

Effective Theory: SM + GR

Jordan Frame Lagrangian

 into Einstein Frame:

Higgs Potential at Weak Scale:

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)

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 = 10 4 : Unitarity of Higgs Inflation Ren, Xianyu, HJH, JCAP 06 (2014) 032

 Higgs inflation near critical point with small ξ = : 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 = M P /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:

Higgs Inflation with TeV New Physics   Higgs Instability ~ GeV New Physics !   Inflation Scale ~ 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) (R) [arXiv: ]

Higgs Inflation in No-Scale SUSY GUT Higgs Inflation in No-Scale SUSY GUT Ellis, He, Xianyu, arXiv:   No-Scale Kahler Potential:   Superpotential up to dim-4:

  GUT breaking:   Doublet-triplet splitting: Higgs Inflation in No-Scale SUSY GUT Higgs Inflation in No-Scale SUSY GUT Ellis, He, Xianyu, arXiv:

  Inflation Potential and Inflaton as EW Higgs Boson: Higgs Inflation in No-Scale SUSY GUT Higgs Inflation in No-Scale SUSY GUT Ellis, He, Xianyu, arXiv:

  Higgs Inflation potential:   Kinetic term of inflaton:   Derive normalized inflaton: Higgs Inflation in No-Scale SUSY GUT Higgs Inflation in No-Scale SUSY GUT Ellis, He, Xianyu, arXiv:

  Two limits: Starobinsky-like potential Quadratic potential Higgs Inflation in No-Scale SUSY GUT Higgs Inflation in No-Scale SUSY GUT Ellis, He, Xianyu, arXiv:

Higgs Inflation in No-Scale SUSY GUT   Predictions for inflation observables: Ellis, He, Xianyu, arXiv: 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