1. Hong-Jian He Tsinghua University
Higgs Theory
Hong-Jian He
Tsinghua University
CLHCP-2016, PKU, Beijing, December 17-19, 2016

2. LHC Run-1,2 Searches: No new discovery yet, but suggest more precise measurements are needed…
LHC New Physics ICHEP-2016 ……

3. What beyond the LHC ?
HL-LHC (up to 3/ab): more precise measurements, but not enough!
HE-LHC (28TeV)? bigger discovery potential, but technology+cost challenges...
Circular Higgs Factory CEPC (up to 250GeV):
→ Will surpass the precision of HL-LHC
→ Will be complementary to HE-LHC-28TeV (if built at all)…
→ 2nd-Phase SPPC will surpass LHC+ and fully explore TeV Scales
LHC(300/fb) + HL-LHC(3/ab)
M. E. Peskin, Snowmass Study,
arxiv:

4. Physics Motivations LHC discovery of h(125GeV) opens up a New Window
2012 is a Turning Point of particle physics.
LHC discovery of h(125GeV) opens up a New Window
for New Physics Searches.
Why is Higgs Boson so Important ?
Because it is the Origin of Mass Generations for
All Elementary Particles.
CEPC is a Higgs Factory for Precision Studies of
Higgs Boson Properties to pin down New Physics deviations .
SPPC is a discovery machine much beyond LHC, to uncover
new physics indicated by CEPC and to fully explore TeV Scales.

5. Making of the Standard Model
Key Role of Higgs Boson in SM:
Mass Generations for W/Z + Quarks/Leptons
Now, 4 Years after 2012:
Why & What New Physics Beyond SM ???

6. Physics Today 64N8 (2011) 29-33. Steven Weinberg：
Why is New Physics Beyond Standard Model (SM) required ??
“It is clearly necessary to go beyond the SM. There is a mysterious spectrum of quark and lepton masses and mixing angles that we have been staring at for decades, as if they were symbols in an unknown language, without our being able to interpret them. Also, something beyond the standard model is needed to account for cosmological dark matter.”

7. SM is Incomplete：Mass Puzzle
－ Yukawa Force is Flavor-dependent & Unnatural！
Why Quark/Lepton Masses differ so much at Tree Level?
－ What are the underlying Scales of Fermion Mass Generations？
－ Why is Higgs Mass itself Unnatural under Loop Corrections?

8. Spin-0 Higgs Boson Itself is New Physics !!!
a Unique Window to New Physics ??
Spin-0 Higgs Boson Itself is New Physics !!!

9. Representation of Lorentz Group
Isomorphic Lorentz Group: SO(3,1) ≈ SU(2)ⅹSU(2)
Irreducible Representation ( j ) of SU(2): j=0, ½, 1, 3/2, 2…
→ Representations of Lorentz Group: ( j, j’ ).
(½ , 0), (0, ½) → Quarks/Leptons; (½ , ½) → Gauge Bosons.
But, the Simplest Lorentz Group Representation is
Scalar Representation:
(0, 0)
★ Special Relativity predicted Scalar Particle (Higgs Boson)
more than 100 years ago !!!

10. Representation of Lorentz Group
Isomorphic Lorentz Group: SO(3,1) ≈ SU(2)ⅹSU(2)
Irreducible Representation ( j ) of SU(2): j=0, ½, 1, 3/2, 2…
→ Representations of Lorentz Group: ( j, j’ ).
(½ , 0), (0, ½) → Quarks/Leptons; (½ , ½) → Gauge Bosons.
The Simplest Lorentz Group Representation is
Scalar Representation: (0, 0) → Scalar (Higgs Boson!)
The Graviton of GR fits in Spin-2 Representation (1, 1).
Then, up to Spin-2, we expect possible new state with Spin-3/2
to fit in representation (1, ½ ), which may be a natural indication
of Gravitino of Spin-3/2 from Supergravity !

11. 3 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).
Stress: SM is not just a collection of particles! More importantly,
it includes Interaction Forces of elementary particles.
E.g. 3 Gauge Forces: U(1)em╳ SU(2)W ╳ SU(3)C .
Spin-0 Higgs not only joins SU(2)W , but also mediates 2
New Forces：Yukawa Forces + Self-Interacting Force.
No direct EXP measurements yet. LHC is far from sensitive.
Yukawa Forces generate all Fermion Masses. Yukawa Couplings vary within 6 orders: yt ≈ 1 → ye = O(10-6) , and have very irregular distributions. These require New Physics to explain.
Higgs Boson is the only particle having strict self-interactions among themselves.

12. Higgs (125GeV): Conclusion
Higgs is not only a New Particle, but also New Forces !!!
Even within SM Forces, strongly motivated to quantitatively probe
Type-2 + Type-3 New Forces:
★ Higgs Yukawa Forces
★ Higgs Self-Interaction-Forces
which are Most likely Places for New Physics !

13. Spin-0 Higgs Boson Itself is New Physics:
Mass Puzzle:
– W,Z Masses (EWSB via Higgs Boson)
– Fermion Masses (Quark/Lepton/Neutrino) ? Why large hierarchy?
– Higgs Boson Mass: Naturalness ? (needs to assume BSM New Cutoff)
Higgs Self-interactions ?
Vaccum Puzzle:
– Vacuum Instability or Metastability ?
– Vacuum Energy (Dark Energy) ?
Inflation Puzzle: – Higgs Boson as Inflaton ?
Dark Matter Puzzle: – Higgs Portal ? (H+H)XX, (H+H)R, ……
Anti-Matter Puzzle: – Baryogenesis, Leptogenesis, … ?

14. Spin-0 Higgs Boson Itself is New Physics ― example: Naturnalness
N-Naturalness: Deconstruction
― Propose a New Mechanism to
stabilize Electroweak Hierarchy.
― Introduce N copies of SM with
varying values of Higgs mass.
― Generically yields a sector whose
weak scale is parametrically removed
from the cuto by a factor of 1/√N.
― Ensuring that reheating deposits a majority of total energy density
into this lightest sector requires a modication of standard cosmological history, providing a probe of this mechanism.
― Current and near future experiments will explore much of the natural parameter space. The SUSY completions which preserve grand unification predict superpartners with mass below mW ╳ Mpl/MGUT∽ 10 TeV.
See: Nima Arkani-Hamed et al, arXiv:

15. SM is Incomplete: Fermion Mass Puzzle
－Yukawa Forces are Flavor-dependent & Unnatural！with Large Hierarchies.
－HL-LHC cannot test tiny 1st+2nd Family Yukawa Couplings (--can be zero! ).
－Question: if Light Fermion Masses (especially 1st +2nd Families) do not come
from h(125GeV), What are Scales for Fermion Mass Generations ??
Upper Bounds on Scales of Fermion Mass Generations:
2nd+3rd Families: TeV
1st Family: TeV
― All these bounds Tied to
O(3-100TeV) Scales !
Dicus and He,
PRL.94 (2005)
PRD.71 (2005)
See: Nima’s Overview
in preCDR

16. Higgs Factory: CEPC (240-250GeV)
LHC(8,13): 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 in10y Higgs Bosons !!

18. CEPC Detector Group

19. Effective Higgs Couplings: Gauge & Yukawa

20. Testing Higgs Couplings: CEPC vs LHC
Ge, HJH, Xiao, JHEP 10(2016)007 [arXiv: ]

21. Indirect Probe of Higgs related New Physics All can be formulated by: Model-Independent Effective Operators @ Dimension-6

22. Effective Operators & Sizes of New Physics
-- Higgs WG Report

23. CEPC Detector Group

24. CEPC Z-Pole and WW Threshold Scans
Detector Group

25. CEPC Sensitivity from EWPO+Z-Pole+MW+HO
Ge, HJH, Xiao, JHEP 10(2016)007 [arXiv: ]

26. Probing New Physics Scales: EWPO+Z-pole+MW vs Higgs Observables(HO)
EWPO +Z-pole+MW+HO
Ge, HJH, Xiao, arXiv:

27. Probing New Physics Scales: Higgs Observables Only
Yukawa-type Dim-6 Operators cannot be probed by (EWPO, Z-pole, MW).
Yukawa-type Dim-6 Operators can only be probed at Higgs Factory !!
~ Fermion Mass Generation!!
Probe New Physics Scales of
Fermion Mass Generation!!
Ge, HJH, Xiao, JHEP 10(2016)007

28. CEPC Probe of h3 Coupling
M. McCullough, arXiv:
Recall: HL-LHC probes h3 to 50%. ILC500 probes h3 to 27%.

29. Sensitivity to Higgs Self-Coupling h3
Comparison: h3 at CEPC(1, 3, 5/ab) and SPPC(3, 30/ab),
vs HL-LHC (3/ab):
-- Higgs WG Rept

30. Probe Higgs Self-Interaction h3 at SPPC
pp(100TeV) with (3, 30)/ab:
pp hh bbγγ
* Including more channels will further improve.
HJH, Ren, Yao, arXiv: , PRD(2015)

31. Probe Higgs Self-Interaction h3
pp(100TeV) with (3, 30)/ab:
pp hh bbγγ
With 3/ab (30/ab) Luminosity:
probe r to 13% (4.2%) precision .
probe x to 5% (1.6%) precision.
HJH, Ren, Yao, arXiv: , PRD(2015)

32. Probing h3 Coupling via gg→hh→WW*WW*
Q. S. Yan et al, 2016

33. Higgs Couplings at SPPC: h3 vs htt
Q. S. Yan et al,

34. Summary of CEPC-SPPC Precision Tests
CEPC produces 106 Higgs Bosons at 250GeV (5/ab).
Higgs Gauge & Yukawa Couplings ~ O(1%)
CEPC Indirect Probe of New Physics Scales:
up to ∽35TeV (44TeV for Og) from EWPO + Z-pole +MW+ HO.
up to ∽35TeV for some operators with EWPO+Z-pole alone.
up to ∽(13, 24, 15, 25)TeV for (b, c, τ, μ) only via HO.
CEPC 5/ab (10/ab) probes h3 Coupling ~ 35% (25%).
SPPC(100TeV) with 3/ab (30/ab) can sensitively probe
h3 Higgs Coupling ~ 5-13% ( %).

35. Overall Summary
Testing Higgs Interaction Forces (Couplings) is the KEY to New Physics.
CEPC is the Ideal Machine to Precision Higgs Physics + related New Physics.
New CEPC(90-250GeV) energy scales can ALL be described
by a set of Gauge-Invariant dim-6 Effective Operators (including Higgs)
which are fully general and model-independent.
At CEPC, it is very important to make both Z-Pole Measurements and
the Higgs Factory Measurements for probing New Physics.
CEPC(90-250GeV) can indirectly probe New Physics up to 20-35TeV range,
which complementarily cover the discovery reach of SPPC(100TeV).
CEPC 5/ab (10/ab) probes h3 Coupling ~ 35% (25%).
SPPC(100TeV) with 3/ab (30/ab) can sensitively probe
h3 Higgs Coupling ~ 5-13% ( %).
CEPC can sensitively probe Exotic Higgs Decays. CEPC & SPPC probe
EW phase transition …

36. SPPC SUSY discovery
Cohen et al, 2014

37. Electroweak Phase Transition Huang, Gu, Yin, Yu, Zhang, PRD2016

38. Sensitivities of future colliders
P. F. Yi et al
Investigation of DM-gamma interactions through mono-photon searches at e+e- colliders
Investigation of DM-Z interactions through mono-Z searches at e+e- colliders
Investigation of DM-Z’ interactions through mono-jet searches at hadron colliders

39. Q. H. Cao, Y. Li, B. Yan, Y. Zhang, Z. Zhang, 1604.07536

40. see: book of Nadis and Yau won Prose Prize 2016
From Great Wall to Great Collider
see: book of Nadis and Yau won Prose Prize 2016
Difference:
Great Wall was to defense the outsiders.
But, Great Collider is to attract outsides for International Collaborations!

41. Great Wall Great Collider (CEPC-SPPC)
Chinese Edition,
(translated by Xianyu & me).
More Excitements Ahead ！ Let us continue to work together and do good works !