1. The LHC and the problem of electroweak breaking
Riunione CSN4 di autunno
Rome, 22 September 2009
The LHC and the problem of electroweak breaking
G.F. Giudice

2. Our knowledge of matter and forces
General relativity
Yang-Mills theory
EW breaking sector
strong & EW quarks & leptons
particle masses
gravity

3. Our knowledge of matter and forces
General relativity
Yang-Mills theory
EW breaking sector
strong & EW quarks & leptons
particle masses
gravity
Elegance & simplicity: ruled by gauge symmetry principle
Few free parameters
Fare marvelously when compared with data

4. Our knowledge of matter and forces
General relativity
Yang-Mills theory
EW breaking sector
strong & EW quarks & leptons
particle masses
gravity
Arbitrary structure not determined by symmetry principle
Many free parameters in flavor sector
Quantum stability of EW scale
Elegance & simplicity: ruled by gauge symmetry principle
Few free parameters
Fare marvelously when compared with data

5. Our knowledge of matter and forces
General relativity
Yang-Mills theory
EW breaking sector
strong & EW quarks & leptons
particle masses
gravity
Arbitrary structure not determined by symmetry principle
Many free parameters in flavor sector
Quantum stability of EW scale
Elegance & simplicity: ruled by gauge symmetry principle
Few free parameters
Fare marvelously when compared with data
The least satisfying sector is also largely unexplored by experiments

6. The LHC plays a crucial role in the quest to expand our understanding of matter and forces
The LHC is a discovery machine aimed at the exploration of uncharted territories
Not just generic motivations, but solid reasons to expect new discoveries

7. 1) EW breaking problem: E
Scattering of longitudinal modes grows with E
 nonsense at E > TeV
New degrees of freedom or new dynamics must exist below TeV  solution within reach of the LHC
Higgs mechanism is the most plausible solution

8. 2) Quantum stability of the EW scale:
H2 very sensitive to high-energy corrections H t
Good reason to speculate the existence of new physics below TeV  spectacular discoveries at the LHC

9. 3) Dark Matter as thermal relic:
Our understanding is limited to 4% of the energy content of the universe
Good reason to believe that there is more than the SM
H0, T, MP
If not a coincidence  DM at the LHC

10. What do we learn from measuring the Higgs?
LEP: MH > GeV (95% CL)
Tevatron: 160 GeV < MH < 170 GeV (excluded 95% CL)
EW: MH < 153 GeV (95% CL)

11. The two best measurements of sin2W do not agree
This makes the argument for a light Higgs less compelling
LEPEWWG 07
The possibility of a heavy Higgs or no Higgs is still open

12. Evading mH upper bound from EWPT?
Actually, both the lower and upper limits on mH can be violated for certain modifications of the SM
Evading mH upper bound from EWPT?
Requires new physics with T=0.20.3 and S small
It can be obtained with a second Higgs doublet with no vev and no coupling to fermions or with a colour-octet Higgs doublet

13. Evading mH lower bound from LEP?
Controversial signal at 115 GeV
2.3 excess at 98 GeV
Change Higgs nature (mixing with other states)
New decay modes (new particles)

14. The Higgs mass carries important information on the underlying theory

15. Limits on TRH from the absence of thermal fluctuations
In the metastable regions, the Higgs mass carries information relevant for cosmology, since large primordial Higgs fluctuations are excluded
1-
2-
metastable
stable
unstable
Limits on TRH from the absence of thermal fluctuations
Limits on HI from the absence of quantum fluctuations during inflation

16. Understanding the mechanism of EW breaking is crucial for expanding our knowledge of the particle world
Its discovery has important intellectual implications in the understanding of the principles of nature
Discovering the Higgs is measuring the quantum excitations associated with a substance filling the vacuum
The LHC addresses the properties of the vacuum in nature

17. Understanding “nothing” has a long history
Western thought was influenced by Artistotle’s proof that vacuum cannot exist in nature
“Any motion will come to a standstill unless some external force keeps driving it” In empty space, why should a body stop in one place rather than another?
“Natural motions (without external agent) make heavy elements (earth, water) fall down and light elements (air, fire) go up” How could natural motions exist in empty space?
Absurd!
The principle of Horror Vacui: Nature will work in a way to prevent the appearance of vacuum

18. Experimental proof of the Horror Vacui principle
Empedocles’ Hydra

19. Experimental proof of the Horror Vacui principle
Empedocles’ Hydra

20. Experimental proof of the Horror Vacui principle
Empedocles’ Hydra

21. Experimental proof of the Horror Vacui principle
Empedocles’ Hydra

22. Evangelista Torricelli’s experiment (1644)
It took Torricelli and Pascal to understand that the effect is due to air pressure
air
Evangelista Torricelli’s experiment (1644)
Blaise Pascal’s vide dans le vide

23. Does nature abhor void after all?
Even if we remove all matter from space, we do not get “nothing”
The walls of the container emit blackbody radiation
Because of Heisenberg’s principle, virtual particles are produced out of nothing
Physical measurable effect: Casimir force

24. LHC:
Nature chooses a vacuum made of “something”, rather than “nothing”, because she saves energy this way
The LHC may discover that nature abhors “nothingness” and desires to fill “emptiness”
Paradoxically, the LHC will show that horror vacui was basically right, after all

25. Is the Higgs elementary or composite?
Determine the nature of the force that breaks EW
SM (with mH < 190 GeV)
SUSY (H,Q,L are all chiral superfields)
Elementary
pseudoGoldstone
Little Higgs
Gauge-Higgs unification
Holographic Higgs ….
Composite: Higgs is a light remnant of a strong force
Signatures at LHC? New resonances, W’,Z’,t’, KK excitations
Distinctive model-independent features of compositeness at the LHC in Higgs interactions

26. General structure of a composite Higgs
quarks, leptons & gauge bosons
strong sector
Communicate via gauge (ga) and (proto)-Yukawa (i)
In the limit I, ga =0, strong sector contains Higgs as Goldstone bosons
Ex. H = SU(3)/SU(2)U(1) or H = SO(5)/SO(4)
Higgs boson described by -model of strong EW dynamics, distorted by gauge and Yukawa interactions

27. Deviations of order v2/f2, where 4f is the compositeness scale 
The effects in h BRh are of the order of
Deviations from SM Higgs couplings can test v2 / f2 up to
LHC 2040 %
SLHC %
ILC %  4f = 30 TeV

28. Genuine signal of Higgs compositeness at high energies
In spite of light Higgs, longitudinal gauge-boson scattering amplitude violates unitarity at high energies h WL
Modified coupling
VLVL scattering is an important channel, even for light Higgs

29. Strong gauge-boson scattering  strong Higgs production
Higgs is viewed as pseudoGoldstone boson: its properties are related to those of the exact (eaten) Goldstones: O(4) symmetry
Strong gauge-boson scattering  strong Higgs production
Can bbbb at high invariant mass be separated from background? h  WW  leptons is more promising
Sum rule (with cuts |and s>M2):

30. CONCLUSIONS
The LHC addresses questions of broad and universal intellectual value
Discovering the Higgs is not just finding a new particle: it is unveiling the phenomenon that gives rise to a fundamental scale in physics
The discovery of the mechanism of EW breaking will open new questions, some of which will be addressed by the LHC