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

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

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

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

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

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

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

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

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

What do we learn from measuring the Higgs? LEP: MH > 114.4 GeV (95% CL) Tevatron: 160 GeV < MH < 170 GeV (excluded 95% CL) EW: MH < 153 GeV (95% CL)

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

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

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)

The Higgs mass carries important information on the underlying theory

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

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

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

Experimental proof of the Horror Vacui principle Empedocles’ Hydra

Experimental proof of the Horror Vacui principle Empedocles’ Hydra

Experimental proof of the Horror Vacui principle Empedocles’ Hydra

Experimental proof of the Horror Vacui principle Empedocles’ Hydra

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

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

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

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

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

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 10 % ILC 1 %  4f = 30 TeV

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

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):

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