Particle Physics at the LHC Start

Particle Physics at the

LHC Start

El Escorial - 25 November ’0 9

Guido Altarelli

Roma Tre/CERN

The LHC physics run will soon start, .... finally!

Top physics priorities at the LHC (ATLAS&CMS):

•

Clarify the EW symmetry breaking sector

•

Search for new physics at the TeV scale

•

Identify the particle(s) that make the Dark Matter in the Universe

•

ALICE: Heavy ion collisions & QCD phase diagram

•

LHCb: precision B physics (CKM matrix and CP violation)

Also:

At this point, fresh input from experiment is badly needed Beams are circulating in the LHC. First collisions starting now.

[LEP was closed at the end of 2000] Start at 3.5 TeV per beam

The SM is a low energy effective theory

(nobody can believe it is the ultimate theory)

It happens to be renormalizable, hence highly predictive.

And is well supported by the data.

However, we expect corrections from higher energies not only from the GUT or Planck scales but also from the TeV scale (LHC!)

But even as a low energy effective theory it is not satisfactory QCD + the gauge part of the EW theory are fine,

but the Higgs sector is so far only a conjecture

Particle physics at a glance

QCD stands as a very solid building block of the SM

QCD

No essential problems of principle in its foundations Comparison with experiment is excellent

Marvelous progress in techniques to extract precise predictions (higher order perturbative, resummation, event simulation, non perturbative, lattice...)

Very important for the LHC preparation: understanding QCD processes is a prerequisite for all possible discoveries

A complex theory and it is difficult to make its content explicit

How do we get predictions from QCD?

• Non perturbative methods

•Lattice simulations (great continuous progress) •Effective lagrangians

* Chiral lagrangians

* Heavy quark effective theories

* SCET

* NRQCD

* AdS/CFT correspondence ••••••

•QCD sum rules

•Potential models (quarkonium)

• Perturbative approach

Based on asymptotic freedom.

It still remains the main quantitative connection

to experiment. Also difficult: α

_s

relatively large

Great progress in lattice QCD

From postdiction to prediction Unquenching

a -> smaller L -> larger m_q -> 0

hadron spectrum smaller m_q

flavour physics

The QCD phase diagram Studied on the lattice and probed by

colliding heavy ions at SPS, RHIC

Establishing confinement Studying deconfinement

& chiral restoration Quark-gluon plasma

high T and density

ALICE will continue this study at the LHC

gg->(N-2)g

QCD for LHC

Fantastic technical skill!!

Essential for the LHC

General algorithms for computer NLO calculations eg the dipole formalism

the antenna pattern Kosower....

Catani, Seymour,...

Matching matrix elements and parton showers

e.g. MC@NLO based on HERWIG POWHEG

Frixione, Nason, Webber Nason, Ridolfi

QCD event simulation

A big boost in the preparation to LHC experiments

Parton showers

collinear emissions factorize

Perturbative (+ resumm.s)

L= large log eg L=log(p_T/m)

hadronization added

Complementary virtues:

the hard skeleton plus the shower development and hadronization

Important recent work on jet recombination algorithms

G. Salam et al SISCone, anti-k_T

It is essential that a correct jet finding is implemented by LHC experiments for an optimal matching of theory and experiment

The SM is a low energy effective theory

(nobody can believe it is the ultimate theory)

It happens to be renormalizable, hence highly predictive.

And is well supported by the data.

However, we expect corrections from higher energies not only from the GUT or Planck scales but also from the TeV scale (LHC!)

But even as a low energy effective theory it is not satisfactory QCD + the gauge part of the EW theory are fine,

but the Higgs sector is so far only a conjecture

Particle physics at a glance

V

_Higgs

= V

₀

− µ

²

φ

^†

φ + λ φ ( )

^†

φ

²

+ [ ψ

^Li

Y

^ij

ψ

^Rj

φ + h. c.]

The main problems of the SM show up in the Higgs sector

Vacuum energy V_0exp~(2.10^-3 eV)⁴

Origin of quadratic divergences.

Hierarchy problem

Possible instability depending on m_H

The flavour problem:

large unexplained ratios of Y_ij Yukawa constants

The Higgs problem is central in particle physics today

The Standard EW theory: L = L

symm

+ L

Higgs

L symm: well tested (LEP, SLC, Tevatron…), L Higgs: ~ untested

No Higgs seen at LEP2 -> m_H > 114.4 GeV (95%cl)

Rad. corr's -> m_H < 186 GeV (95%cl, incl. direct search bound) v=<φ>=~174 GeV ; m_W=m_Zcosθ_W doublet Higgs

with

All

we know from experiment about the SM Higgs:

In the H search the Tevatron has now reached the SM sensitivity

12 fb^-1 by ‘11: could perhaps exclude 115 < m_H < 185 GeV !!!

Excluded at 95%cl: 163 < m_H < 166 GeV (previously was 160-170 GeV)

That some sort of spontaneous symmetry breaking mechanism is at work has already been established

(couplings symmetric, spectrum totally non symmetric)

The question is on the nature of the Higgs mechanism/particle(s)

•

One doublet, more doublets, additional singlets?

•

SM Higgs or SUSY Higgses

•

Fundamental or composite (of fermions, of WW....)

•

Pseudo-Goldstone boson of an enlarged symmetry

•

A manifestation of extra dimensions (fifth comp.

of a gauge boson, an effect of orbifolding or of boundary conditions....)

•

Some combination of the above

Suppose we take the gauge symmetric part of the SM and put masses by hand.

Gauge invariance is broken explicitly. The theory is no more renormalizable. One loses understanding of the observed accurate validity of gauge predictions for couplings.

Still, what is the fatal problem at the LHC scale?

The most immediate disease that needs a solution is

the occurrence of unitarity violations in some amplitudes

To avoid this either there is one or more Higgs particles or some new states (e.g. new vector bosons)

Thus something must happen at the few TeV scale!!

Zwirner

With no Higgs unitarity violations for E_CM ~ 1-3 TeV

If no Higgs then something must happen!

A crucial question for the LHC

What saves unitarity?

•

^{the Higgs}

•

some new vector boson W’, Z’

KK recurrences

resonances from a strong sector ...

Theoretical bounds on the SM Higgs mass

Λ

: scale of new physics beyond the SM

Upper limit: No Landau pole up to Λ

Lower limit: Vacuum (meta)stability

If the SM would be valid up to M

_GUT

, M

_Pl

then m

_H

would be limited in a small range

Hambye, Riesselmann

The LHC was designed to cover the whole range

128 GeV < m_H < 180 GeV

Lower now because of m_t

No Landau pole

Vacuum stability

Status of the SM Higgs fit

Summer ‘09

Rad Corr.s ->

log_{1 0}m_H(GeV) = 1.94±0.15

This is a great triumph for the SM: ~right in the narrow

allowed range log_{1 0}m_H ~2 - 3

Sensitive to log m_H

Direct search: m_H > 114.4 GeV

At 95 % cl

m_H < 157 GeV (rad corr.’s)

m_H < 186 GeV (incl. direct search bound) m_H=87+35-26 GeV

Tevatron exclusion

Radiative corr’s indicate a light H

Sensitivity to m

_H

of precision tests

Gfitter

Is it possible that the Higgs is not found at the LHC?

Looks pretty unlikely!!

Rad. corr’s indicate a light Higgs (whatever its nature) A heavy Higgs would make perturbation theory to

collapse nearby (violations of unitarity for m_H > ~ TeV)

Such nearby collapse of pert. th. is very difficult to reconcile with EW precision tests plus simulating a light Higgs

The SM good agreement with the data favours forms of new physics that keep at least some Higgs light

The LHC discovery range is large enough: m_H < ~1 TeV

the Higgs should be really heavy!

e.g. strongly interacting WW or WZ scattering

Here “Higgs” means the “the EW symmetry breaking mechanism”

The Standard Model works very well

So, why not find the Higgs and declare particle physics solved?

Because of both:

• Quantum gravity

• The hierarchy problem

• The flavour problem

•••••

and experimental clues:

• Neutrino masses

• Coupling unification

• Baryogenesis

• Dark matter

• Vacuum energy

•••••

Conceptual problems

First, you have to find it!

LHC

Some of these problems point at new physics

at the weak scale: eg Hierarchy

Dark matter

0 4 2 8 1 0

6

-2

t b c τ

s µ

d u

e

Log_{1 0}m/eV

(Δm²_atm)^1/2 (Δ m²_sol)^1/2

Upper limit on mν

Neutrino masses are really special!

m_t/(Δm²_atm)^1/2~10^{1 2}

WMAP

KamLAND

Massless

ν

^’s?

•

^no

ν

_R

•

L conserved

Small

ν

^masses?

• ν

_R very heavy

•

L not conserved Neutrino masses point to M_GUT, well fit into the SUSY picture and in GUT’s

ν

masses and mixings

The first

beyond the (minimal) SM physics found!

ν's are nearly massless because they are Majorana particles and get masses through L non conserving interactions

suppressed by a large scale M ~ M_GUT

A very natural and appealing explanation:

m

_ν

~ m

²

M m: ≤ m

_t

~ v ~ 200 GeV M: scale of L non cons.

Note:

m

_ν

∼ (Δ m

²_atm

)

^1/2

~ 0.05 eV m ~ v ~ 200 GeV

M ~ 10

¹⁴

- 10

¹⁵

GeV

Neutrino masses are a probe of physics at M

_GUT

!

A signal in 0νββ would be an essential confirmation

All we know from experiment on

ν

masses strongly indicates that

ν '

s are Majorana particles and that L is not conserved (but a direct proof still does not exist).

Detection of 0νββ would be a proof of L non conservation.

Thus a big effort is devoted to improving present limits and possibly to find a signal.

0νββ = dd -> uue^-e^-

Heidelberg-Moscow IGEX

Cuoricino Nemo

Sokotvina CUORE GERDA

•••••

TB mixing agrees with data at ~ 1 σ

At 1 σ:

sin

²

θ

₁₂

=1/3 : 0.2 9-0.3 3 sin

²

θ

₂₃

=1/2 : 0.4 1-0.5 4 sin

²

θ

₁₃

= 0 : < ~0.02

G.L.Fogli et al ’08

A coincidence or a hint? If a hint -> discrete flavour groups Tri-Bimaximal (TB)

The neutrino mixing matrix is reasonably well known by now

1−λ²/2 λ Aλ³(ρ−iη)

−λ 1−λ²/2 Aλ²

Aλ³(1-ρ−iη) − Aλ² 1

V ~ + o(λ⁴)

Very much different than V_CKM for quark mixing

A priority for exp.!!

T ~ 10

^12±3

GeV

(after inflation)

Only survives if Δ (B-L) is not zero

(otherwise is washed out at T_ew by instantons)

Main candidate: decay of lightest

ν

_R ^{(M~1012 GeV)}

L non conserv. in

ν

_R out-of-equilibrium decay:

B-L excess survives at T_ew and gives the obs. B asymmetry.

Quantitative studies confirm that the range of m_i from ν oscill's is compatible with BG via (thermal) LG

Buchmuller,Yanagida, Plumacher, Ellis, Lola, Giudice et al, Fujii et al

…..

m_i <10^-1 eV

Baryogenesis by decay of heavy Majorana ν 's BG via Leptogenesis near the GUT scale

In particular the bound was derived for hierarchy

Buchmuller, Di Bari, Plumacher;

Giudice et al; Pilaftsis et al;

Hambye et al Can be relaxed for degenerate neutrinos

So fully compatible with oscill’n data!!

Dark Matter

Most of the Universe is not made up of atoms: Ω_tot~1, Ω_b~0.045, Ω_m~0.27

Most is Dark Matter and Dark Energy

Most Dark Matter is Cold (non relativistic at freeze out) Significant Hot Dark matter is disfavoured

Neutrinos are not much cosmo-relevant: Ω_ν<0.015 WMAP, SDSS,

2dFGRS….

SUSY has excellent DM candidates: eg Neutralinos (--> LHC) Also Axions are still viable (introduced to solve strong CPV) (in a mass window around m ~10^-4 eV and f_a ~ 10^{1 1} GeV but these values are simply a-posteriori)

Identification of Dark Matter is a task of enormous importance for particle physics and cosmology

LHC?

LHC has good chances because it can reach any kind of WIMP:

WIMP: Weakly Interacting Massive Particle with m ~ 10¹-10³ GeV

For WIMP’s in thermal equilibrium after inflation the density is:

can work for typical weak cross-sections!!!

This “coincidence” is a good indication in favour of a WIMP explanation of Dark Matter

LHC will tell yes or no to WIMPS

SUSY Dark Matter: best candidate the neutralino [in SUSY the gravitino is a non-WIMP alternative]

Ellis, Olive, Santoso, Spanos

g-2

WMAP 0.1<Ω^h2<0.3 This is for the CMSSM

With less constraints, more space

Direct WIMP search It is not easy to reach the

sensitivity for Axions as DM

Experimental hints for dark matter?

Annual modulations (DAMA/LIBRA)

e+ excess in cosmic rays detectors (PAMELA)

γ

excess (EGRET) now disfavoured (FERMI)

If really those effects are signals of DM, they point to more exotic forms of DM

G. Kane et al,

Arkani-Hamed et al, Cirelli et al

...

ATIC bump now disfavoured (FERMI)

The PAMELA e⁺ excess The ATIC bump in e spectrum

not confirmed by FERMI

If DM it would need large masses and

enhanced rates (production and/or decay)

> 200 papers

An astrophysical interpretation appears possible

nothing in antiprotons (PAMELA)

the blu curves:

pulsars within 1Kpc

with some parameter fitting

This hierarchy problem demands new physics near the weak scale

Λ: scale of new physics beyond the SM

• Λ>>m_Z: the SM is so good at LEP

• Λ~ few times G_F^-1/2 ~ o(1TeV) for a natural explanation of m_h or m_W

For the low energy theory: the “little hierarchy” problem:

e.g. the top loop (the most pressing): m_h²=m²_bare+δm_h²

h h

t

The LEP Paradox: m_h light, new physics must be so close but its effects were not visible at LEP2

Λ~o(1TeV)

Barbieri, Strumia

The B-factory Paradox: and not visible in flavour physics

A crucial question for the LHC

What damps the top loop

Λ

² dependence?

•

the s-top

•

some new fermion t’

KK recurrences of the top ...

Precision Flavour Physics

Another area where the SM is good, too good...

With new physics at ~ TeV one would expect the SM suppression of FCNC and the CKM

mechanism for CP violation to be sizably modified.

But this is not the case

an intriguing mystery and a major challenge for models of new physics

Adding effective operators to SM generally leads to very large Λ

(or anyway small)

But the hierarchy problem demands Λ in the few TeV range

eg in Minimal Flavour Violation (MFV) models

D'Ambrosio, Giudice, Isidori, Strumia'02 G. Isidori

Solutions to the hierarchy problem

•

Supersymmetry: boson-fermion symm.

exact (unrealistic): cancellation of Λ ² in δm_h² approximate (possible): Λ ~ m_SUSY-m_ord

•

The Higgs is a ψψ condensate. No fund. scalars. But needs new very strong binding force: Λ_new~10³Λ_QCD (technicolor).

•

Extra spacetime dim’s that “bring” M_Pl down to o(1TeV)

The most widely accepted

Strongly disfavoured by LEP. Coming back in new forms

Exciting. Many facets. Rich potentiality. No baseline model emerged so far

•

Models where extra symmetries allow m_h only at 2 loops and non pert. regime starts at Λ~10 TeV

"Little Higgs" models. Some extra trick needed to solve problems with EW precision tests

top loop Λ~ m_stop

•

Ignore the problem: invoke the anthropic principle

The scale of the cosmological constant is a big mystery.

Ω_Λ ~ 0.75 ρ_Λ ∼ (2 10^-3 eV)⁴ ~ (0.1mm^)-4

In Quantum Field Theory: ρ_Λ ∼ (Λ_cutoff)⁴

If Λ_cutoff ~ M_Pl ρ_Λ ∼ 10¹²³ ρ_obs Exact SUSY would solve the problem: ρ_Λ = 0 But SUSY is broken: ρ_Λ ~ (Λ_SUSY)⁴ ~ 10^{5 9} ρ_obs

It is interesting that the correct order is (ρ_Λ)^1/4 ~ (Λ_EW)²/M_Pl Other problem:

"Why now"?

t ρ

Λ rad m

Now Quintessence?

Similar to m_ν!?

The anthropic route

"Quintessence"

Λ as a vev of a field φ? Coupled to gauge singlet matter, eg ν_R, to solve magnitude and why now?

Is naturalness relevant?

Speculative physics reasons to doubt:

•

The empirical value of the cosmological constant

Λ

poses a tremendous, unsolved naturalness problem

Perhaps we live in a very unlikely Universe but one that allows our existence

•

Possibly our Universe is just one of infinitely many continuously created from the vacuum by

quantum fluctuations

•

Different physics in different Universes according to the multitude of string theory solutions (~10⁵⁰⁰)

yet the value of

Λ

is close to the Weinberg upper bound for galaxy formation

I find applying the anthropic principle to the SM hierarchy problem not appropriate

After all we can find plenty of models that reduce the fine tuning from 10^{1 4} to 10²:

so why make our Universe so terribly unlikely?

The case of the cosmological constant is a lot different:

the context is not as fully specified as the for the SM

(quantum gravity, string cosmology, branes in extra dims., wormholes thru different Universes....)

In broken SUSY Λ² is replaced by (m_stop²-m_t²)logΛ m_H >114.4 GeV, m_χ+ >100 GeV, EW precision tests, success of CKM, absence of FCNC, all together,

impose sizable Fine Tuning (FT) particularly on minimal realizations (MSSM, CMSSM…).

Yet SUSY is a completely specified, consistent, computable model, perturbative up to M_Pl quantitatively in

agreement with coupling unification (GUT’s) (unique among NP models)

and has a good DM candidate: the neutralino (actually more than one).

Remains the reference model for NP

$G_S$ and $G_T$

The hierarchy problem:

SUSY: boson fermion symmetry

SUSY is unique in providing a weakly interacting theory up to the GUT/Planck scale

Other BSM models (little Higgs, composite Higgs, Higgsless....) all become strongly interacting at a multi-TeV scale

SUSY effects could modify the SM fit

“light SUSY”=

= light s-leptons and charginos;

s-quarks ~1 TeV

G.A, Caravaglios, Gambino, Giudice, Ridolfi ‘01

A recent study indicates that m_h goes up in CMSSM when b->s

γ

^,

a_µ, Ω_DM are added

O. Buchmuller et al ’07, ‘0 8 [0808.4128]

also:

J. Ellis et al ‘0 7

relatively light SUSY is indicated

accesssible at the LHC

Could be new physics eg light SUSY

a_µ is a plausible location for a

new physics signal!!

Muon g-2 and SUSY

Status of MEG

Large neutrino mixing angles + SUSY GUT’s make a signal near the present limit plausible

Present limit on Br 1.1 10^-11

MEG 2008 3 10^-11

Present MEG sensitivity 1-2 10^-11

Data taking has resumed in September Ultimate sensitivity 1 0^-12 -10^-13

Little Higgs Models

global gauged SM

H is (pseudo)-Goldstone boson of G: takes mass only

at 2-loops (needs breaking of 2 subgroups or 2 couplings)

cutoff Λ ~10 TeV Λ² divergences canceled by:

δm²_H|top new coloured fermion χ with Q=2/3 δm²_H|gauge W', Z', γ'

δm²_H|Higgs new scalars

~1 TeV

2 Higgs doublets ~0.2 TeV

Georgi (moose)/Arkani-Hamed et al/Low, Skiba,

Smith/Kaplan, Schmaltz/Chang,Wacker/Gregoire et al

recall: G_F ~g² -> g⁴

Technically sophisticated. But the main drawback is:

Little Higgs provides just a postponement:

UV completion beyond ~10 TeV? GUT's?

Still important as it offers well specified signals and signatures for searching at the LHC:

a light Higgs, a new top-like fermion χ to damp the top loop, new W’, Z’ for the W, Z loops,...

T parity interchanges the two SU(2)xU(1) groups

Standard gauge bosons are T even, heavy ones are T odd With some tension Little Higgs models can work.

Cheng, Low

Lightest T-odd particle stable --> Dark Matter

Extra Dimensions (ED)

String Theory ---> ED at M_Pl

Perhaps ED have a direct impact on physics below M_Pl

Exciting possibilities (a large domain of contemporary BSM)

•

GUT’s in ED (M_GUT)

•

ED as (part of the) solution of the hierarchy probem (M_EW)

•

EW symmetry breaking from ED (M_EW)

Early formulation Solve the hierachy problem by bringing gravity down from M_Pl to o(1TeV)

• Large compactified extra dimensions: 1/R <~ 1 TeV • SM fields are on a brane

• Gravity propagates in the whole bulk

y=0 "our"

brane (possibly with thickness r) R

y: extra dimension R: compact'n radius

y

G_N~1/M²_Pl:

Newton const.

M_Pl large as G_N weak

The idea is that gravity appears weak as a lot of lines of force escape in

extra dimensions

Arkani-Hamed, Dimopoulos/ Dvali+Antoniadis

r

Generic feature of extra dim. models:

p=n/R m²= n²/R² (quantization in a box)

Many

possibilities:

•

SM fields on a brane or in bulk cfr:

•

Gravity always on bulk

•

Factorized metric:

•

Warped metric: Randall-Sundrum (R-S)

m_weak=M_Plexp(-mRπ) emerges as

the most promising

formulation Rm~12

compact dim. Kaluza-Klein (KK) modes

Randall-Sundrum:

This non-fact.ble metric is

solution of Einstein eq.s with 2 branes at φ=0,π and specified 5-dim cosmological term

φ=0 φ=π

Warp factor e^-2mRφ

m~M_Pl for all mR: m² ~ M_Pl²(1-e^-2mRφ)

All 4-dim masses m₄ are scaled down with respect to 5-dim masses m₅ ~ M_Pl by the warp factor: m₄=M_Ple^-mRπ

Planck TeV

The hierarchy problem demands that mR ~ 12: not too large!!

Stabilization of mR at a compatible value can be assured by a scalar field in the bulk with a suitable potential

Goldberger, Wise R not large in this case!

"radion"

All SM particles in bulk except the H

H is here

star

seen from A the B frequency is smaller:

as if the photon kinetic energy lost by climbing out of grav. field

Similarly in RS mc² is smaller by the corresponding factor g_{0 0}^1/2--> m₄=M_Ple^-mRπ

γ

B

A 2 identical atoms in

A and B emit light with frequencies ν_A and ν_B

ν_B ν_A ⁼

g₀₀(B)

g₀₀(A) <1

Good tutorials:

R. Sundrum ‘0 4 TASI lectures R. Rattazzi ’05 Cargese Lectures

• Gauge Symmetry Breaking (Higgsless theories)

M_Pl TeV

SU(2)_LxSU(2)_RxU(1) SU(2)L x U(1)Y SU(2)D xU(1)

Warped R-S background

Symmetries broken by

Boundary Conditions (BC) on the branes

Altogether only U(1)_Q unbroken

•

Unitarity breaking (no Higgs) delayed by KK recurrences

Csaki et al/Grojean/Papucci/Nomura/Davoudiasl et al/Barbieri, Pomarol, Rattazzi;....

•

Dirac fermions on the bulk (L and R doublets). Only one chirality has a zero mode on the brane

The only models were no Higgs would be found at LHC.

But signals of new physics would be observed

Applications

With no Higgs unitarity violations, eg:

At E ~ 1.2 TeV unitarity is violated

In Higgsless models unitarity breaking is delayed by the exchange of KK recurrences

Z_k = k_th KK Cancellation guaranteed

by sum rules implied by 5-dim symmetry

The small W, Z mass implies a small KK gap --> W’, Z’ at the LHC

No convincing, realistic Higgsless model for EW symmetry breaking emerged so far

However be alerted of possible signals at the LHC: no Higgs but KK recurrences of W, Z and additional gauge bosons

Serious problems with EW precision tests

e.g. Chivukula et al ‘02, Barbieri, Pomarol, Rattazzi '03;

also with Z->bb

Substantial fine tuning required

Best try: Cacciapaglia et al '06

m_W fixes the KK gap and it is not sufficiently large

A new way to look at walking

technicolor using AdS/CFT corresp.

• Composite Higgs in a 5-dim holographic theory

Agashe, Contino, Pomarol...

The Higgs is a PGB and EW symmetry breaking is triggered by bulk effects (in 4-dim the bulk appears as a strong sector).

The 5-dim theory is weakly coupled so that the Higgs potential and EW observables can be computed

The Higgs is rather light: m_H < 185 GeV

M_Pl TeV

SO(5)xU(1)

SU(2)L x U(1)Y SO(4)xU(1)

Warped R-S background As in Little Higgs models

All SM fields in the bulk (but the Higgs is localised on the TeV brane)

Also in these models a sizable fine-tuning is required

A qualitative description of flavour

Higgs couplings modified

Composite Higgs: a more model independent approach

The light Higgs is a bound state of a strongly interacting sector.

Pseudo-Goldstone boson of an enlarged symmetry.

eg. SO(5)/SO(4)

m_ρ

m_H m_W

Georgi, Kaplan ‘84

Agashe/ Contino/Pomarol/Sundrum/ Grojean/Rattazzi....

v ~ EW scale f ~ SI scale

~ f < m_ρ <~ 4π f ξ = (v/f)²

ξ interpolates between SM [ξ ~ 0]

and some degree of compositeness

[ξ ~ o(1) limited by precision EW tests]

WW -> WW ξ

WW -> hh H Br Ratios Detectable ξ effects at the LHC

•

Higgs couplings

•

WW scattering

•

2-Higgs Production

Contino et al

Higgs compositeness: more in detail

Contino,Kramer, Son, Sundrum’06 Giudice, Grojean, Pomarol, Rattazzi’0 7 [see also BESS: Casalbuoni at al, ‘87]

L=L_elem+L_comp+L_mixing

SM minus the Higgs sector

H are pseudo Goldstone bosons of larger broken gauge group, eg SU(3)xSU(2)_L xSU(2)_RxU(1)

(ρ_µ corresponding massive vector boson)

g_el<<g*

M_* ~ TeV A low energy theory from

truncation of some UV completion

The vector boson mass terms make a total of

The SM gauge bosons (orthogonal combinations)

remain massless before EW symmetry breaking.

The SM couplings are

Mixing generates mass eigenstates:

light:

heavy:

But the Higgs is totally composite: sinθ_H= 0 (also t_R could be a composite)

The hierarchy problem: the Higgs is light because only acquires mass thru interactions with the elementary sector from their

composite components

New physics in the composite sector is well hidden because light particles have small mixing angles

The top loop occurs with the mediation of the composites, so that the diagram has no quadratic divergence

A pragmatic effective description that can be applied to diverse underlying theories

Lessons from model building

In all the new physics models we mentioned

there is a light Higgs (< 200 GeV)

[except in Higgsless models (if any) but new light new vector bosons exist in this case]

there is at least a % fine tuning

Fine tuning appears to be imposed on us by the data

Is it possible that the LHC does not find the Higgs particle?

Yes, it is possible, but then something else must be found

Is it possible that the LHC finds the Higgs particle but no other new physics (pure and simple SM)?

Yes, it is technically possible but it is not natural Is it possible that the LHC finds neither the Higgs nor new physics?

No, it is “approximately impossible”

In conclusion