QCD FOR NEW PHYSICS DISCOVERY

Carlo OleariUniversità di Milano-Bicocca, Milan

13 March 2007

•• QCD: the theory of quarks and

gluons

•• The Higgs boson and the LHC

•• The pheno group in Bicocca

.

Rutherford scattering

Only with the assumption that the positive charge is concentrated

in a small volume, Rutherford could explain the large angle scat-

tering ofα particles (helium nucleus) on gold.

Thus he demonstrated the existence of the nucleus.

Carlo Oleari QCD for New Physics Discovery 2

Deep Inelastic Scattering

It is more difficult to show the existence of quarks. This is due to the fact that the

“strong” force is so strong that it is not possible to free quarks from the proton.

The distribution of the scattered electron is compatible with the scattering by an

almost free particle of spin 1/2, whose dimensions are a lot smaller than the dimen-

sions of the proton (SLAC, end of ’60s)

Mesons and baryons

J = 0

J = 1

mesons q1q̄2 J =12 ⊗

12

J = 12

J = 32

baryons q1q2q3 J =12 ⊗

12 ⊗

12

SU(4) : u, d, s, c

Quarks and gluons

The theory that describes quarks and gluons is called

QUANTUM CHROMODYNAMICS

•• a quark is a pointlike particle of spin 1/2 (like the electron) that carries

another property: the COLOR. Each quark comes in three colors (red,

blue and green)

•• the strong force is carried by the gluons. The gluons carry color. This is

different from electromagnetism, where the photon carries no charge.

There are eight gluons.

•• the coupling constant is called gs, equivalent to the electric charge e

by A. Pich

Quark masses

MeV = 106 eV mu ∼ 5 md ∼ 8 ms ∼ 150 ⇐= LIGHT

GeV = 109 eV mc ∼ 1.5 mb ∼ 5 mt ∼ 175 ⇐= HEAVY

mu : mt = 1 : 35000 =:

Three main issues

•• “experimental evidence” of the existence of quarks and gluons

•• the color

•• asymptotic freedom

Carlo Oleari QCD for New Physics Discovery 8

LEP: Large Electron Positron collider

27 Km of circumference to accelerate e+e−

Ee ∼ 100 GeV = 1011 eV, so that ve = 0.99999999998 c

e+e− → qq̄

q

qe-

e+

Z/γ

Carlo Oleari QCD for New Physics Discovery 10

e+e− → Z/γ → qq̄

Z / γ

q

q

e+e− → Z/γ → qq̄g

Z / γ

q

q

g

e+e− → Z/γ → qq̄gg e+e− → Z/γ → qq̄q′q̄′

q

q

g

g

q

q

q′q′

COLOR

q

qe-

e+

γ

R ≡σ(e+e−→ hadrons)

σ(e+e− →µ+µ−)∼

∑qσ(e+e−→ qq̄)σ(e+e− →µ+µ−)

∼ Nc∑q

Q2q

=

6

9Nc (u, d, s)

10

9Nc (u, d, s, c)

11

9Nc (u, d, s, c, b)

fractional

charges!!

R

Nc = 3

The photon quantum corrections

Running coupling

α = e2/(4π)

α(q2) =α(m2e )

1−α(m2e )

3πlog

(

q2

m2e

)

•• α(q2) increases with q2

α(q2) decreases at large distances.

The electric charge inNOT a constant.

•• The vacuum behaves like a polarized dielectric

medium

•• α(m2e ) = 1/137.03599911(46)

α(m2Z) = 1/128.95± 0.05

Carlo Oleari QCD for New Physics Discovery 16

The gluon quantum corrections

The strong couplingαs = g2s /(4π) “runs” according to

αs(q2) =

αs(q20)

1+β0α(q20) log

(

q2

q20

)

where

β0 =11Nc − 2n f

12π> 0 Nc = 3 n f = 6

αs(q2) decreases at short distances =⇒ asymptotic freedom

Asymptotic freedom

QCDO(α )

245 MeV

181 MeV

ΛMS(5) α (Μ )s Z

0.1210

0.1156

0.1

0.2

0.3

0.4

0.5

α s(Q)

1 10 100Q [GeV]

Heavy QuarkoniaHadron Collisionse+e- AnnihilationDeep Inelastic Scattering

NL

O

NN

LO

TheoryData La

ttice

211 MeV 0.1183s4 {

Carlo Oleari QCD for New Physics Discovery 18

Hadronization

αs(q2) increases at low energies

confinement of quarks and gluons into hadrons

Confinement still has to be proven!

$1 million, Millennium Prize by the Clay Mathematics Institute

Carlo Oleari QCD for New Physics Discovery 19

Open questions

QCD is part of the Standard Model: the theory of the strong and electroweak interactions.

The Standard Model is not the whole story.

Gravity, neutrino masses and oscillation, dark matter/dark energy, baryogenesis, the

cosmological constant . . . are still unresolved issues (see Barbieri’s talk).

Probably the most impelling one is the Higgs boson.

The Higgs boson

In the Standard Model, masses to all particles are

given through the interaction with a scalar particle,

the Higgs boson, and through a particular mecha-

nism, the spontaneous symmetry breaking.

Peter Higgs and his kid: “the Higgs boson”

Up to now, no direct evidence of the existence of the Higgs boson has been found.

But there are indirect measurements that suggest a Higgs boson mass between the limits

114 GeV < mH < 251 GeV

Carlo Oleari QCD for New Physics Discovery 21

LHC: the Large Hadron Collider

Proton–proton beams at Ep ∼ 7 TeV = 7× 1012 eV, so that vp = 0.99999998 c

http://lhc.web.cern.ch/lhc/

LHC: the Large Hadron Collider

LHC

proton – proton collider

•• center-of-mass energy:

14 TeV = 14× 1012 eV

•• 2808 × 2808 bunches

separation: 25 ns

•• 1.15× 1011 protons/bunch

bunch crossing rate: 40 MHz

•• proton–proton collisions: ∼ 109/sec

(superposition of 23 pp collisions per

bunch crossing)

•• 363 MJ/beam = enough to melt 15000 Kg

of Pb

ATLAS

http://atlasexperiment.org/ http://cms.cern.ch/

Proton-proton collisions are more complex!!

Proton-antiproton collision

Movie time

ENJOY!!!

Pheno group in Bicocca

•• Even if the StandardModel Lagrangian of the strong sector is simpler than

the electroweak one, most of the problems that one meets when doing

phenomenology come from QCD.

•• In fact, the calculation of cross sections in the perturbative framework is

very involved and can easily take months/years to be completed, at a

level of accuracy needed nowadays.

•• Strong interactions often enter the regime of low energies, and the strong

coupling constant becomes large.

The perturbative calculations, valid at high scales, fail to converge, and

the resummation of these contributions becomes mandatory.

Our group is composed by experts in the strong-interaction sector.

Carlo Oleari QCD for New Physics Discovery 29

Giuseppe Marchesini is an expert of resummation

of soft gluons, and he is one of the authors of HER-

WIG, a Monte Carlo shower program, which is able

to generate hadronic events as if they were collected

by a “real” detector. He has worked also on BFKL,

on the interplay small-x large-x regime, power cor-

rections. . .

Andrea Banfi works on resummation

too, in the framework of both hadronic

and leptonic collisions. Multi-jet pro-

duction, event shapes, automated re-

summation of jet observables in QCD.

Paolo Nason is an expert of hadron collisions.

He has worked on fixed-order calculation, re-

summation, heavy quarks. Recently he has

proposed a new formulation of the procedure

of merging next-lo-leading order effect with

the Monte Carlo shower.

Carlo Oleari (me) has worked on fixed order cal-

culation (at the next-to-leading and next-to-next-to-

leading order precision level), on heavy-quark pro-

duction, on Higgs and (di-)boson production at the

LHC. Recently he has been involved in the next-to-

leading order plus parton-shower project too.

.