Elementary Particles Lezione 7 - fisica.uniud.itcobal/Site/Lezione_FSNS_1_quak.pdf · Lezione 7...

�Elementary Particles�Lezione 7

Marina CobalUniUD e INFN Trieste

1) Introduction

2) Cosmic Rays

3) Basis 1) Quantum mechanics, Radioactivity

2) Scattering theory

4) Leptons

5) Hadrons

1) Strangeness, quark model

2) Symmetries, Isospin

6) Standard Model

1) Gauge invariance, QED: EM interaction

2) Parity, neutrinos: Weak interaction

3) QCD: Strong interaction

7) e+e- and DIS

8) Higgs and CKM

Plan

1900-1940

1945-1965

1965-1975

1975-2000

2000-2013

Quark model

Discovery strangeparticles

Discovery strange particles

Strange particles: kaon discovery

• Why were these particles called strange?• Large production cross section (10-27 cm2)• Long lifetime (corresponding to process with cross section 10-40 cm2)




• Associated production!




New quantum number:

Ø Strangeness, S

Ø Conserved in the strong interaction, ΔS=0§ Particles with S=+1 and S=-1

simultaneously produced

Ø Not conserved in individual decay, ΔS=1

π

π

π

π

pK

Λ




New quantum number:

Ø Strangeness, S

Ø Conserved in the strong interaction, ΔS=0§ Particles with S=+1 and S=-1

simultaneously produced

Ø Not conserved in individual decay, ΔS=1

π

π

π

π

pK

Λπ

π

π

π

pK

Λ

Production:π-p→K0Λ0

Decay:K0 → π-π+Λ0 → π-p

Strange mesons and baryons

Were called so because, being produced in strong interactions, had quite long lifetimes and decayed weakly rather than strongly

The most light particles containing s-quark

v mesons K+, K- and : Kaons,lifetime of K+ = 1.2x10-8 s

v baryon L, lifetime of 2.6x10 s

Principal decay modes of strange hadrons:

00 Κ,Κ

)36.0()64.0()21.0(

)64.0(

0

0

=+®L

=+®L

=+®

=+®

-

++

++

BnBpBK

BK

p

p

pp

nµ µ

Problem:While the first decay in the list is clearly a weak one, decays of Lcan be very well described as strong ones, if not the long lifetime:

However, this decay should have t ~ 10-23 s. Thus, L cannot be another sort of neutron....

Solution:Introduce a new quark, bearing a new quark number –“strangeness”- which does not have to be conserved in weakinteractions

In strong interactions, strange particles haveto be produced in pairs to save strangeness:

( ) ( ) )(uudududd +®

L+®+- 0Kpp

m1 m2MSpecific (m1=m2=m):

afterbefore

Kinematics

m1 m2M

Kinematics

Particle decay: momentum final state particles (pf)

General:

Specific: (m1=m2=m)

( )MmME

2

22

2,1D±

=

More strange particles: S=2

Strange particles

Particle Mass S

K0 497.7 +1

K+ 493.6 +1

K- 493.6 -1

K0bar 497.7 -1

Particle Mass S

S+ 1189.4 -1

S0 1192.6 -1

S- 1197.4 -1

L0 1115.6 -1

X0 1314.9 -2

X- 1321.3 -2

Mesons Baryons

Corresponding anti-baryons have positive Strangeness

Wha

t is

diff

eren

t…?

50-60: Many particles discovered à ‘particle zoo’

• Will Lamb:

“The finder of a new particle used to be awarded the Nobel Prize, but such a discovery now ought to be punished with a $10,000 fine.”

• Enrico Fermi:

“If I could remember the names of all these particles, I'd be a botanist.”

• Wolfgang Pauli:

“Had I foreseen that, I would have gone into botany."

Strange particles

Particle Mass S

n 938.3 0

p 939.6 0

S+ 1189.4 -1

S0 1192.6 -1

S- 1197.4 -1

L0 1115.6 -1

X0 1314.9 -2

X- 1321.3 -2

The 8 lightest strange baryons: baryon octet

Breakthrough in 1961 (Murray Gell-Mann): “The eight-fold way” (Nobel prize 1969)Also works for: Eight lightest mesons - meson octet

Other baryons - baryon decuplet

1232 MeV

1385 MeV

1533 MeV

Not all multiplets complete…

Gell-Mann and Zweig predicted the Ω- … and its properties

Discovery of W-

1232 MeV

1385 MeV

1533 MeV

1680 MeV

Not all multiplets complete…

Gell-Mann and Zweig predicted the Ω- … and its properties

Discovery of W-

Quark model

Gell-Mann en Zweig (1964):“All multiplet patterns can be explained if you assume hadrons are composite particles built from more elementary constituents: quarks”

§ First quark model:§ Three types up, down en strange (and anti-quarks)§ Baryons: 3 quarks§ Mesons: 2 quarks

26 à 3+3

mesons

baryonsup down strange

p = uudΣ+ = uusΞ0 = uss

n = uddΛ0 = uds

• Mesons:• Octet

• Baryons: • Octet• Decuplet

Quark model

Multiplets

Pattern (mass degeneracy) suggest internal degree of freedom

Baryon decuplet

m = 1232 MeV

m = 1672 MeV

m = 1530 MeV

m = 1385 MeV

The number of ‘elementary’ particles

Particle classification

1) Are quarks ‘real’ or a mathematical tric?2) How can a baryon exist, like Δ++ with (u↑u↑u↑), given the Pauli

exclusion principle?

“Problems”

sW-

D++

‘Problem’ of quark model

ss

uuu

J=3/2, ie. fermion, ie. obey Fermi-Dirac statistics: anti-symmetric wavefunction

- 3 values: red, green, blue- Only quarks, not the leptons

New quantum number: color!

às s s s

Intrinsic spin: = symmetric

quarks: = symmetric

Intrinsic spin: = symmetric

quarks: = symmetric

Force carier: γ

Leptons: e-,μ-,τ-,υe,υμ,υτ

Mesons: π+,π0,π-,K+,K-,K0,ρ+,ρ0,ρ-

Baryons: p,n,Λ,Σ+,Σ-,Σ0,Δ++,Δ+,Δ0, Δ-, Ω,…

http://pdg.lbl.gov/

mass

<1x 10-18 eV

~0 – 1.8 GeV

0.1-1 GeV

1-few GeV

The Particle Zoo

Protons and neutrons

Proton and neutron identical under strong interaction

proton neutron

mp = 938.272 MeV mn = 939.565 MeV

Nucleon+ internal degree of freedom to distinguish the two

?

• Introduction of quarks• Introduction of quantum numbers• Strangeness• Isospin

Eightfold way

Symmetries

Conserved quantitiesHamilton formalism:Time dependence of observable U:

U conserved à U generates a symmetry of the system

If U commutes with H, [U,H]=0 (and if U does not depend on time, dU/dt=0)

Then U is conserved: d/dt<U> = 0

Other symmetries:

Transformation Conserved quantity

Translation (space) MomentumTranslation (time) EnergyRotation (space) Orbital momentumRotation (iso-spin) Iso-spin

Quantum mechanics: orbital momentum

Sequence matters!Lx and Ly cannot be known simultaneously

L2 and Li (i=x,y,z) can be known simultaneously Can both be used to label states

[L2,H] = [Lz,H] = 0 Provided V = V(r), ie not θ dependentL2 and Lz label eigenstates

Quantum mechanics: orbital momentum

m = -l, -l+1, …, 0, … , l-1, l

flm=Yl

m

spherical harmonics

Lz

Lx

Ly

2

1

0

-1

-2

2

Different notation:

Spin is characterized by: - total spin S - spin projection SZ

Quantum mechanics: (intrinsic) spin

Rotations: SO(3) group Internal symmetry: SU(2) group similar

Spin is quantized, just as orbital momentum

Eigenfunctions |s,ms>:

spin-½ particles

spin-up

spin-down

general |α|2 prob for Sz = +

|β|2 prob for Sz = -

Complex numbers

Pauli matrices: any complex 2x2 matrix can be written as: A = aσ1+bσ2+cσ3

spin-½ particles

-

Pauli (1925): “No 2 electrons in an atom can have the same 4 quantum numbers: n, l, ml and ms”

e-

nucleuse-

n,l,m,s

1,0,0,+

1,0,0,-

2,0,0,-

2,0,0,+

2,1,1,+

2,1,1,-2,1,-1,+

2,1,-1,-2,1,0,+

2,1,0,-

Pauli exclusion principle

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