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Elementary Particles
1) Introduction
2) Quantum numbers and their conservation
laws
3) Antiparticles
4) Strange particles
5) Resonances
6) Hadron structure
7) Quark model
8) Particles of standard model
Scheme of pair top antitop quark creation during
collision of proton and antiproton. The W bosons are
decaying to leptons in shown case. Created quarks
produce jets. First production and observation of top
quark was performed at Fermilab (USA).
Experiment DELPHI at CERN
Introduction
Four types of interactions – gravitation, electromagnetic, weak and strong.
Particle classification according to acting interactions (gravitation acts on all particles ):
Leptons – interact weakly and charged also electromagnetically, they do not interact strongly (e,
μ, τ, νe, νμ, ντ) – in the present experiments they are point like
Hadrons – interact in addition also strongly – they have structure and size ≈1 fm
Hadrons are divided to:
Mesons - (π+, π-, π0, K+, K-, K0, ρ+, ρ-, ρ0…)
Baryons – (p, n, Λ, Σ+, Σ-, Σ0, Δ++, Δ+, Δ0, Δ-, N, Ω-…)
Particle classification according to statistics:
Bosons: Bose-Einstein statistic → arbitrary number of particles in given state – integral spin
Wave function – symmetric:
ΨB(x1,x2,x3, …,xn) = ΨB(x2,x1,x3, …,xn)
Mesons and field particles (photons, gravitons, gluons, … )
Fermions: Fermi-Dirac statistic → Pauli exclusion principle → only one identical particle
in given state – half-integral spin. Wave function is antisymetric:
ΨF(x1,x2,x3, …,xn) = -ΨF(x2,x1,x3, …,xn)
Leptons and baryons
Antiparticles – the same mass as particle, opposite sign of quantum numbers (charge, baryon
number, lepton number, strangeness …). In the most cases antiparticle is signed by overline above
appropriate symbol:
but:
e- →e+, μ-→μ+, τ-→τ+
p  p , n  n,    ,  e   e
Conservation laws of quantum numbers
No existence of some reactions which are energetically (kinematical) possible → indication of
conservation law existence
No existing reactions with total charge non-conservation → charge conservation law
Number of fermions is conserved → conservation laws of baryon and lepton numbers
Baryon number: if its conservation law is strictly valid, proton (the lightest baryon) is stable. We
do not observe decay:
p → e+ + π 0
Single lepton numbers – Le, Lμ a Lτ
Necessity of introduction of lepton number conservation law results from many experimental
evidences:
No observed reactions: e- + e- → π - + π Conservation law of single lepton numbers:
Existed muon decay
μ- → e- + γ
μ- → e- + e+ + e-
  e  e  
Neutrino oscillations – violation of single lepton number conservation laws, total lepton number is
conserved.
Observation using solar neutrino detection by Superkamiokande detector
Violation of total lepton number conservation – yet no observed
Violation of baryon number conservation law – yet no observed (sign of its existence is baryon
asymmetry of universe)
Such violation assume theories of interaction unification.
Antiparticles
Particles with zero spin are relativistically described by Klein-Gordon equation (linear partial
diferential equation of second order):
1  2  2  2  2 m 2c 2
for particle motion direction in axe x:
 ( x, t )  e
Its solution for free particle:
We substitute: 
2

2
2
2 2
0
2
E 2  p 2 c 2  m 02 c 4
Positive and negative solutions exist:
2
2

z
2

0
2

 0
Effort to obtain relativistic
quantum relation of motion:
 i(Et px ) / 
1 E i(Etpx ) p i(Etpx) m c i(Etpx)
e
 2e

e
0
c2  2


We obtain condition:

c t
x
y
1  2  2 m 02c 2

 2  0
c 2 t 2 x 2

2


p  i 
r
E  i

t
2
2
2 
E  p c  m c  
 
 m 2c 4
2
2
t
r
2
2 2
E1  E (  )   p 2 c 2  m 2 c 4
2 4
2
E 2  E ()   p 2c 2  m 2c 4
Possible interpretation of solution E2: positive energy, opposite charge → antiparticle.
Leaving of interpretation, that intrinsic values of Hamiltonian give energy of particle.
Similar situation is obtained for the Dirac equation. Its solution describes particles with spin 1/2.
In this case we have 4 solutions for wave function:
Particles with spin projection +1/2 a –1/2
Antiparticles with spin projection +1/2 a –1/2
Existence of electron and positron. Similarly also for other fermions.
Discovery of first antiparticle:
1932 - positron in cosmic rays
1955 – antiproton (BEVATRON), 1956 - antineutron
Simulation of electron positron pair creation during gamma ray
motion through electromagnetic. Motion of created particles
at magnetic field
Get together of particle and antiparticle → annihilation
Annihilation and creation of quarks
Annihilation and creation
leptons
Antiproton annihilation – creation
of K-, K0 a π+:
Review of physical quantities from the view of relation between particle and antiparticle:
Quantity
particle
antiparticle
Mass m
same
same
Spin (magnitude)
same
same
Lifetime τ
same
same
Isospin (magnitude)
same
same
Electric charge
Q
-Q
Magnetic moment
μ
-μ
Baryon number
B
-B
Lepton number
L
-L
Strangeness
S
-S
z component of isospin
Iz
Iz
-Iz
Intrinsic parity P
Same for bosons
Opposite - fermions
Neutral particles:
Fermions: antiparticles are different in baryon and lepton numbers
Bosons: if I=B=L=S=0 and μ=0 → particle identical with antiparticle
0  0
Get together of particle and antiparticle → annihilation to photons and mesons
Conservation laws → production of fermions in pairs of particle-antiparticle.
For example „reversal annihilation“ – creation of electron positron pairs during passage of photons
through electric field of nucleus
Antiparticles of most of known particles were found.
Production of antiatoms (yet only antihydrogen), production of antinuclei. → existence of antimatter
Production of slow
antiprotons at CERN
Production of antihydrogen in
experiment ATHENA
Charge conjugation symmetry - C-invariance – identity of processes during confusion between
particles and antiparticles and vice versa.
Violation of C-invariance and combined CP-invariance
Existence of antimatter in the Universe – in cosmic rays only antiprotons and other antiparticles
produced by high energy proton collisions.
Baryon asymmetry of universe – excess of matter above antimatter
Strange particles
1) New particles with much longer lifetime ~ 10-10s – they decay slowly, even if considerable
energy is released.
2) Production of these particles in pairs.
3) No existence of some types of decay:
Existing decay:
Σ0 → Λ0 + γ
S = -1
-1 0
Non-existent decay:
Σ+ → p + γ
S = -1
0 0
Sign of existence of new conservation law – strangeness conservation law (it is valid for strong and
electromagnetic interactions, it is not valid for weak) → introduction of quantity strangeness (S)
Also for weak decay only ΔS = ± 1: Non-existent decay: Ξ- → n + π S = -2
0 0
Hyperon (strange baryon) Ξ- is decaying through two steps:
Ξ-→ Λ + π –
S = -2 -1 0
Λ → n + π0
S = -1
0 0
We introduce hypercharge: Y = B + S
Isospin:
Independency of strong interaction on charge. → proton and neutron are two charge
state of single particle – nucleon.
Value of isospin I is such, that number of its projection to third axe 2I+1 gives
number of charge states.
Charge of hadrons :
Q = e(Iz + Y/2)= e(Iz + (B+S)/2)
First strange particles: K mesons, lambda – turn of forties and fifties
Proton
Positive pion
Reaction of π - with nucleus in bubble
chamber produces K0 and Λ
Negative
pion
Negative pion
Lambda
Neutral kaon
Negative pion
Production of Ω- (S=2) particle – picture of bubble
chamber at CERN
Resonances
Existence of very short living particles (typical lifetime ~10-23s) → observed as resonance structures
in excitation functions:
a) during particle scattering (for example π-N scattering)
b) during particle multiproduction
(resonance structures are studied in dependency of cross section on invariant mass of scattering
system or produced particle system –
  2 2
2
2
s12  MSc 
E1  E2   p1  p2  c
Occurrence of resonance maxima with shape described by Breit-Wigner function.
 (M) ~  M  ~
2
1
M  M0 2   2 / 4
Cross section
Width of maxima Γ is connected with lifetime τ of particle by Heisenberg uncertainty
principle: τ ~ ħ/Γ. It defines also uncertainty in the particle rest mass determination.
Occurrence of resonances for exactly given values of charge, isospin and other quantum
numbers → particle.
Shape of resonance with M0 = 10 and Γ = 3
above constant background of cross section 1.0
background
resonance
Mass
Along quantum numbers → baryon (nucleon, hyperon) and meson (non-strange and strange)
resonances
Nature of resonances – very often excited states of hadrons.
Short lifetime → decay through strong interaction.
Hundreds of resonances are known totally.
Examples of resonances (only a few with strangeness S = 0):
Baryon resonances:
N+, N0 – excited states of nucleons (structure uud a udd) – izospin I = 1/2, strangeness S = 0
Δ++ Δ+ Δ0 Δ - - Δ baryons and their excited states (structure uuu, uud, udd a ddd), I = 3/2, S = 0
Meson resonances:
Combinatorial
background
ρ meson and its excited state
η – excited states of η mesons
Experimental problems – background, resonance
overlapping, long decay lifetimes (smear of
resonance by measuring device response), very
short decay lifetime  very broad resonances.
Simulation of meson resonances
observation by HADES spectrometer
Hadron structure
Evidences of hadron structure existence:
1) Scattering experiments – charge distribution measured by high energy electrons (they do
not interact strongly) → parton structure
2) Jets – cluster of high energy particles (hadrons) created during deep inelastic scattering of
quarks
3) Anomalous magnetic moments of nucleons – μp = 2.792 μJ,
μn = -1.913 μJ
4) Excited states of hadrons (nucleons) – of proton (N+), of neutron (N0) – belong to resonances –
different orbital moment of constituents
5) Systematic of elementary particles – distribution to isospin multiplets (particle masses at isospin
multiplet are very similar)
Octuplet (J = ½)
Decuplet (J = 3/2)
Multiplet particles are placed in plane
characterized by isospin and hypercharge
Two examples of baryon
multiplet
Explanation by three particle existence – quarks (actually by six – three quarks and three
antiquarks) , from which elementary particles consisted of.
Quark structure of hadrons
Baryons → three quarks: n = udd, p = uud, Σ+ = uus, Σ0= uds, Λ = uds, Ω = sss (Σ0, Λ differ by
isospin)
Mesons → quark – antiquark:    du,    ud, K -  su
Baryon decuplet (resonances):
Identical quarks (fermions) at ground state – Pauli exclusion principle → necessity of new quantum
number – color – quantum chromodynamics (QCD)
Additional particles → three new quarks – new quantum numbers
Review of quarks:
Quark
Q [e]
u
+2/3
d
I(JP)
Iz
S
C
B
T
1/2(1/2+) +1/2
0
0
0
0
-1/3
1/2(1/2+)
-1/2
0
0
0
0
s
-1/3
0(1/2+)
0
-1
0
0
0
c
+2/3
0(1/2+)
0
0
+1
0
0
b
-1/3
0(1/2+)
0
0
0
-1
0
t
+2/3
0(1/2+)
0
0
0
0
+1
Quark structure of proton:
Colored quarks held together by strong
interaction (exchange of gluons transferring
color)
Discovery of Ω- particle by bubble chamber
at Brookhavenu laboratory
Very intensive field of strong interaction →
complicated structure of vacuum – virtual quarkantiquark pairs and gluons
Picture of K+ meson creation and decay
during flight obtained by bubble
chamber at CERN
Particles of standard model
Our understanding of matter structure and interactions so far culminate in standard model.
Standard model includes all known fundamental particles:
1) Particles of matter – quarks and leptons
2) Particles of interactions – intermediate bosons (gluons, W±, Z0, photon and Higgs boson)
Look as point like particles for accessible energies.
Three families of leptons:
 e 
 
e
  
 

  
 
 
Three families of quarks in different collors:
 ua 
 a
d 
 
 sa 
 a
c 
 
 ba 
 a
t 
 
where a = red, green, blue
Quarks only bonded to colorless hadrons. Quarks are directly observed:
1) In high energy electron scattering on hadrons (u,d)
2) As hadron jets during high energy deep inelastic scattering – transformation („decay“)
and hadronisation of c, b and t quarks
The search of standard model particles was completed during last years:
1) Production and observation of quark t (in the form of t, anti-t pairs) – v r. 1995 Fermilab
USA (CDF and D0 experiments on Tevatron accelerator with colliding beam of p, anti-p - √s
= 1.7 TeV), last value of mt = (176±7) GeV/c2
2) Observation of ντ neutrino – at 2000 year at Fermilab USA (E872 experiment - DONUT)
3) Sign of Higgs boson existence – at 2000 year by LEP at CERN Schwitzerland (ALEPH,
DELPHI, L3, OPAL), mass 115 GeV/c2 so far not unquestionable evidence – problem with
background and statistical significance of effect on background