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

IntroductionFour 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 spinWave 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

ee , ,nn ,pp

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+

Conservation laws of quantum numbersNo 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+ + π0

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: μ- → e- + γ μ- → e- + e+ + e-

Existed muon decay ee

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.

AntiparticlesParticles with zero spin are relativistically described by Klein-Gordon equation (linear partial diferential equation of second order):

0cm

zyxtc

12

220

2

2

2

2

2

2

2

2

2

for particle motion direction in axe x: 0cm

xtc

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2

2

2

2

Its solution for free particle:/)pxi(Et)tx,( e

We substitute: 0ecm

ep

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1 px)i(Et2

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We obtain condition:42

0222 cmcpE

4222)(2 cmcpEE

Positive and negative solutions exist:4222)(

1 cmcpEE

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 –1/2Antiparticles with spin projection +1/2 a –1/2

Existence of electron and positron. Similarly also for other fermions.

rip

t

iE

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2242222 cm

rtcmcpE

Effort to obtain relativistic quantum relation of motion:

OK

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 numbersBosons: if I=B=L=S=0 and μ=0 → particle identical with antiparticle

00

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

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

Production of slow antiprotons at CERN

Production of antihydrogen in experiment ATHENA

Strange particles1) 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

Reaction of π - with nucleus in bubble chamber produces K0 and Λ

Production of Ω- (S=2) particle – picture of bubble chamber at CERN

Negative pion

Neutral kaon

Negative pion

Negative pion

Proton

Positive pion

Lambda

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 – 22

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Occurrence of resonance maxima with shape described by Breit-Wigner function.

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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 Mass

background

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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: 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

Combinatorialbackground

Hadron structureEvidences of hadron structure existence:

1) Scattering experiments – charge distribution measured by high energy electrons (they do not interact strongly) → parton structure

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)

Multiplet particles are placed in plane characterized by isospin and hypercharge

Explanation by three particle existence – quarks (actually by six – three quarks and three antiquarks) , from which elementary particles consisted of.

Two examples of baryonmultiplet

2) Jets – cluster of high energy particles (hadrons) created during deep inelastic scattering of quarks

Octuplet (J = ½) Decuplet (J = 3/2)

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: usK ,du ,ud -

Baryon decuplet (resonances):

Quark Q [e] I(JP) Iz S C B T

u +2/3 1/2(1/2+) +1/2 0 0 0 0

d -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

Review of quarks:

Additional particles → three new quarks – new quantum numbers

Identical quarks (fermions) at ground state – Pauli exclusion principle → necessity of new quantum number – color – quantum chromodynamics (QCD)

Discovery of Ω- particle by bubble chamber at Brookhavenu laboratory

Quark structure of proton:

Colored quarks held together by strong interaction (exchange of gluons transferring color)

Picture of K+ meson creation and decay during flight obtained by bubble chamber at CERN

Very intensive field of strong interaction → complicated structure of vacuum – virtual quark-antiquark pairs and gluons

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:

Three families of quarks in different collors:

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a

a

d

u

a

a

c

s

a

a

t

bwhere 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