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, ν e, ν μ, ν τ ) – 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 -, π 0, K +, K -, K 0, ρ +, ρ -, ρ 0 …) Baryons – (p, n, Λ, Σ +, Σ -, Σ 0, Δ ++, Δ +, Δ 0, Δ -, N, Ω - …) Particle classification according to statistics: Bosons: Bose-Einstein statistic → arbitrary number of particles in given state – integral spin Wave function – symmetric: Ψ B (x 1,x 2,x 3, …,x n ) = Ψ B (x 2,x 1,x 3, …,x n ) 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: Ψ F (x 1,x 2,x 3, …,x n ) = -Ψ F (x 2,x 1,x 3, …,x n ) 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 +

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 – L e, L μ a L τ 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 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): for particle motion direction in axe x: Its solution for free particle: We substitute: We obtain condition: Positive and negative solutions exist: Possible interpretation of solution E 2 : 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. Effort to obtain relativistic quantum relation of motion: OK

Discovery of first antiparticle: positron in cosmic rays 1955 – antiproton (BEVATRON), 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 -, K 0 a π + :

Review of physical quantities from the view of relation between particle and antiparticle: Quantityparticleantiparticle Mass msame Spin (magnitude)same Lifetime τsame Isospin (magnitude)same Electric chargeQ-Q Magnetic momentμ-μ Baryon numberB-B Lepton numberL-L StrangenessS-S z component of isospin I z IzIz -I z Intrinsic parity PSame for bosonsOpposite - 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

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 particles 1) New particles with much longer lifetime ~ s – 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: Σ 0 → Λ 0 + γ S = Non-existent decay: Σ + → p + γ S = 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 = Hyperon (strange baryon) Ξ - is decaying through two steps: Ξ - → Λ + π – S = Λ → n + π 0 S = 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(I z + Y/2)= e(I z + (B+S)/2)

First strange particles: K mesons, lambda – turn of forties and fifties Reaction of π - with nucleus in bubble chamber produces K 0 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 ~ s) → 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 – Occurrence of resonance maxima with shape described by Breit-Wigner function. 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 M 0 = 10 and Γ = 3 above constant background of cross section 1.0 Mass background resonance Cross section

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 +, N 0 – excited states of nucleons (structure uud a udd) – izospin I = 1/2, strangeness S = 0 Δ ++ Δ + Δ 0 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 Combinatorial background

Hadron structure Evidences 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 – μ p = μ J, μ n = μ J 4) Excited states of hadrons (nucleons) – of proton (N + ), of neutron (N 0 ) – 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 baryon multiplet 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, Σ 0 = uds, Λ = uds, Ω = sss (Σ 0, Λ differ by isospin) Mesons → quark – antiquark: Baryon decuplet (resonances): QuarkQ [e]I(J P )IzIz SCBT u+2/31/2(1/2 + )+1/20000 d-1/31/2(1/2 + )-1/20000 s-1/30(1/2+)0000 c+2/30(1/2+) b-1/30(1/2+)0000 t+2/30(1/2+) 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±, Z 0, photon and Higgs boson) Look as point like particles for accessible energies. Three families of leptons: Three families of quarks in different collors: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 Fermilab USA (CDF and D0 experiments on Tevatron accelerator with colliding beam of p, anti-p - √s = 1.7 TeV), last value of m t = (176±7) GeV/c 2 2) Observation of ν τ 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/c 2 so far not unquestionable evidence – problem with background and statistical significance of effect on background