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Lecture 04 - Hadrons ● Quarks multiplets ● Hadron decays ● Conservation laws Resonances FK7003 1 The fundamental forces Different exchange particles mediate the forces: electromagnetic strong weak Interaction Relative strength Range Exchange Mass (GeV) Charge Spin Strong 1 Short ( fm) Gluon 0 0 1 Electromagnetic 1/137 Long (1/r2) Photon 0 0 1 Weak 10-9 Short ( 10-3 fm) W+ W-,Z 80.4,80.4 , 91.2 +e,-e,0 1 Gravitational 10-38 Long (1/r2) Graviton ? 0 0 2 FK7003 No quantum field theory yet for gravity 2 The quarks Quark Q (e) Mass (GeV) u- up 2/3 0.003 d- down -1/3 0.005 s- strange -1/3 0.15 c- charm 2/3 1.2 b- bottom -1/3 4.2 t-top 2/3 171 Spin ½ particles Multiplets: u c t d s b + antiquarks: u , d , s , c , b , t opposite charge: Q -Q FK7003 3 Hadrons Two types: mesons quark+antiquark and baryons quark+quark+quark Later lectures to show why those combinations are possible. Full particle listings from the Review of Particle Physics: http://pdg.lbl.gov/2008/listings/contents_listings.html FK7003 4 The quarks Spin ½ particles Quark Q + antiparticles Mass (GeV) B S C B T (e) u- up 2/3 0.003 1/3 0 0 0 0 d- down -1/3 0.005 1/3 0 0 0 0 s- strange -1/3 0.15 1/3 -1 0 0 0 c- charm 2/3 1.2 1/3 0 1 0 0 b- bottom -1/3 4.2 1/3 0 0 -1 0 t-top 2/3 171 1/3 0 0 0 1 For antiquarks: internal quantum numbers change sign. Charge: Q -Q, Baryon number: B - B Flavour: (strangeness) S -S , ("charmness") C -C , ("bottomness") B - B , T T Charge is always conserved. Flavour quantum numbers are conserved in strong and electromagnetic decays but need not be conserved in weak decays. FK7003 5 Hadron quantum numbers Baryons: Particle Mass (MeV) B Q S C B p (uud) 938 1 1 0 0 0 n (udu) 940 1 0 0 0 0 L (uds) 1116 1 0 -1 0 0 Lc (udc) 2285 1 1 0 1 0 Lb (udb) 5624 1 0 0 0 -1 General rule for all hadrons. Total strangeness S strangeness N s N s = (no. s quarks - no. s quarks) Similarly C N c N c ; B N b N v (4.01) (obs! No "top" hadrons) Baryon number: B= quark-baryon-number (4.02) FK7003 6 Hadron properties Mesons (bosons) Particle Mass (MeV) B Q S C B p+ (ud) 140 0 1 0 0 0 K- (su) 494 0 -1 -1 0 0 D- (cd) 1869 0 -1 0 -1 0 Ds+ (cs ) 1971 0 1 0 1 0 (bb) 9460 0 0 0 0 0 FK7003 7 Evidence for a new quantum number: colour (4.03) FK7003 8 Hadrons and the strong force The strong force occurs between particles carrying "colour" charge. Range of the strong force 10 15m. q (R) q (G) Coupling at a vertex: S (more later) A quark can carry 3 colours: Red (R), Green (G), Blue (B) q(R) Gluon (RG) q (G) There are eight gluons: (later lecture in detail) Gluons themselves carry colour and self-interact: The theory of the strong force is quantum chromodynamics (QCD). FK7003 9 Colour combinations We have never seen a quark or gluon! Nature abhors naked colour. Every particle in nature is colourless/colour singlet FK7003 10 A strong reaction: FK7003 11 QCD Description of the Strong Nuclear Force Yukawa model proposed pion exchange Interaction results from internal gluon lines and quark exchange FK7003 12 Some words about decays Impossible to quote a set of simple rules for lifetimes which are correct in all cases. There are some general observations which can be made. Lifetimes: strong 1022 1024 s , weak 107 1013 s , electromagnetic 1016 1021 s These are approximate and there are exceptions. Eg A B + C Decay rate from golden rule: 2p f | H int | i f | H int | i 2 2 E ' (2.4) - depends on the dynamics of the force causing the decay. E ' relates the amount of phase space available for the decay. If mA mB + mC there is little phase space for the decay and the decay is suppressed. Eg neutron lifetime 15 minutes. The strong force has a peculiar rule, known as OZI suppression which we'll also cover today. FK7003 13 Strong decay p+ u p +p + d u u d p u u u u d d u FK7003 p+ p 14 OZI rule f decays preferentially to K+K- than p+ p0 p even though it is less energetically favourable. Decays in which all gluon lines can be ”cut” are suppressed. Rule proposed by Okubo, Zweig and Iizuka in 1960s FK7003 15 FK7003 16 Weak decays of hadrons n p + e + e S 0 L p +p L S 1! s Strangeness is violated. d u } p Strangeness (and the other flavour quantum numbers, C,B) are not conserved in weak decays. FK7003 17 Conserved quantities/symmetries Quantity Strong Weak Electromagnetic Energy Linear momentum Angular momentum Baryon number Lepton number Isospin - - Flavour (S,C,B) - Charges (em, strong and weak forces) Parity (P) - C-parity (C) - G-parity (G) - - CP - T - CPT FK7003 18 Short-lived particles Free particle moving in + x direction with energy ER Ψ(x,t) ei(xp ERt) ei(xp ) e i ( ERt) φ(x)ψ(t) (4.04) Unstable add exponential time dependence. ψ '(t) ψ(t)e Γt 2 e i ( ER i ) t 2 (4.05) Modify energy term for unstable particle: ER ER i Ψ '(x,t) φ(x)ψ '(t) e i ( ER i ) t i(xp ) 2 e Γ (4.06) 2 (4.07) 1 mean (proper) lifetime Γ A stable particle (Γ 0 ) is a plane wave corresponding to a particle of a single energy ER .Consider new waveform to be an infinite sum of | Ψ 'Ψ '* |2 e t (4.08) where τ waves corresponding to particles of different energies FK7003 19 Use Fourier transform to get E -dependent wave function Φ(E) ψ '(t)eiEt dt e t i ( E R E ) 2 dt 1 (4.09) 0 0 i ER E + 2 1 2 Probability density Φ (E) (4.10) - Breit Wigner 2 2 ER E 4 Seen in decays of nuclear and atomic energy levels. Nmax Ndecay 0.5 Nmax ER FK7003 Γ 2 ER ER Γ 2 20 Resonances Measured mass from decay : Shape of excited state mass distribution follows Breit-Wigner distribution Rate 1 m m0 2 + 4 2 p +p (4.11) m E Mass reconstruc ted from decay : 1 Δm (4.12) τ Δmτ 1 (nu) Δm c 2 τ p + +p Γ (MKS) Consistent with uncertainty principle E t (1.27) Owing to the short lifetimes - strong decays often appear as resonances. 770 MeV – ”nominal” mass FK7003 21 Summary ● Hadrons introduced ● Decays via em, weak and strong forces. ● Conservation laws ● Width of a resonance provides a lifetime FK7003 22