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The Quark Parton Model

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The Quark Parton Model The Quark Parton Model • Quark Model • Pseudoscalar JP = 0– Mesons • Vector JP = 1– Mesons • Meson Masses P + • J = 3/2 Baryons P + • J = ½ Baryons • Resonances • Resonance Detec?on • Discovery of the ω meson • Dalitz Plots Quark Model BeGinninG of 60s: ReGulari?es in the hadron spectra indicated that they are formed by 3 (valence) quarks: u, d, s and their an?par?cles u, d, s • Quarks are not observed as free par?cles “symmetry driven” model in 1964; 10 more years were needed to develop a dynamical model • BeGinninG of 70s: deep-inelas?c scaerinG of leptons off hadrons (Rutherford-like eXperiment): result: inside the nucleons there are light, quasi-free, point-like fermions called partons (our quarks!) • Their effec?ve mass is: m ~1/3 of the baryon mass, with a momentum p: ~1/R (~1 fm) • For heavy quarks the non-relavis?c approXimaon holds: m>>1/R • ReGulari?es in the hadron spectra were accounted for by the quark model ( mul?plets) Classificaon of Hadrons Classificaon of Hadrons πN Scaering Strangeness Quark Model d u s =0 s = 1 s Quarks Antiquarks s = -1 s Q = 2/3 s =0 u d Q = -1/3 Q = -2/3 Q = 1/3 • Par?cles with same spin, parity and charGe conjuGaon symmetry described as mulplet - Different Iz and Y • RaisinG and lowerinG operators to naviGate around the mulplet • Gell-Mann and ZweiG: Paerns of mul?plets eXplained if all hadrons were made of quarks Q Q • Model oriGinally developed usinG Group theory alone Q - No need for physical quarks Q - Fact that quark charGes non-inteGer suGGested Q perhaps they were not real par?cles Mesons Mesons are built with quark/an?-quark pairs. If we assume only u, d, s quarks (with their an?-quarks) we could have families with 32=9 elements each (nonets). One has then: J=1 spin triplet states (↑↑, 1/√2 (↑↓+↓↑), ↓↓) with J=1 and Jz=1, 0, -1 J=0 spin sinGlet states (1/√2 (↑↓-↓↑)) with J=0 S K*0 K*+ +1 e.G. the JP=1- meson nonet - 0 + ρ ρ φ ρ I3 vector mesons: JPC=1-- -1 -1/2 ω +1/2 +1 (as the photon) *- K K*0 -1 Mesons Pseudoscalar JP= 0– Mesons Quark plus an?quark with spins ½ + -½ = 0 (↑ ↓) (→ 9 combinaons) ⇥0 :(uu¯ dd¯)/⇥2 − η :(uu¯ + dd¯ 2ss¯)/⇥6 − η :(uu¯ + dd¯+ ss¯)/⇥3 1 Pseudoscalar JP= 0– Mesons Vector JP= 1– Mesons Quark plus an?quark with spins ½ + ½ = 1 (↑ ↑) (→ 9 combinaons) 0 ρ = 1/√2 (dd – uu) ω = 1/√2 (dd + uu) ϕ = ss Vector Mesons JP= 1– Vector Mesons Higher Masses States shown so far have no anGular momentum between the qq or the qqq HiGher mass states are obtained by havinG orbital anGular momentum between the qq or the qqq → J = 2, 3, . .5/2, 7/2 . Meson Masses Vector Meson Decays Vector meson decays into lepton pairs: one more proof of the hadron quark composi?on and charGe assiGnment The leptonic par?al width Γ(e+e-) is propor?onal to the square of the quark charGes (Rutherford): 16πα 2Q2 Γ(V → l+l− ) = ψ(0) 2 Amplitude squared for the two quarks interac?nG with the photon in 2 one point of the space-?me =1/volume of the meson MV 2 2 with Q = ΣaiQi (square of the mean quark charGe, with ai amplitude coefficients) The formula is derived takinG into account a (1/q2)2 propagator term, the phase space € for 2-body decay (q2) and the couplinG of the photon to the quarks in the meson: € q l + √α Q √α 1/q2 q l + 1 2 1 2 1 2 1 e.G. for the ρ : (uu − dd) one has: Q = [ ( − (− )] = 2 2 3 3 2 1 2 1 2 1 2 1 (uu + dd) Q = [ ( + (− )] = ω : 2 2 3 3 18 1 1 € € Q2 = (− )2 = φ : ss 3 9 € € € € Vector Meson Decays Indeed, the measured leptonic widths for the various vector mesons are quite different: Γe + e − (ρ) = 6.8 ± 0.3 Γe + e − (ω) = 0.6 ± 0.02 Γe + e − (φ) =1.37 ± 0.05 But their differences are completely understood within the quark meson charGe assiGnment and composi?on: € Γe + e − (ρ) 2 =13.6 ± 0.6 Σai Qi Γe + e − (ω) 2 =10.8 ± 0.4 Σai Qi Γe + e − (φ) 2 =12.3± 0.5 Σai Qi € The Quark Parton Model EXperimentally hadron states classified by mass, spin and parity and associated into families P + Baryons with J = 3/2 Mass I = – 3/2 –1 – 1/2 0 +1/2 +1 +3/2 StranGeness 3 (MeV/c2) – 0 + ++ 1230 0 I = 3/2 Δ Δ Δ Δ I = 1 Σ*– Σ*0 Σ*+ 1380 -1 I = ½ Ξ*– Ξ*0 1530 -2 I = 0 Ω– 1670 -3 P + J = 3/2 Baryons These can all be eXplained by a basic set of 3 different spin ½ 'quarks' u, d, s combined in sets of 3 i.e. qqq with their spins aliGned to Give: ½ + ½ + ½ = 3/2 (↑ ↑ ↑) 2 with mu ≈ md and ms ≈ mu + 150 MeV/c Quark B J I I3 S Q u ⅓ ½ħ ½ +½ 0 ⅔e d ⅓ ½ħ ½ -½ 0 -⅓e s ⅓ ½ħ 0 0 -1 -⅓e P + J = 3/2 Baryons d → u d → s Not known at the time These are stronGly decayinG resonances P + J = 3/2 Baryons ReGulari?es in the hadron spectra: baryon JP = 3/2+ decuplet I3 = -3/2 I3 = 0 I3 = +3/2 S Λ- Λ0 (ddu) Λ+ (duu) Λ++ (uuu) S = 0 (ddd) I = 3/2 Q = +2 Σ- (dds) Σ0 (dus) Σ+ (uus) I S = -1 3 I = 1 Q = +1 - S = -2 Ξ (dss) Ξ0 (uss) I = 1/2 Q = 0 S = -3 Ω- (sss) Q = - 1 I = 0 Q B + S Y = I + = I + | e | 3 2 3 2 € P + Ground State J = 1/2 Baryons 3 quarks with spins ½ + -½ + ½ = ½ (↑ ↓ ↑) 0 Λ = 1/√2 (ud – du) s 0 Σ = 1/√2 (ud + du) s LiGhtest baryons Decay weakly (eXcept proton which is stable) P + J = 1/2 Baryons Why are there no uuu, ddd or sss here? With u, d and s quarks there are 3 × 3 × 3 = 27 combinaons From symmetry arGuments these can be Grouped into 1 (Singlet) + 8 (Octet) + 8 (Octet) + 10 (Decuplet) The 10 are the JP = 3/2+ shown first and one of the 8 are these JP = 1/2 + Baryons are fermions (spin 1/2, 3/2, . .) so the overall wavefunc?on must be an?symmetric (A) The space × spin × flavour part must be symmetric (S) With anGular momentum ℓ = 0 the space part ~ (-1) ℓ = +1 so we want spin × flavour to be symmetric Resonances There are over 100 known hadrons – most are 'Resonances' i.e. EXcited States with the same quark content but hiGher internal anGular momentum p, n → N*, Δ K0, K± → K* Λ, Σ → Λ*, Σ* π0, π± → ρ, ω Resonances are formed and decay via the StronG Interac?on Life?mes very short ~ 10-22 to 10-23 s By Uncertainty Principle: Width Γ~ 66 MeV At speed of liGht only travel 3 × 108 × 10-23 ~ 3 × 10-15 m → leave no tracks in detectors Resonance Detec=on Detect their presence via stable (or lonGer lived) par?cles into which they decay or are produced + ++ + π + p → Δ (1232) → π + p π – + p → Δ0(1232) → π – + p Beam momentum Equivalent CM EnerGy 1.0 1.25 1.75 2.0 Discovery of the ω Meson Note: ω (omeGa) meson not Ω– baryon Take bubble chamber pictures of p annihilaon - look at events with eXactly 5 pions produced + + – – 0 p + p → π + π + π + π + π Plot invariant mass of all possible 3π combinaons: + + – π + π + π – – + π + π + π All have net electric charGe → + + 0 π + π + π No structure seen – – 0 π + π + π The only neutral combinaon + – 0 π + π + π → Sharp peak at M = 790 MeV/c2, Γ = 12 MeV/c2 Discovery of the ω Meson Peak Dalitz Plots – + – In π + p → π + π + n there could be intermediate short lived states: long lived Delta Δ ≡ eXcited nucleon (Nπ) rho ρ ≡ eXcited pion (ππ) (a) ρ0 (= ππ resonance) is (b) Δ (= Nπ resonance) is produced via π eXchanGe produced via ρ eXchanGe How to tell if either (or both) happen? → Dalitz Plot Dick Dalitz Dalitz Plots Measure many thousand 'events' (= collisions of this type) and plot result on 2-D histoGram Intermediate states (ρ0, Δ+) cause clusterinG of points at specific values of M² giving 'bands' on Dalitz Plot Spread of M² (width of band) Gives measure of width of resonance (some?mes increased or masked by eXperimental resolu?on) Dalitz Plots Note: Stas?cal treatment – cannot iden?fy specific events So many hadrons discovered like this no lonGer considered 'fundamental' Discovery of the Ω- Discovery of the Ω- (aer beinG postulated to complete the decuplet) 1964, Brookhaven Lab. Ω- (sss) uud Combinaons For uud Can have flavour symmetric (uud + udu + duu) and spin symmetric (↑↑↑ + ↑↑↑ + ↑↑↑) 3 Same quantum → J = /2 numbers so can form linear or combinaons flavour an?symmetric (uud) It's symmetric if it stays the same if and spin an?symmetric you swap any two flavours or spins (↑↑↓) → J = ½ + So there is a uud state in both the J = 3/2 decuplet (Δ ) and the J = ½ octet (p) uuu Combinaons For uuu (or ddd or sss) Can have only have flavour symmetric (uuu) and spin symmetric (↑↑↑) → J = 3/2 No flavour an?symmetric and spin an?symmetric (↑↑↓) possible ++ So there is only a uuu state in the J = 3/2 decuplet (Δ ) and not in the J = ½ octet Construcng Baryon States Baryon Masses .
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