Quark Model. Quark Model

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1 Quark odel Outline Hadrons Isosin Strangeness Quark odel Flavours u d s esons Pseudoscalar and vector mesons Baryons Deculet octet Hadron asses Sin-sin couling Heavy Quarks Charm bottom Heavy quark esons To quark Hadrons known in 96 otivation for Quark odel Particle Zoo roliferates the finder of a new article used to be rewarded by a Nobel rize but such a discovery ought to be unished by a $ fine Lamb 955 Nuclear and Particle Physics Franz uheim

2 Nucleons Isosin Isosin Proton and neutron have almost equal mass Strong nuclear force is charge indeendent V V n V nn and n form art of single entity with isosin ½ analogous to and of sin ½ Isosin I is conserved in strong interactions Addition by rules of angular momentum Isosin ultilets Useful for classification of hadrons see slide I states in a isosin mulilet I I > Quark odel Gives natural exlanation for Isosin I ( n n n n ) u Isosin works well d d u n i number of i quarks asses of u and d quark are almost equal Nuclear and Particle Physics Franz uheim

3 Nuclear and Particle Physics Franz uheim Isosin Isosin Conservation Conservation Conservation Law Isosin I is conserved in strong interactions Allows to calculate ratios of cross sections and branching fractions in strong interactions Delta() Resonance Cross sections In agreement with I/ Isosin rediction n ( ) ( ) ( ) x mb x 7 mb all 9x mb σ σ σ Production Isosin addition atrix element deends on I not I : : : n ( ) ( ) ( ) n ass ev Width ev H H σ

4 Strangeness Strange Particles Discovered in 947 V fork and K kink Rochester and Butler Production of V(K Λ) and K ± via strong interaction weak decay Associated Production K Strange articles roduced in airs Pais Strangeness S Additive quantum number Gell-ann Nishijima Conserved in strong and electromagnetic interactions Violated in weak decays Non-zero for Kaons S : and hyerons S : Naturally exlained in quark model ( s) Nuclear and Particle Physics Franz uheim 4 K Λ Λ K τ O τ τ Λ K.89.6 n... S : K Λ Σ... S : Ξ S n s n s s K s K

5 Quark odel Quark Flavours u d s introduced by Gell-ann & Zweig Quark Charge Q[e] Isosin I I > u (u) / ½ ½ Strangeness S down (d) -/ ½ -½ strange (s) -/ - Gell-ann Zweig Charge Isosin and Strangeness Additive quark quantum numbers are related Q I ½(S B) not all indeendent Gell-ann Nishijima redates quark model valid also for hadrons Baryon number B quarks B / anti-quarks B -/ Hyercharge Y S B is useful quantum number Quark model gives natural exlanation for Isosin and Strangeness Nuclear and Particle Physics Franz uheim 5

6 esons Bound qq States Zero net colour charge Zero net baryon number B / (-/) Angular omentum L For lightest mesons Ground state L between quarks Parity P Intrinsic quantum number of quarks and letons P for fermions P- for anti-fermions L P( qq ) Pq Pq ( ) L ( )( )( ) for L Total Angular omentum J J r L r S include quark sins S qq sins anti-aligned or J P - Pseudo-scalar mesons S qq sins aligned or J P - Vector mesons Quark flavours ud us du ds su sd non-zero flavour states uu dd ss zero net flavour states have identical additive quantum numbers Physical states are mixtures Nuclear and Particle Physics Franz uheim 6

7 esons Pseudoscalar esons J P - Kaons: Strangeness S K K anti-k K - Pions: - Etas: η η Vector esons J P - Isosin I Kstar: Strangeness S K * K * anti-k * K *- rho: ρ ρ ρ - omega/hi: ω φ Isosin I Nuclear and Particle Physics Franz uheim 7

8 Baryon Deculet Baryon Wavefunction Ψ(total) Ψ(sace) Ψ(sin) Ψ(flavour) Ψ(colour) Sace symmetric - L Flavour symmetric e.g. uuu (ududuuuud)/ Sin symmetric all quarks aligned S / Colour antisymmetric Total antisymmetric - obeys Pauli Exclusion Princile Strangeness S Baryon Deculet J P / uuu <ass> Delta ev Sigma* 85 ev Cascade* 5 ev Omega - 67 ev Isosin Quark model redicted unobserved state Ω - (sss) Nuclear and Particle Physics Franz uheim 8

9 Baryon Octet Baryon Wavefunction Ψ(sace) symmetric (L ) ixed symmetric Ψ(sin flavour) Flavour Sin Sin-flavour Ψ(colour) antisymmetric mixed symmetric: e.g. (ud - du) u/ as flavour: e.g. ( - ) / e.g. (u d -d u -u d d u ) u / 6 Symmetrisation by cyclic ermutations Ψ(roton s½) ( u u d - u u d - u u d Baryon Octet J P ½ Strangeness S d u u -d u u - d u u u d u -u d u - u d u ) / 8 Isosin <ass> n Sigma 98.9 ev 9 ev Lambda 6 ev Cascade 8 ev (Xi) Lightest baryons Antibaryons ( n...) stable or long-lived also form Octet and Deculet Nuclear and Particle Physics Franz uheim 9

10 Ω - (sss) Hyeron Discovery of Ω - Hyeron - baryon with at least one s quark Quark model redicted existence and mass issing member of baryon deculet J P / discovered 964 at Brookhaven K - beam onto hydrogen target Bubble Chamber detector K. Ω K K a Ξ a Λ a γ γ a e a e e a Nuclear and Particle Physics Franz uheim e

11 Hadron asses Quark asses u d & s quark masses light at short distance q > GeV m u < m d ~ 5 ev m s ~ ev Constituent mass is relevant for quark model q < GeV eson asses m(k) > m() m(ρ) > m() m u m d ~ ev m s ~ 5 ev due to m s > m u m d same quark content e.g. ρ : (u-dbar) ass difference is due to quark sins Chromomagnetic ass Slitting Sin-sin couling of quarks S S / analogous to hyerfine slitting in el. mag. interaction r r r r r S S S S E αs ( qq ) S m qq m mm A A m m r r S S eson asses m m m u m d ev m s 48 ev r r r ( S S S ) ( S( S ) S ( S ) S ( S ) ) A (m u ) 6 ev Excellent agreement What about eta( )? S S Nuclear and Particle Physics Franz uheim m m ass [ev] eson Prediction Exeriment 4 8 K ρ ω K* φ 9

12 Heavy Quarks Charm and bottom quarks Charmonium (c-cbar) --- see QCD lecture 977 Discovery of Usilon States Interretation is Bottomonium (b-bar) Sectroscoy Charmonium and Usilon m c ~..4 GeV m b ~ GeV Heavy-light esons and Baryons Charmed (c-quark) hadrons J J J J J J P P P D D Λ * c cu cu cud D D * cd cd Bottom-quark hadrons P P P B B Λ * b ub ub bud B B * db db cs To quark Decays before forming bound states m t ~ 74 GeV discovered in 995 at Fermilab Nuclear and Particle Physics Franz uheim B D s B s D cs * s sb * s sb