Dr Victoria Martin, Prof Steve Playfer Spring Semester 2013

Transcription

1 Particle Physics Dr Victoria Martin, Prof Steve Playfer Spring Semester 2013 Lecture 12: Mesons and Baryons Mesons and baryons Strong isospin and strong hypercharge SU(3) flavour symmetry Heavy quark states 1

2 Review from Friday Using high energy deep inelastic scattering, e p e X, we find out the proton consists of partons: three valance quarks: two up quarks, one down quark gluons pairs of quark anti-quark sea quarks In today s lecture consider the valance quark content of the mesons and baryons 2

3 Mesons and Baryons Mesons are quark-antiquark bound states with symmetric colour wavefunction which is colour neutral: χ c = 1 3 r r + b b + gḡ Baryons are three quark bound states. They have an antisymmetric colour wavefunction which is colour neutral: χ c = 1 6 [rgb rbg + gbr grb + brg bgr] As hadrons are colour neutral, they do not interact with each other by single gluon exchange. Instead they couple to each other by hadron exchange, typically through the lightest qq meson, pion (π +, π 0, π ) Yukawa (1935) the finite range of strong interactions between hadrons is due to the pion mass of ~140 MeV 3

4 Constituent Quark Masses Because of QCD renormalisation, there is an ambiguity as how to define an absolute mass. The most commonly used definition of a mass is known as the M S scheme. mu= 2.4 MeV, md = 4.8 MeV, ms =104 MeV These are too small to account for the hadron masses! The majority of the mass of hadrons comes from QCD interactions. 4

5 Flavour Symmetries: Isospin Flavour symmetries are symmetries between interchange of quark flavour. Flavour symmetries were proposed before quarks were hypothesised to explain observed phenomena. Strong interactions are (approximately) invariant under flavour symmetry rotations. Assign quantum numbers to characterise these symmetries. Strong Isospin (I, I3); Quark flavour quantum numbers: Strangeness (S), Charm (C), Beauty (B), Truth (T) Strong hypercharge (Y) Strong isospin is a symmetry between u and d quarks Strong interactions are invariant under strong isospin rotations u d, or equivalently, p n The u and d quarks form an isospin doublet: They have the same total strong isospin (I), but different third-components (I3) I = 1/2 with I3(u)= +1/2 and I3(u)= 1/2 (by analogy to S=1/2 with spin states and ) 5

6 SU(3) Flavour Symmetry An SU(3) flavour symmetry is exhibited between u, d and s quarks The symmetry is broken by the s quark mass ms ~ 100 MeV >> mu, md Strong interactions are almost invariant under SU(3) flavour symmetry The s quark is assigned a strangeness S= 1 ( s has S=+1) Two useful combinations: Strong Hypercharge Y = S + B (where B = ⅓ [N(q) N(q )] is baryon number) Electric charge: Q = I3 + Y/2 These are the basic building blocks for constructing meson (q q ) and baryon (qqq) multiplets Baryons generally have with no orbital angular momentum (L) between the quarks. 6

7 The J=0 Pseudoscalar Mesons Total angular momentum, J=0: orbital angular momentum, L=0; one spin-up and one spin-down quark The allowed flavour combinations are given by the Gell Mann λ matrices, same matrices that describe the allowed colour combinations of gluons. S Y 0 +1 K 0 (d s ) K + (u s ) M(K 0, K 0) = 498 MeV M(K +,K ) = 494 MeV M(π +,π ) = 140 MeV M(π 0 )=135 MeV 1 0 π (d u ) π 0,η 1,η 8 π + (u d ) M(η)=550 MeV M(η )=960 MeV π 0 = 1/ 2 [ d d u u ] η 8 = 1/ 6 [ d d + u u 2 s s ] 2 1 K (s u ) K 0 (s d ) η 1 = 1/ 3 [ d d + u u + s s ] 1 1/2 0 +1/2 +1 I 3 Observed η,η mesons are mixtures of η 1 and η 8 7

8 The J=1 Vector Mesons Total angular momentum, J=1: L=0, both quarks with same spin S Y M(K* +,K* ) = 892 MeV M(K* 0, K* 0 ) = 896 MeV M(ρ +,ρ ) = 776 MeV M(ρ 0 )=767 MeV M(ω)=783 MeV M(φ)=1019 MeV 2 1 ω = 1/ 2 [ d d + u u ] φ = s s ρ 0 = 1/ 2 [ d d u u ] 1 1/2 0 +1/2 +1 I 3 8

9 The J=1/2 Baryon Octet L=0, Quark spin composition is S Y 0 +1 ddu uud M(n) = 940 MeV M(p) = 938 MeV 1 0 M(Λ) = 1116 MeV dds uus M(Σ) = 1193 MeV 2 1 dss uss M(Ξ) = 1318 MeV 1 1/2 0 +1/2 +1 Λ 0 = [uds] isospin singlet state I=0 Σ 0 = [uds] isospin triplet state I=1 I 3 9

10 The J=3/2 Baryon Decuplet Total angular momentum J=3/2: all spins aligned, L=0 S Y 0 +1 M(Δ) = 1232 MeV 1 0 M(Σ )=1383 MeV 2 1 M(Ξ )=1532 MeV 3 2 M(Ω)=1672 MeV 3/2 1 1/2 0 +1/ /2 I 3 10

11 Δ ++ and Baryon Wavefunctions The overall wavefunction of a system of identical fermions must be antisymmetric under exchange of any two fermions ψ (Δ ++ ) = u u u = χc χf χs χl The Δ ++ wavefunction is symmetric in flavour χf and spin χs (J=3/2) There is no orbital angular momentum L=0, spatially symmetric χl Hence it must have an antisymmetric colour wavefunction χc Further evidence for quark colour Why are there no J=1/2 uuu, ddd, sss baryons? Full proton wave function is: Baryon Colour Flavour Spin Spatial Total Δ ++ A S S S A p A A or S A or S S A ψ(p) = 1 18 [u u d +u u d 2u u d +u d u +u d u 2u d u +d u u +d u u 2d u u ] 11

12 Heavy Quark Mesons and Baryons Can define an SU(4) symmetry u d s c Heavy quark mesons and baryons obtained by replacing one (or more) of the light u,d,s quarks by a heavy c or b quark There are no bound state hadrons containing t quarks Lowest lying charm meson states with M(D) ~ 1.9 GeV: D + ( c d ), D ( c d ), D 0 ( c u ), D 0 ( c u ), Ds + ( c s ), Ds ( c s ) Lowest lying bottom meson states with M(B) ~ 5.3 GeV: B 0 ( b d ), B 0 ( b d ), B ( b u ), B + ( b u ), B S 0 ( b s ), Bs 0 ( b s ) Baryons Λc (cud), Λb (bud) Charmonium ( c c ) and Bottomonium ( b b ) 12

13 Resonances Some hadrons decay due to strong force, hadrons have very short lifetime τ ~ s Evidence for the existence of these states are resonances in the experimental data Shape is Breit-Wigner distribution: σ = σ max Γ 2 /4 (E M) 2 +Γ 2 /4 (with Γ calculated from Fermi s Golden rule, Γ~ M 2 ρ) 2010 Subatomic: Particle Physics 2 pπ scattering 2. Draw a Feynman diagram for the process pπ + ++ pπ +.!"#$$%$&'()#*%+, π + p total 10 P lab GeV/c The down and anti-down quarks annihilate by producing a gluon. The gluon can be absorbed by any of the quarks. Remember as long as the flavour of the quark doesn t change, a gluon can be emitted or absorbed by any quark. After about πp s (any) one of the quarks emits a gluon which turns into a d d pair. It decays s GeV so quickly as the strong coupling constant is large, so the quarks are very likely to πd emit 60 an energetic enough gluon to make a d d, and because the minimum energy state is favoured. The mass of the pion and the proton is smaller than the mass of 10 2 the ++. π + p elastic You have to think of the constituents quarks. We have uud+ du uuu uud+ du. This looks like a pretty silly Feynman diagram, but the uuu state actually lives for 13 slightly longer than just three quarks would if they didn t form a bound state.

14 Discovery of the Heavy Quarks Collider experiments discovered the charm (1974), bottom (1977) and top quarks (1995) Produced in pairs by e + e cc e + e bb At threshold (E~2mq) bound cc, bb states are narrow resonances Produced in pairs at hadron colliders through one gluon and two gluon diagrams (Single c,b,t production requires an intermediate W boson) Can identify heavy quark jets by tagging decays of c and b quarks with lifetimes τc ~0.4ps, τb~1.5ps 14

15 Charmonium & Bottomonium } 1st observed by ATLAS in 2011 Analogous to hydrogen spectroscopy with quark-quark potential Vqq (r) = 4/3 αs/r + kr (see lecture 9) 15

16 t t W + b W b candidate event Lines are project paths of charged particles through the detector. Not all particles originate from collision point. Particle produced and travelled short distance before decaying, indicates production of a b-quark! 16

17 Summary Quarks are confined to colourless bound states, collectively known as hadrons: mesons: quark and anti-quark. Bosons (s=0, 1) with a symmetric colour wavefunction. baryons: three quarks. Fermions (s=1/2, 3/2) with antisymmetric colour wavefunction. anti-baryons: three anti-quarks. Lightest mesons & baryons characterised by strong isospin (I, I3), strangeness (S) and strong hypercharge Y strong isospin I=½ for u and d quarks; (isospin combined as for spin) I3=+½ (strong isospin up) for up quarks; I3= ½ (strong isospin down) for down quarks S=+1 for strange quarks (additive quantum number) strong hypercharge Y = S + B Hadrons display SU(3) flavour symmetry between u d and s quarks. The symmetry predicts the allowed meson and baryon states. Strong decays of hadrons cause resonances due to very short lifetimes. Residual strong force interactions between colourless hadrons propagated by mesons. 17