1. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen1 Outline lecture (HL-2) Quarkonium Charmonium spectrum quark-antiquark potential chromomagnetic interaction strong / em. decay widths Mesons in the quark model multiplets meson masses neutral Kaon decay CP violation Literature: PR 13-14; BJ 10.3,10.5,10.7

2. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen2 Intermediate hadron state (decaying into leptons, hadrons) interpreted as bound state (J P =1 - ) hadron resonances J/  production J/  resonance:  e =   = 4.8 keV,  h = 59 keV (lepton universality)  = 69 keV ee  hh ++ -- e-e- e+e+ cc bound states :  transitions between excited states

3. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen3 Crystal Ball (structure like Plastic Ball) hollow sphere from ca. 900 NaI crystals around interaction point

4. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen4 charmonium  decay spectrum Level scheme reminds of positronium states n 2S+1 L j states characterized by parity P = (-1) L+1 charge conjugation parity C = (-1) L+S strong electric dipole  L=1,  S=0 transitions

5. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen5 charmonium level scheme narrow states below threshold: hindered by energy limit and OZI suppressed only J PC = 1 – directly accessible in e + e - production  C states reached by magnetic dipole  L=0,  S=1 spin-flip transitions (weaker than electric transitions)

6. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen6 quark-antiquark potential level sequence reminds of positronium system: Coulomb-like potential (g exchange force, short range color charge 4/3 ) with linear confinement (asymptotic freedom) hints for ln(r) dependence from bottonium levels

7. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen7 realistic qq potential from Lattice QCD solving Schr. eq. with QCD Lagrangian on a discrete space-time lattice r 0 =0.5 fm hybrid potential from glue excitations: states predicted ground state potential discovery possible at future GSI accelerator

8. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen8 access to charmonium states in annihilation many unknown states and transitions hyperfine S-state splitting 120 MeV

9. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen9 chromomagnetic interaction strong (hyperfine) splitting of S states, like in positronium: zero-range spin-spin interaction, point interaction of magnetic moments of e + e - modified for color-magnetic qq force: (eff. interaction, constituent mass) color-magnetic energy splitting

10. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen10 charmonium and bottonium levels smaller hyperfine splitting in system due to larger b-quark mass

11. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen11 bottonium level scheme flavour independent qq potential, surprising: mass difference of lowest states:  (9460) = resonance “upsilon”  =53 keV  :  m(2S-1S) = 563 MeV  :  m(2S-1S) = 589 MeV sensitive to long-range part of qq potential  r,  ln(r) similar level structure (m c  1.3 GeV, m b  4.3 GeV) :

12. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen12 quarkonium em / strong decay width positronium decay width: 2  decay width: (including higher order radiative corrections  rad. ) 2g decay width: ratio of decay widths: consistent with  S from level spectrum

13. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen13 Outline lecture (HL-2) Quarkonium Charmonium spectrum quark-antiquark potential chromomagnetic interaction strong / em. decay widths Mesons in the quark model multiplets masses neutral Kaon decay CP violation

14. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen14 mesons in the quark model    s s and                                 u d d u axisaboutrotationisospinC CCiCRG GG C qq parityG 2 and 01 10 |)1(| :parity- for seigenvalue good no :parity- triplet- - ofproduct 33 22 00 0    conjugate triplet I-I- I+I+ in isospin (I 3 ) and hypercharge (Y) similar light quark masses: treated on same footing: Y=B+S

15. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen15 products of SU(3) representations Y=B+S I3I3 add conjugate representation to each point of fundamental triplet 1/3 1 1/2 u d s meson nonet reduced to singlet {1} and octet {8} states

16. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen16 meson multiplets (lowest L=0 states) pseudoscalar (J P = 0 - ) octet + singlet vector (J P = 1 - ) octet + singlet

17. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen17 mixing of multiplet states SU(3) symmetry broken by s-quark mass larger than u, d mass  mixing of I=0 multiplet states  of same J P  physical states  from experimental meson masses: for pseudoscalar (0 - ), vector (1 - ) and tensor (2 + ) mesons ideal mixing (35 o )  octet state pure  explanation of branching fractions: ss

18. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen18 color-magnetic energy splitting J = 1 mass gap 600 MeV/c 2 J = 0 remember: charmonium S-state splitting 120 MeV

19. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen19 meson masses calculated from constituent quark masses and color-magnetic mass splitting: free parameters: constituent q masses:

20. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen20 decay channels of lightest mesons strong decay I-spin forbidden strong decay strong decay not possible for lightest meson mixing

21. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen21 CP eigenstates Parity violating decay fastslow (phase-space restricted)  3 and 2 0  K construct CP eigenstates (physical states) as linear combination of S-eigenstates S- but not CP eigenstates

22. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen22 K 0 mixing and regeneration 450 GeV p

23. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen23 Summary lecture (HL-2) Quarkonium Charmonium spectrum (partly explored)  quark-antiquark potential (Coulomb like) level splitting: chromomagnetic interaction  long range part (asymptotic freedom) strong / em. decay widths  coupling strength Mesons in the quark model multiplets masses  broken SU(3) symmetry: mixing neutral Kaon decay: CP eigenstates CP violation

24. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen24 Addition: Baryons in the quark model production multiplets masses Literature: PR 15; BJ 9, 10.4 -10.6

25. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen25 pion nucleon scattering Isospin coupling, invariant mass (4-mom. sum) and phase-shift analysis yield energy (mass), I, L, J resonance assignment: L 2I,2J (mass) and width (lifetime)  (1232) P 33  (1950) N(1680) N(1520)

26. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen26 phase-shift analysis quantum scattering in 3 dimensions (halfplane  =0)

27. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen27 phase-shift analysis (2) will contain interferences of partial waves l  particular angular distributions total cross section:

28. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen28 phase-shift analysis (3) elastic scattering: max. cross section for: resonance condition! at resonance energy E = E R : purely imaginary!!

29. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen29 phase-shift analysis (4) expand partial wave amplitude T l around resonance energy:

30. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen30 phase-shift analysis (5) generalization: Breit-Wigner resonance (non-relativistic):

31. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen31 quark-flow diagrams quark composition in intermediate (10 -23 s) state

32. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen32 baryon multiplets color-neutral lowest energy (L=0) qqq states require symmetric small (.1%) e.m. splitting of Isospin multiplets; strong SU(3) breaking

33. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen33 baryon mass spectrum  -  mass splitting 80 MeV/c 2 due to spin-spin interaction I(  )=0=I(s)=I(ud)  (ud) antisymmetric  (ud) antisymmetric  spin(ud)=0  spin(  )=spin(s)=1/2 uds usd

34. HL-2 April 2004Kernfysica: quarks, nucleonen en kernen34 Summary addition: Baryons in the quark model multiplets and SU(3) breaking masses: spin-spin interaction