1. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
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
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

2. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
hadron resonances
J/ production h + - e- e+
Intermediate hadron state
(decaying into leptons, hadrons)
interpreted as
bound state (JP=1-) 
J/ resonance: e== 4.8 keV, h = 59 keV
(lepton universality)  = 69 keV e c c
bound states :  transitions between excited states
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

3. Crystal Ball (structure like Plastic Ball, now at KVI)
HL-2 May 2006
Crystal Ball (structure like Plastic Ball, now at KVI)
hollow sphere from ca. 900 NaI crystals around interaction point
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

4. charmonium  decay spectrum
HL-2 May 2006
charmonium  decay spectrum
Level scheme reminds
of positronium states
n 2S+1 Lj
states characterized by
parity P = (-1)L+1
charge conjugation
parity C = (-1)L+S
strong electric dipole
L=1, S=0
transitions
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

5. charmonium level scheme
HL-2 May 2006
charmonium level scheme
only JPC = 1–
directly accessible
in e+ e- production
C states reached by
magnetic dipole
L=0, S=1
spin-flip transitions
(weaker than electric
transitions)
D mesons:
narrow states below threshold:
hindered by energy limit and suppressed (“OZI rule”)
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

6. low-energy hadron resonances
HL-2 May 2006
low-energy hadron resonances +
 - e- e+ 0 K-
K + e- e+ 0 K0 e- e+ 0
=150 MeV
=4.4 MeV, why not 3 decay? (18%)
requires
3g coupling,
amplitude
suppressed by OZI rule
(Okubo, Zweig, Iizuka)
stronger suppression for J/
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

7. quark-antiquark potential
HL-2 May 2006
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
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

8. realistic qq potential from Lattice QCD
HL-2 May 2006
realistic qq potential from Lattice QCD
solving Schrödinger equation with
QCD Lagrangian on a discrete space-time lattice
hybrid potential from
glue excitations:
states predicted
discovery possible at
future GSI accelerator
ground state
potential
r0=0.5 fm
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

9. Kernfysica: quarks, nucleonen en kernen
Hot News!
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen

10. access to charmonium states in annihilation
HL-2 May 2006
access to charmonium states in annihilation
many unknown states
and transitions
hyperfine S-state
splitting 120 MeV
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

11. chromomagnetic interaction
HL-2 May 2006
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
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

12. charmonium and bottonium levels
HL-2 May 2006
charmonium and bottonium levels
smaller hyperfine splitting in system due to larger b-quark mass
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

13. bottonium level scheme
HL-2 May 2006
bottonium level scheme
similar level structure (mc 1.3 GeV, mb 4.3 GeV) :
flavour independent
qq potential,
surprising: very similar
mass difference of lowest
states: 
: m(2S-1S) = 563 MeV 
: m(2S-1S) = 589 MeV 
(9460) = resonance “upsilon”
=53 keV
sensitive to long-range part
of qq potential  r,  ln(r)
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

14. quarkonium em / strong decay width
HL-2 May 2006
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
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

15. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
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
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

16. mesons in the quark model
HL-2 May 2006
similar light quark masses: treated on same footing: ø è Ä s
and ÷ ö ç æ - = ×
> u d
axis
about
rotation
isospin C i R G q
parity 2 1 | ) ( :
for
eigenvalue
good no
triplet of
product 3 t p
conjugate triplet I- I+
in isospin (I3) and hypercharge (Y)
Y=B+S
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

17. products of SU(3) representations
HL-2 May 2006
products of SU(3) representations
add conjugate representation to each point of
fundamental triplet
Y=B+S
meson nonet
reduced to
singlet {1} and octet {8} states 1 u d s
1/3
1/2 I3
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

18. meson multiplets (lowest L=0 states)
HL-2 May 2006
meson multiplets (lowest L=0 states)
pseudoscalar (JP = 0- ) octet + singlet vector (JP = 1- ) octet + singlet
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

19. mixing of multiplet states
HL-2 May 2006
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 JP
physical states 
from experimental meson masses:
for pseudoscalar (0-), vector (1-) and tensor (2+) mesons
ideal mixing (35o) octet state pure
explanation of branching fractions: s s
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

20. color-magnetic energy splitting
HL-2 May 2006
color-magnetic energy splitting
remember: charmonium
S-state splitting 120 MeV
J = 1
mass gap 600 MeV/c2
J = 0
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

21. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
meson masses
calculated from constituent quark masses
and color-magnetic mass splitting:
free parameters:
constituent q masses:
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

22. decay channels of lightest mesons
HL-2 May 2006
strong decay not
possible for lightest
meson
strong decay
I-spin forbidden
strong decay
mixing
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

23. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
CP eigenstates
Parity violating decay
fast slow (phase-space restricted) K 2 p
and 3 p
S- but not CP eigenstates
construct CP eigenstates
(physical states) as linear
combination of S-eigenstates
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

24. K0 mixing and regeneration
HL-2 May 2006
K0 mixing and regeneration
450 GeV p
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

25. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
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
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

26. Addition: Baryons in the quark model
HL-2 May 2006
Addition: Baryons in the quark model
production
multiplets
masses
Literature: PR 15; BJ 9,
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

27. pion nucleon scattering
HL-2 May 2006
(1232) P33
(1950)
N(1680)
N(1520)
pion nucleon scattering
Isospin coupling,
invariant mass (4-mom. sum)
and
phase-shift analysis
yield energy (mass), I, L, J
resonance assignment:
L2I,2J (mass)
and width (lifetime)
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

28. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
phase-shift analysis
quantum scattering in 3 dimensions (halfplane =0)
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

29. phase-shift analysis (2)
HL-2 May 2006
phase-shift analysis (2)
will contain interferences of partial waves l
 particular angular distributions
total cross section:
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

30. phase-shift analysis (3)
HL-2 May 2006
phase-shift analysis (3)
elastic scattering:
max. cross section for:
resonance condition!
at resonance energy E = ER:
purely imaginary!!
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

31. phase-shift analysis (4)
HL-2 May 2006
phase-shift analysis (4)
expand partial wave amplitude Tl around resonance energy:
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

32. phase-shift analysis (5)
HL-2 May 2006
phase-shift analysis (5)
generalization:
Breit-Wigner resonance (non-relativistic):
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

33. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
quark-flow diagrams
quark composition in intermediate (10-23 s) state
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

34. Kernfysica: quarks, nucleonen en kernen
baryon multiplets
HL-2 May 2006
color-neutral
lowest energy (L=0)
qqq states
require
symmetric
small (.1%) e.m. splitting
of Isospin multiplets;
strong SU(3) breaking
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

35. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
baryon mass spectrum
I()=0=I(s)=I(ud)
(ud) antisymmetric
(ud) antisymmetric
spin(ud)=0
spin()=spin(s)=1/2
-  mass splitting
80 MeV/c2
due to
spin-spin interaction
uds
usd
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

36. Kernfysica: quarks, nucleonen en kernen
HL-2 May 2006
Summary addition:
Baryons in the quark model
multiplets and SU(3) breaking
masses: spin-spin interaction
HL-2 May 2006
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen