Outline lecture (HL-2)

1
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

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hadron resonances
J/? production
?h
Intermediate hadron state (decaying into leptons,
hadrons) interpreted as bound state (JP1-)
??
J/? resonance ?e?? 4.8 keV, ?h 59 keV
(lepton universality)
? 69 keV
?e
c
c
bound states ? transitions between excited
states
3
Crystal Ball (structure like Plastic Ball)
hollow sphere from ca. 900 NaI crystals around
interaction point
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charmonium ? decay spectrum
Level scheme reminds of positronium states n 2S1
Lj states characterized by parity P
(-1)L1 charge conjugation parity C
(-1)LS strong electric dipole ?L1,
?S0 transitions
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charmonium level scheme
only JPC 1 directly accessible
in e e- production ?C states reached
by magnetic dipole ?L0, ?S1 spin-flip
transitions (weaker than electric transitions)
narrow states below threshold hindered
by energy limit and OZI suppressed
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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
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realistic qq potential from Lattice QCD
solving Schr. eq. 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
r00.5 fm
8
access to charmonium states in
annihilation
many unknown states and transitions
hyperfine S-state splitting 120 MeV
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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
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charmonium and bottonium levels
smaller hyperfine splitting in system due
to larger b-quark mass
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bottonium level scheme
similar level structure (mc ?1.3 GeV, mb ?4.3
GeV)
flavour independent qq potential, surprising mas
s difference of lowest states
?
(9460) resonance upsilon ?53
keV
sensitive to long-range part of qq potential ? r,
? ln(r)
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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
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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

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mesons in the quark model
similar light quark masses treated on same
footing
in isospin (I3) and hypercharge (Y)
YBS
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products of SU(3) representations
YBS
1
1/3
1/2
I3
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meson multiplets (lowest L0 states)
pseudoscalar (JP 0- ) octet singlet
vector (JP 1- ) octet singlet
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mixing of multiplet states

• SU(3) symmetry broken by s-quark mass larger than
  u, d mass
• mixing of I0 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
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color-magnetic energy splitting
remember charmonium S-state splitting 120 MeV
J 1 mass gap 600 MeV/c2 J 0
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meson masses
calculated from constituent quark masses and
color-magnetic mass splitting
free parameters constituent q masses
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decay channels of lightest mesons
strong decay not possible for lightest meson
strong decay I-spin forbidden
strong decay
mixing
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CP eigenstates
Parity violating decay fast slow
(phase-space restricted)
p
p
0

3

and

2
K
S- but not CP eigenstates
construct CP eigenstates (physical states) as
linear combination of S-eigenstates
22
K0 mixing and regeneration
450 GeV p
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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

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AdditionBaryons in the quark model

• production
• multiplets
• masses
• Literature PR 15 BJ 9, 10.4 -10.6

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pion nucleonscattering
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)

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phase-shift analysis
quantum scattering in 3 dimensions (halfplane ?0)
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phase-shift analysis (2)
will contain interferences of partial waves l ?
particular angular distributions
total cross section
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phase-shift analysis (3)
elastic scattering
max. cross section for resonance condition!
at resonance energy E ER
purely imaginary!!
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phase-shift analysis (4)
expand partial wave amplitude Tl around resonance
energy
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phase-shift analysis (5)
generalization
Breit-Wigner resonance (non-relativistic)
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quark-flow diagrams
quark composition in intermediate (10-23 s) state
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baryon multiplets
color-neutral lowest energy (L0) qqq states
require symmetric
small (.1) e.m. splitting of Isospin
multiplets strong SU(3) breaking
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baryon mass spectrum
I(?)0I(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
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Summary addition

• Baryons in the quark model
• multiplets and SU(3) breaking
• masses spin-spin interaction