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HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 1
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 5
charmonium level scheme
narrow states below threshold:hindered by energy limit and OZI suppressed
DD
only JPC = 1–
directly accessible in e+ e- production
C states reached bymagnetic dipoleL=0, S=1 spin-flip transitions (weaker than electric transitions)
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 6
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)
)5.1(2.0
/1
)(
34
),(
2 GeVcm
fmGeVk
rkr
cmmrV
cS
Sqq
hints for ln(r) dependencefrom bottonium levels
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 7
realistic qq potential from Lattice QCD
solving Schr. eq. with QCD Lagrangian on a discrete space-time lattice
r0=0.5 fm
hybrid potential fromglue excitations:
gcc states predicted
ground statepotential
cc
discovery possible atfuture GSI accelerator
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 8
access to charmonium states in annihilationpp
many unknown statesand transitions
hyperfine S-state splitting 120 MeV
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 9
chromomagnetic interactionstrong (hyperfine) splitting of S states, like in positronium:zero-range spin-spin interaction,point interaction of magnetic moments of e+ e-
i
ii m
e 2
rmmc
eeVee
ss 213
32
)(
modified for color-magnetic qq force: (eff. interaction, constituent mass)
1for 1
0for 3 with
32
34
)(3
S
Sr
mmcqqV qq
qq
qqSss
color-magnetic energy splitting
MeVrmmc
qqEqq
Sss 120
98
4)(3
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 10
charmonium and bottonium levels
smaller hyperfine splitting in system due to larger b-quark massbb
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 11
bottonium level scheme
flavour independent qq potential,surprising:mass difference of loweststates:
(9460) = resonance “upsilon” =53 keV
bb
: m(2S-1S) = 563 MeV
: m(2S-1S) = 589 MeV
sensitive to long-range partof qq potential r, ln(r)
2
2.,
2
n 2E :levels Coulomb
n
cm redqS
similar level structure (mc 1.3 GeV, mb 4.3 GeV) :
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 12
quarkonium em / strong decay width
positronium decay width: rcm
Se
32
2
01 4)21(
)1(43)21( .3
2
24
01
radq
q rcm
zS
qq 2 decay width:
(including higher order radiative corrections rad. )
qq 2g decay width: )1(432
)21( .3
2
2
01
radq
S rcm
gS
ratio of decay widths: 4exp2
2
01
01
10698
)21(
)21( eriment
SgS
S
17.0)(
20.0)(2
2
cm
cm
bbS
ccS
consistent with S from level spectrum
cc
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 13
Mesons in the quark model•multiplets•masses•neutral Kaon decay•CP violation
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 14
mesons in the quark model
ss
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+
in isospin (I3) and hypercharge (Y)
similar light quark masses: treated on same footing:
Y=B+S
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 15
products of SU(3) representations
Y=B+S
I3
add conjugate representation to each point of fundamental triplet
1/3
1
1/2
su
ds us
sd
ud
s
meson nonet 1833
reduced tosinglet {1} and octet {8} states
|)|2|(|6
10,0|8
|)|(|2
10,1|8
||1,1|8
)||(|3
10,0|1
0
ssdduu
dduu
du
ssdduu ´
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 16
meson multiplets (lowest L=0 states)
su sd
ds us
pseudoscalar (JP = 0- ) octet + singlet vector (JP = 1- ) octet + singlet
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 17
mixing of multiplet states
SU(3) symmetry broken by s-quark mass larger than u, d massmixing of I=0 multiplet states of same JP
physical states
8
1
8
1
cossin
sincos
from experimental meson masses:for pseudoscalar (0-), vector (1-) and tensor (2+) mesonsideal mixing (35o) octet state pure explanation of branching fractions:
32,40,11 TVP
ss
0%89
%83
KK
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 18
color-magnetic energy splitting
1for 1
0for 3 with
3
2
3
4)(
3
J
Jr
mmcqqV qq
qq
qq
Sss
J = 1
mass gap 600 MeV/c2
J = 0
remember: charmonium S-state splitting 120 MeV
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 19
meson massescalculated from constituent quark masses and color-magnetic mass splitting: ´JJqqqq
MmmM
2
2,
/483
/310
cMeVm
cMeVm
s
du
free parameters:constituent q masses:
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 20
decay channels of lightest mesons
strong decay I-spin forbidden
strong decay
strong decay notpossible for lightest meson
mixing
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 21
CP eigenstates
Parity violating decay fast slow (phase-space restricted)
3 and 20 K
320
2
02
0232
222
22
)1()1()1(
)1()1()1(
11
111
1111
C
CPCPCPCP
CCP ll
0000 )1( and )1( KKKK CPCP
construct CP eigenstates (physical states) as linear combination of S-eigenstates
0
2000
2
01
0001
)1(2
1
)1(2
1
KKKK
KKKK
CPCP
CPCP
S- but not CP eigenstates
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 22
K0 mixing and regeneration
450 GeV p0 50% LK 0 100% LK
0 .reg
)1()1(
)()1(10
10
fnKpSK
ffYMNSKf
f
0%50 SK
00LS KK
)1(
2
1
)1(2
1
8
11
10500002
10900001
CPKKKK
CPKKKK
sL
sS
02
0100. 222
1K
ffK
ffKfKfreg
! violation i.e. )103( 3 CPBR
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 23