HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 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
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 2
Intermediate hadron state(decaying into leptons, hadrons)interpreted as bound state (JP=1-)
hadron resonances J/ production
4/)12(
)(22
2
msJ
s
c fif
scfm 203 10/103
eeee
hadronsee
ee
J/ resonance: e== 4.8 keV, h = 59 keV (lepton universality) = 69 keV
e
h+ -
e- e+
cc bound states : transitions between excited states
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 3
Crystal Ball (structure like Plastic Ball)
hollow sphere from ca. 900 NaI crystals around interaction point
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 4
charmonium decay spectrum
Level scheme remindsof positronium statesn 2S+1 Lj
states characterized by parity P = (-1)L+1
charge conjugation parity C = (-1)L+S
strong electric dipole L=1, S=0transitions
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
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
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 April 2004 Kernfysica: quarks, nucleonen en kernen 14
mesons in the quark model
ss
and
u
d
d
u
axisaboutrotationisospinC
CCiCRG
GG
C
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
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
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 April 2004 Kernfysica: quarks, nucleonen en kernen 24
Addition:Baryons in the quark model
•production•multiplets•masses
Literature: PR 15; BJ 9, 10.4 -10.6
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 25
pion nucleonscattering
Isospin coupling,invariant mass (4-mom. sum)and phase-shift analysisyield energy (mass), I, L, J
resonance assignment:L2I,2J (mass)and width (lifetime)
(1232) P33
(1950)
N(1680)
N(1520)
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 26
phase-shift analysisquantum scattering in 3 dimensions (halfplane =0)
ikzin e
)( fr
eikr
scatt
0)(cot
2/
2/11
2
1)(
)()(cos)12(1
)(
)2/(
.
2
0
.
.
lreson
resonl
EEl
reson
EEill
lll
E
iEEie
iET
ETPlk
f
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 27
phase-shift analysis (2)
0
2
1( ) (2 1) (cos ) ( )
( )
l ll
f l P T Ek
df
d
will contain interferences of partial waves l particular angular distributions
total cross section:
0
2
20
1( ) (2 1) (cos ) ( )
(2 1) 2 ( )
l ll
ll
f l P T Ek
dd l iT E
d k
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 28
phase-shift analysis (3)
22
0
1
4(2 1)sin
l
elastic ll
lk
elastic scattering:
max. cross section for:resonance condition!
/ 2l
1 1
( ) sin2 cot ( )
l l l li i i il l
l
T E e e e ei E i
at resonance energy E = ER: / 2l
( )l RT E i purely imaginary!!
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 29
phase-shift analysis (4)
2
0 cot ( ) 0 cot ( ) :
2
2cot ( )
1 1 / 2( ) 1
2 / 2
R
R
Rl
l R R l E E
R
l E E
E Eil l
R
dE E E E
dE
E E
dE
dE
T E ei i E E i
expand partial wave amplitude Tl around resonance energy:
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 30
2
2
2
22 2
42 1
4 / 42 1
/ 4
lelastic R l R
R
E E l T E Ek
lk E E
phase-shift analysis (5)
generalization:
1 21 2
2 1( )
2 1 2 1
Jg J for J s s
s s
������������������������������������������
Breit-Wigner resonance (non-relativistic):
( )( ) 22 2
( )/ 4
elastic in elasticlin elastic R
R
E E g Jk E E
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 31
quark-flow diagrams
quark composition in intermediate (10-23 s) state
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 32
baryon multiplets
colorspinflavorspace
total
A
color-neutrallowest energy (L=0)qqq states requiresymmetric spinflavor
small (.1%) e.m. splittingof Isospin multiplets;strong SU(3) breaking
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 33
baryon mass spectrum
- mass splitting80 MeV/c2
due tospin-spin interaction
I()=0=I(s)=I(ud)(ud) antisymmetric(ud) antisymmetric spin(ud)=0spin()=spin(s)=1/2
uds
usd
HL-2 April 2004 Kernfysica: quarks, nucleonen en kernen 34
Summary addition:Baryons in the quark model•multiplets and SU(3) breaking•masses: spin-spin interaction