spectra and decays of hybrid charmonia
DESCRIPTION
Spectra and decays of hybrid charmonia. Yu.S.Kalashnikova , ITEP in collaboration with A. Nefediev , PRD77 054025 (2008). Y(4260): hybrid charmonium ?. QCD string model:. Based on Vacuum Correlator Method Confinement: gluonic correlators responsible for - PowerPoint PPT PresentationTRANSCRIPT
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Spectra and Spectra and decaysdecays
of hybrid of hybrid charmoniacharmonia
Yu.S.Kalashnikova, ITEPYu.S.Kalashnikova, ITEP
in collaboration with A. Nefediev, PRD77 054025 in collaboration with A. Nefediev, PRD77 054025 (2008) (2008)
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Y(4260): hybrid Y(4260): hybrid charmonium?charmonium?
Yu.S.Kalashnikova, ITEP 2
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QCD string model:QCD string model:
Yu.S.Kalashnikova, ITEP 3
Based on Vacuum Correlator MethodBased on Vacuum Correlator Method
Confinement: gluonic correlators responsible forConfinement: gluonic correlators responsible for area law asymptotic for the Wilson looparea law asymptotic for the Wilson loop
QCD string model corresponds to the limit of smallQCD string model corresponds to the limit of small gluonic correlation length gluonic correlation length
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Excitations of the QCD string:Excitations of the QCD string: q qqq -> “minimal” string -> “minimal” string
q
q
Yu.S.Kalashnikova, ITEP
P = (-1)P = (-1)L+1L+1 C = (-1) C = (-1)L+SL+S
4
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Hybrid excitations:Hybrid excitations:gluon with two “minimal” gluon with two “minimal” strings attachedstrings attached q
qg
Yu.S.Kalashnikova, ITEP 5
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Quantum numbersQuantum numbers
Magnetic (lMagnetic (lg g = j= jgg)) Electric (lElectric (lg g = j= jgg1)1)
Yu.S.Kalashnikova, ITEP
1
( 1)
( 1)
qq g
qq qq
l j
l s
P
C
1
1
( 1)
( 1)
qq g
qq qq
l j
l s
P
C
Lowest magneticLowest magnetic
0 1qq gl j 0 1
1 , 0,1,2
s
s J J
6
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Zero-order Hamiltonian:Zero-order Hamiltonian:
Yu.S.Kalashnikova, ITEP
2 2 2 2 4
3s
cc q qH p m p m rr
2 2 2 2 2
3 3
2 2 6
ccg q q g qg qg
s s s
qg qg qq
H p m p m p r r
r r r
quarkonium
hybrid
7
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Einbein fields:Einbein fields:
Yu.S.Kalashnikova, ITEP
2 221
2 2 2
m xm x
00
0 0
( ) ( )
( )( ) 0
( , ,... )
nl
nlnl nl
H H E
EE E
n l
8
00 -> constituent mass (calculated) -> constituent mass (calculated)
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Spin-independent Spin-independent corrections:corrections:
3
2
26str
LV
r
2 21 1 1 1
2 2( ) 1 2,
6g g q q
strqg g g q q
L L L LV q q
r
Charmonium:
Self-energy
String correction
Hybrid:
Self-energy (the same as for cc)
String correction
9Yu.S.Kalashnikova, ITEP
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Spin-dependent forceSpin-dependent force
Yu.S.Kalashnikova, ITEP
non-perturbative spin-orbit non-perturbative spin-orbit (Thomas)(Thomas)
perturbative spin-orbitperturbative spin-orbit
hyperfinehyperfine
spin-tensorspin-tensor
10
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Trial wavefunctionTrial wavefunction charmoniumcharmonium
2 21exp
2r
2 2 2 2,
1 1exp
2 2cc cc gr
1 2 2
1 2
2
1 2 1 1 2 2
1 2 1 2
( ) 1 ( )0 1 1 1
1( ) ( )1 1 1 1 1 1
ˆ1 ( , ) ( )
ˆ( , ) ( )
cc m g
Jm cc g
r S C Y S
J r C S C Y S
hybridhybrid
11Yu.S.Kalashnikova, ITEP
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20.16 GeV 1.48 GeV 0.55 =0.29c Sm
Model parametersModel parameters
11SS00 33SS11
33PP00 11PP11
33PP11 33PP22
ExpExp 29298080
30930977
34341515
35235266
35351111
35535566
ModModelel
29298181
31031044
34344949
35235288
35351414
35535522
Charmonium spectrum Charmonium spectrum (MeV)(MeV)
20.16 1.48 0.55 0.29c sGeV m GeV
12Yu.S.Kalashnikova, ITEP
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Yu.S.Kalashnikova, ITEP 13
Zero-order hybrid mass:Zero-order hybrid mass:
MM0000 = 4573 MeV = 4573 MeV
Constituent masses:Constituent masses:cc=1598 MeV, =1598 MeV, gg=1085 =1085 MeVMeV
Spin-independent correction -> -90 MeVSpin-independent correction -> -90 MeV
Gluon spin-orbit common for all states -> -103 MeVGluon spin-orbit common for all states -> -103 MeV
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Predictions for hybrids:Predictions for hybrids: 1. Spin splittings1. Spin splittings
0M(1 )M
(1 )M
(0 )M
(2 )M
14Yu.S.Kalashnikova, ITEP
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Predictions for hybrids:Predictions for hybrids:2. Mass of the vector hybrid2. Mass of the vector hybrid
(1 ) 4397ccgM MeV
LGT 4379 LGT 4379 149 MeV 149 MeVX.-Q.Luo and Y.Liu, PRD 74 034502 X.-Q.Luo and Y.Liu, PRD 74 034502
(2006)(2006)
15Yu.S.Kalashnikova, ITEP
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Predictions for hybrids:Predictions for hybrids:
3. Masses of C-even states3. Masses of C-even states
(0 ) 4252
(1 ) 4320
(2 ) 4457
ccg
ccg
ccg
M MeV
M MeV
M MeV
LGTLGT
~ 4400 MeV C.Michael, hep-ph/0308293~ 4400 MeV C.Michael, hep-ph/0308293
4405 4405 38 MeV Y.Liu and X.-Q.Luo PRD73 38 MeV Y.Liu and X.-Q.Luo PRD73 054510 (2006)054510 (2006)
16Yu.S.Kalashnikova, ITEP
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Yu.S.Kalashnikova, ITEP 17
Both these Both these calculationscalculations and lattice and latticeplace a vector hybrid at 4400 MeVplace a vector hybrid at 4400 MeV
Y(4260) is not a hybrid?Y(4260) is not a hybrid?
Y(4320):Y(4320):
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Strong decays of magnetic Strong decays of magnetic hybrids:hybrids:
Yu.S.Kalashnikova, ITEP
hh
DD
DD
1 21
1 1ˆ( , ) ( ) ( ) ( )2 2h M M
g g
dpdQ p Q QY Q p Q k p Q k
18
QQ-Q -Q = 0 for S+S mesons = 0 for S+S mesons
Hybrid wavefunctionHybrid wavefunction
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Selection rule:Selection rule:
Yu.S.Kalashnikova, ITEP 19
hhmagnetimagneti
cc
DD(*)(*)DD(*)(*)
DD(*)(*)DDJJ(*)(*)
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Vector:Vector:
Yu.S.Kalashnikova, ITEP 20
* * 1 30 1 1 1 1
* 3 *1 1 2
1 1 11 ( ) ( )
2 26
1 1 5( )
2 62 2
D D D D P DD P
D D P D D
MMthth=4327 MeV=4327 MeV MMthth=4285 MeV=4285 MeV
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Yu.S.Kalashnikova, ITEP 21
Due to the coupling of vectorDue to the coupling of vector hybrid to S-wave thresholds Dhybrid to S-wave thresholds D**DD00
and DDand DD1 1 the state should be attractedthe state should be attracted to these thresholdsto these thresholds
If the coupling is strong enoughIf the coupling is strong enough an extra state can be generatedan extra state can be generated dynamically dynamically
Y(4260) and Y(4325) ?Y(4260) and Y(4325) ?
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JJ-+-+::
Yu.S.Kalashnikova, ITEP 22
* 10 1 1
1 10 (4252) ( )
2 2DD D D P
* 1 * 10 1 1 1 1
3 * 3 *1 1 1 1 2
1 1 11 (4320) ( ) ( )
3 2 2 2
1 1 1 5( ) ( )
4 4 32 2
D D DD P D D P
DD P D D P D D
* 1 * 31 1 1 1 2
*2
1 3 12 (4457) ( ) ( )
42 2 2 2
3
4
D D P D D P DD
D D
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Yu.S.Kalashnikova, ITEP 23
Y(4260) and Y(4320) as hybrids:Y(4260) and Y(4320) as hybrids:
No visible decays into DD pairsNo visible decays into DD pairs
Small eSmall e++ee-- width width
The masses are a bit too lowThe masses are a bit too low
DDDD11 and D and D**DD00 thresholds can attract the thresholds can attract the state state
If Y’s are hybrids, C-even partners are to If Y’s are hybrids, C-even partners are to bebe foundfound
11-+-+(4320) couples strongly to D(4320) couples strongly to D**DD00 -> -> interestinginteresting threshold effectthreshold effect