spectra and decays of hybrid charmonia

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)

Y(4260): hybrid Y(4260): hybrid charmonium?charmonium?

Yu.S.Kalashnikova, ITEP 2

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

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

Hybrid excitations:Hybrid excitations:gluon with two “minimal” gluon with two “minimal” strings attachedstrings attached q

qg

Yu.S.Kalashnikova, ITEP 5

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

qq

qq

s

s J J

6

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

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)

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

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

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

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

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

Predictions for hybrids:Predictions for hybrids: 1. Spin splittings1. Spin splittings

0M(1 )M

(1 )M

(0 )M

(2 )M

14Yu.S.Kalashnikova, ITEP

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

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

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):

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

Selection rule:Selection rule:

Yu.S.Kalashnikova, ITEP 19

hhmagnetimagneti

cc

DD(*)(*)DD(*)(*)

DD(*)(*)DDJJ(*)(*)

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

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) ?

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

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