Charmonium

CharmoniumCharmonium

Ted BarnesPhysics Div. ORNLDept. of Physics, U.Tenn.

1) Basic physics2) Theoretical spectrum versus known states3) NEW: open-flavor strong widths4) E1 transitions5) X(3872)

The numbers quoted in 2-4) will appear in T.Barnes, S.Godfrey and E.S.Swanson (in prep.)

I will mainly quote cc potential model results, which provide a useful intuitive picture of charmonium. LGT (C.Morningstar) is not yet competitive for higher mass cc states but is of course the preferred technique and will eventually solve everything.

CharmoniumCharmonium

e

g

Small qq separation

Large qq separation

The QCD flux tube (LGT, G.Bali et al; hep-ph/010032)

LGT simulation showing

the QCD flux tube

Q Q

R = 1.2 [fm]

“funnel-shaped” VQQ(R)

Coul. (OGE)

linear conft.(str. tens. = 16

T)

Physically allowed hadron states (color Physically allowed hadron states (color singlets)singlets)

qq

q3 Conventional quark modelmesons and baryons.

q2q2, q4q,…

multiquarks

g2, g3,…

glueballs

maybe 1 e.g.

qqg, q3g,…

hybrids

maybe 1-3 e.g.s

100s of e.g.s

”exotica” :ca. 106 e.g.s of (q3)n, maybe 1-3 others

(q3)n, (qq)(qq), (qq)(q3),…

nuclei / molecules

(q2q2),(q4q),…

multiquark clusters

controversiale.g.

_

Basis state mixing may be very important in some sectors.

cc mesons states and spectrum

The nonrelativistic quark model treats conventional charmonia

as cc bound states.

Since each quark has spin-1/2, the total spin is

Sqq = ½ x ½ = 1 + 0

Combining this with orbital angular momentum Lqq gives states

of total Jqq = Lqq spin singlets Jqq = Lqq+1, Lqq, Lqq-1 spin triplets

tot.

xxxxx

Parity Pqq

= (-1) (L+1)

C-parity Cqq

= (-1) (L+S)

cc mesons quantum numbers

1S: 3S1 1 ; 1S

0 0 2S: 23S

1 1 ; 21S

0 0 …

1P: 3P2 2 ; 3P

1 1 ; 3P

0 0 ; 1P

1 1

2P …

1D: 3D3 3 ; 3D

2 2 ; 3D

1 1 ; 1D

2 2

2D …JPC forbidden to qq are called “JPC-exotic quantum numbers”.

0 ; 0 ; 1 ; 2 ; 3 …

Plausible JPC-exotic candidates =

hybrids, glueballs (high mass), maybe multiquarks (fall-apart decays).

The resulting cc NL states N2S+1LJ have JPC =

Charmonium

Theoretical spectrum versus known states

Charmonium (cc)A nice example of a QQ spectrum.

Expt. states (blue) are shown with the usual L classification.

Above 3.73 GeV:Open charm strong decays(DD, DD* …):broader statesexcept 1D

2 22

3.73 GeV

Below 3.73 GeV: Annihilation and EM decays.

, KK* , cc, , ll..):narrow states.

Fitting cc potential model parameters.s, b, mc, fixed from 1P c.o.g. and all 1S and 2S masses.

blue = expt, red = theory.

s = 0.5111

b = 0.1577 [GeV2]m

c = 1.4439 [GeV]

= 1.1667 [GeV]

Predicted spin-dependent cc 1P multiplet splittings

(sensitive test of OGE)Parameters s, b, mc, fixed from 13PJ c.o.g. and all 1S, 2S masses, prev slide.

blue = expt, red = theory. s = 0.5111

b = 0.1577 [GeV2]m

c = 1.4439 [GeV]

= 1.1667 [GeV]

OGE + lin. scalar conft.1P

1 (not shown) is 8 MeV

below the 3PJ c.o.g.

Scalar conft. gives neg. L*S

23S1 (3672)

21S0 (3635)

33S1 (4073)

31S0 (4047)

43S1 (4407)

41S0 (4387)

33P2 (4320)

33P1 (4272)

33P0 (4202)

31P1 (4281)

23P2 (3976)

23P1 (3927)

23P0 (3853)

21P1 (3936)3P

2 (3560)

3P1 (3507)

3P0 (3424)

1P1 (3517)

23D3 (4170)

23D2 (4161)

23D1 (4144)

21D2 (4160)

3D3 (3810)

3D2 (3803)

3D1 (3787)

1D2 (3802)

23F4 (4351)

23F3 (4355)

23F2 (4353)

21F3 (4353)

3F4 (4025)

3F3 (4032)

3F2 (4032)

1F3 (4029)

3S1 (3087)

1S1 (2986)

Fitted and predicted cc spectrum

blue = expt, red = theory.

s = 0.5538

b = 0.1422 [GeV2]m

c = 1.4834 [GeV]

= 1.0222 [GeV]

Previous fit (1S,2S,1Pcog

.):

s = 0.5111

b = 0.1577 [GeV2]m

c = 1.4439 [GeV]

= 1.1667 [GeV]

cc from the “standard” potential modelS.Godfrey and N.Isgur, PRD32, 189 (1985).

Godfrey-Isgur model cc spectrum (SG, private comm.)

cc from LGT

exotic cc-H at 4.4 GeV

oops… cc has been withdrawn.

Small L=2 hfs.

What about LGT??? An e.g.: X.Liao and T.Manke, hep-lat/0210030 (quenched – no decay loops)Broadly consistent with the cc potential model spectrum. No radiative or strong decay predictions yet.

Charmonium

Open-flavor strong decays

Experimental R summary (2003 PDG)Very interesting open experimental question:Do strong decays use the 3P

0 model decay mechanism

or the Cornell model decay mechanism or … ?

br

vector confinement??? controversial

ee, hence 1 cc states only.

How do strong decays happen at the QCD (q-g) level?

“Cornell” decay model:

(1980s cc papers)(cc) (cn)(nc) coupling from qq pair production by linear confining interaction.

Absolute norm of is fixed!

The 3P0 decay model: qq pair production with vacuum quantum numbers.

L I = g

A standard for light hadron decays. It works for D/S in b1 .

The relation to QCD is obscure.

R and the 4 higher 1-- states

3770

4040

4160

4415

(plot from Yi-Fang Wang’s online BES talk, 16 Sept 2002)

What are the total widths of cc states above 3.73 GeV?

(These are dominated by open-flavor decays.)

< 2.3 MeV

23.6(2.7) MeV

52(10) MeV

43(15) MeV

78(20) MeV

PDG values

Strong Widths: 3P0 Decay Model

1D

3D3

0.6 [MeV]

3D2

-

3D1

43 [MeV]

1D2

-

DD 23.6(2.7) [MeV]

Parameters are = 0.4 (from light meson decays), meson masses and wfns.


33S1

74 [MeV]

31S0

67 [MeV]

3S

DDDD*D*D*D

sD

s

52(10) MeV

partial widths [MeV](3P

0 decay model):

DD = 0.1 DD* = 32.9 D*D* = 33.4 [multiamp. mode]D

sD

s = 7.8

Theor R from the Cornell model.Eichten et al, PRD21, 203 (1980): 4040

DD

DD*

D*D*

4159

4415

famous nodal suppression of a 33S

1 (4040) cc DD

D*D* amplitudes(3P

0 decay model):

1P1 = 0.056

5P1 = 0.251

5F1

= 0

std. cc and D meson SHO wfn. length scale


2D 23D3

148 [MeV]

23D2

93 [MeV]

23D1

74 [MeV]

21D2

112 [MeV]

DDDD*D*D*D

sD

s

DsD

s*

78(20) [MeV]

partial widths [MeV](3P

0 decay model):

DD = 16.3 DD* = 0.4 D*D* = 35.3 [multiamp. mode]D

sD

s = 8.0

DsD

s* = 14.1

Theor R from the Cornell model.Eichten et al, PRD21, 203 (1980): 4040

DD

DD*

D*D*

4159

4415

std. cc SHO wfn. length scale

D*D* amplitudes:(3P

0 decay model):

1P1 = 0.081

5P1 = 0.036

5F1 = 0.141


2P23P

2 83 [MeV]

23P1

162 [MeV]

23P0

29 [MeV]

21P1

86 [MeV]

DDDD*D

sD

s


1F3F

4 9.0 [MeV]

3F3

87 [MeV]

3F2

165 [MeV]

1F3

64 [MeV]

DDDD*D*D*D

sD

s

Charmonium

Radiative transitions

n.b.

I will discuss only E1 because of time limitations.

Yes, M1 is interesting too! J/

c and ’ ’

c give m

c,

and ’ c tests S*S corrections to

orthog. 1S-2S wfns.

1P -> 1S3P

2 3S

1 472 [keV]

3P1 3S

1 353 [keV]

3P0 3S

1 166 [keV]

1P1 1S

0 581 [keV]

426(51) [keV]288(48) [keV]119(19) [keV] -

E1 Radiative Partial Widths

2S -> 1P

23S1 3P

2 39 [keV]

23S1 3P

1 57 [keV]

23S1 3P

0 67 [keV]

21S0 1P

1 74 [keV]

18(2) [keV]24(2) [keV]24(2) [keV] -

Same model, wfns. and params as the cc spectrum. Standard |<

f | r |

i >|2 E1 decay rate formula.

Expt. rad. decay rates from PDG 2002


1D -> 1P

3D3 3P

2 305 [keV]

3D2 3P

2 70 [keV]

3P1

342 [keV]

3D1 3P

2 5 [keV]

3P1

134 [keV]

3P0

443 [keV]

1D2 1P

1 376 [keV]


3S -> 2P 33S1 23P

2 12 [keV]

33S1 23P

1 38 [keV]

33S1 23P

0 10 [keV]

31S0 21P

1 114 [keV]

3S -> 1P 33S1 3P

2 0.8 [keV]

33S1 3P

1 0.6 [keV]

33S1 3P

0 0.3 [keV]

31S0 1P

1 11 [keV]


2D -> 1P23D

3 3P

2 35 [keV]

23D2 3P

2 8 [keV]

3P1

30 [keV]

23D1 3P

2 1 [keV]

3P1

17 [keV]

3P0

32 [keV]

21D2 1P

1 48 [keV]

2D -> 1F

23D3 3F

4 67 [keV]

3F3

5

[keV] 3F

2 15

[keV]

23D2 3F

3 46 [keV]

3F2

6 [keV]

23D1 3F

2 49 [keV]

21D2 1F

3 54 [keV]

2D -> 2P23D

3 23P

2 246 [keV]

23D2 23P

2 54 [keV]

23P1

319[keV]

23D1 23P

2 6 [keV]

23P1

173 [keV]

23P0

515 [keV]

21D2 21P

1 355 [keV]


1F -> 1D

3F4 3D

3 351 [keV]

3F3 3D

3 43 [keV]

3D2

375 [keV]

3F2 3D

3 2 [keV]

3D2

66 [keV]

3D

1 524 [keV]

1F3 1D

2 409 [keV]

X(3872)

Belle Collab. S.-K.Choi et al, hep-ex/0309032; K.Abe et al, hep-ex/0308029.

J

DD*MeV

Accidental agreement?X = cc 2 or 2 or …,or a molecular state?

MeV

= 3D1 cc.

If the X(3872) is 1D cc,an L-multiplet is split much more than expected assuming scalar conft.

n.b.DD*MeV

MeV

X(3872) from CDFG.Bauer, QWG presentation, 20 Sept. 2003.

n.b.most recent CDF II: D.Acosta et al, hep-ex/0312021,5 Dec 2003.M = 3871.3 pm 0.7 pm 0.4 MeV

cc from the “standard” potential modelS.Godfrey and N.Isgur, PRD32, 189 (1985).

(3D2 is a typo)

The obvious guess if cc is 2 or 2 .No open-flavor strong decays – narrow.

Charmonium Options for the X(3872)

T.Barnes and S.Godfrey, hep-ph/0311169.

Our approach:

Assume all conceivable cc assignments for the X(3872):

all 8 states in the 1D and 2P cc multiplets.

Nominal Godfrey-Isgur masses were

3D3(3849) 23P

2(3979)

3D2(3838) 23P

1(3953)

3D1(3.82) [(3770)] 23P

0(3916)

1D2(3837) 21P

1(3956)

We assigned a mass of 3872 MeV to each stateand calculated the resulting strong and EM partial widths.

If X = 1D cc:

Total width eliminates only 3D1.

Large, ca. 300 – 500 keV E1 radiative partial widths to J and h

c

are predicted for 1D assignments ( 3D3, 3D

2 ) and 1D

2.

If tot

= 1 MeV these are 30% - 50% b.f.s!

The pattern of final P-wave cc states you populate identifies the initial cc state.

If X = 1D2

cc, you are “forced” to discover the hc!

If X = 2P cc:

23P1 and

21P

1 are possible based on total width alone.

These assignments predict weaker but perhaps accessible radiative branches to J, ’ and

c

c’ respectively.

NOT to J states. (E1 changes parity.)

We cannot yet exclude 5 of the 8 1D and 2P cc assignments.

DD* molecule options

This possibility is suggested by the similarity in mass,

N.A.Tornqvist, PRL67, 556 (1991); hep-ph/0308277.F.E.Close and P.R.Page, hep-ph/0309253.C.Y.Wong, hep-ph/0311088.E.Braaten and M.Kusunoki, hep-ph/0311147.E.S.Swanson, hep-ph/0311229.

n.b. The suggestion of charm meson molecules dates back to 1976:(4040) as a D*D* molecule;(Voloshin and Okun; deRujula, Georgi and Glashow).

XMeV

DD*MeV

(I prefer this assignment.)

Interesting prediction of molecule decay modes:

E.Swanson, hep-ph/0311299: 1 DoD*o molecule with additional comps. due to rescattering.

JJ

Predicted total width ca. = expt limit (2 MeV).

Very characteristic mix of isospins: J andJdecay modes expected.

Nothing about the X(3872) is input: this all follows from OE and C.I. !!!

X(3872) summary:

The X(3872) is a new state reported by Belle and CDF

in only one mode: J . It is very narrow, < 2.3 MeV.The limit on

is comparable to the observed J.

The mass suggests that X is a deuteronlike DoD*o-molecule.Naïvely, this suggests a narrow total X width of ca. 50 keV

and 3:2 b.f.s to DoDo and DoDo.

However, internal rescatter to (cc)(nn) may be important.

This predicts (X) = 2 MeV and remarkable, comparable b.f.s to Jand J [E.S.Swanson, hep-ph/0311299]. The bleedin’ obvious decay mode Jshould be searched for, to test C(X) and establish whether =

Possible “wrong-mass” cc assignments to 1D and 2P levels can be tested by their (often large) E1 radiative transitions to (cc).

Charmonium: Charmonium: SummarySummary

1) The spectrum fits a OGE + linear scalar conft. potential model reasonably well. More cc states will be useful to test this. (Pt. 4.)

2) Some cc states above 3.73 GeV in addition to 2 and 2

are expected to be relatively narrow, notably33DD

33 ( = 0.6 MeV) and 33FF

44 ( = 9 MeV).

3) The multiamplitude strong decays D*D* can be used to establish the dom. strong decay mechanism. b.f.s to DD, DD*, D

s Ds … will be useful too.

[ 3) is my favorite new-age cc topic.]

4) E1 rad: 2 tests S-wave comp.

, DD search for new C=(+) cc states.

5) The X(3872) is likely a Do D*o molecule.

J andJdecay modes?

X = cc options predict large E1 b.f.s to + P-wave cc.

Charmonium

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