Higher Higher Charmonium Charmonium

1)1) SpectrumSpectrum

2)2) Strong decays (main topic)Strong decays (main topic)

3)3) L’oopsL’oops

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

GHP2004 Fermilab, 24-26 Oct. 2004

abstracted from T.Barnes, S.Godfrey and E.S.Swanson, in prep.

1. Spectrum

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.

s = 0.5538

b = 0.1422 [GeV2]m

c = 1.4834 [GeV]

= 1.0222 [GeV]

Fitted and predicted cc spectrumCoulomb (OGE) + linear scalar conft. potential

model blue = expt, red = theory.

S*S OGE

L*S OGE – L*S conft, T OGE

cc from LGT

exotic cc-H at 4.4 GeV

cc has returned.

Small L=2 hfs.

A LGT 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.

2. Strong decays (open flavor)

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 open-flavor 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.

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

X(3872)

Strong Widths: 3P0 Decay Model

1D

3D3

0.5 [MeV]

3D2

-

3D1

43 [MeV]

1D2

-

DD 23.6(2.7) [MeV]

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

X(3872)

E1 Radiative Partial Widths

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]

X(3872)

Strong Widths: 3P0 Decay Model

1F3F

4 8.3 [MeV]

3F3

84 [MeV]

3F2

161 [MeV]

1F3

61 [MeV]

DDDD*D*D*D

sD

s

X(3872)

Strong Widths: 3P0 Decay Model

33S1

74 [MeV]

31S0

80 [MeV]

3S

DDDD*D*D*D

sD

s

X(3872)

52(10) MeV

After restoring this “p3 phase space factor”, the BFs are:

D0D0 : D0D*0 : D*0D*0

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 = 1P

1

5F1

= 0

std. cc and D meson SHO wfn. length scale

Strong Widths: 3P0 Decay Model

2D 23D3

148 [MeV]

23D2

92 [MeV]

23D1

74 [MeV]

21D2

111 [MeV]

DDDD*D*D*D

sD

s

DsD

s*

78(20) [MeV]

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 1P

1

5F1 = 0.141

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

Strong Widths: 3P0 Decay Model

4S 43S1

78 [MeV]

41S0

61 [MeV]

DDDD*D*D*DD

0*

DD1

DD1’

DD2*

D*D0*

DsD

s

DsD

s*

Ds*D

s*

DsD

s0*

43(15) [MeV]

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

DD

DD*

D*D*

4159

4415

DD1 amplitudes:

(3P0 decay model):

3S1 = 0 !!!

3D1 = + 0.110

partial widths [MeV](3P

0 decay model):

DD = 0.4 DD* = 2.3 D*D* = 15.8 [multiamp.]

New mode calculations:

DD1 = 30.6 [m] MAIN MODE!!!

DD1’ = 1.0 [m]

DD2* = 23.1

D*D0* = 0.0

DsD

s = 1.3

DsD

s* = 2.6

Ds*D

s* = 0.7 [m]

An “industrial application” of the (4415).

Sit “slightly upstream”, at ca. 4435 MeV, and you should have a copious source of D*

s0(2317). (Assuming it is largely cs 3P

0.)

3. L’oops

Future: “Unquenching the quark model”

Virtual meson decay loop effects,qq <-> M

1 M

2 mixing.

DsJ

* states (mixed cs <-> DK …, how large is the mixing?)

Are the states close to |cs> or |DK>, or are both basis states important?

A perennial question: accuracy of the valence approximation in QCD.

Also LGT-relevant (they are usually quenched too).

|DsJ

*+(2317,2457)> = DK molecules?

T.Barnes, F.E.Close and H.J.Lipkin, hep-ph/0305025, PRD68, 054006 (2003).

3. reality

Reminiscent of Weinstein and Isgur’s “KK molecules”.

(loop effects now being evaluated)

S.Godfrey and R.Kokoski,PRD43, 1679 (1991).

Decays of S- and P-wave D Ds B and Bs flavor mesons.

3P0 “flux tube” decay model.

The L=1 0+ and 1+ cs “Ds” mesons are predicted to Have rather large total widths, 140 - 990 MeV. (= broad tounobservably broad).

Charmed meson decays (God91)

How large are decay loop mixing effects?

JP = 1+ (2457 channel)

JP = 0+ (2317 channel)

The 0+ and 1+ channels are predicted to have very largeDK and D*K decay couplings.This supports the picture of strongly mixed

|DsJ

*+(2317,2457)> = |cs> + |(cn)(ns)> states.

Evaluation of mixing in progress. Initial estimates for cc …

L’oops evaluated

[ J/ - M1M

2 - J/

3P0 decay model,

std. params. and SHO wfns.

M1M

2 M [J/] P

M1M

2 [J/]

DD

- 30. MeV 0.027

DD*

- 108. MeV 0.086

D*D*

- 173. MeV 0.123

DsD

s - 17. MeV 0.012

DsD

s*

- 60. MeV 0.041

Ds*D

s*

- 97. MeV 0.060

famous 1 : 4 : 7 ratio DD : DD* : D*D*

Sum = - 485. MeV Pcc

= 65.% VERY LARGE mass shift and large non-cc component!

Can the QM really accommodate such large mass shifts??? Other “cc” states?

1/2 : 2 : 7/2 DsD

s : D

sD

s* : D

s*D

s*

L’oops

[ cc - M1M

2 - cc

3P0 decay model,

std. params. and SHO wfns.

Init.

Sum M P

cc

J/ - 485. MeV 0.65

c - 447. MeV 0.71

2 - 537. MeV 0.43

1

- 511. MeV 0.46

0- 471. MeV

0.53 hc

- 516. MeV 0.46

Aha? The large mass shifts are all similar; the relative shifts are “moderate”.

Continuum components are large; transitions (e.g. E1 radiative) will have to berecalculated, including transitions within the continuum.

Apparently we CAN expect DsJ

-sized (100 MeV) relative mass shifts due to decay

loops in extreme cases. cs system to be considered. Beware quenched LGT!

1) Spectrum

The known states agree well with a cc potential model, except:small multiplet splittings for L.ge.2 imply that the X(3872) isimplausible as a “naive” cc state.

2) Strong decays (main topic)

Some cc states above 3.73 GeV are expected to be rather narrow (in addition to 2- states), notably 3D3 and 3F4.

Of the known states, (4040),(4159) and (4415) all have interesting decay modes: 1st 2, D*D* relative amps, and for(4415) we predict DD1 dominance; also a D*

s0(2317) source.

3) L’oops

Virtual meson decay loops cause LARGE mass shifts and cc <-> M1M2 mixing. These effects are under investigation.