Recent developments in cc , cn and cs spectroscopy:

X(3872), DsJ

*(2317)+ and Ds1

*(2457)+.

1) Basic physics. How well qq worked (charmonium e.g.)

2) The X(3872), DsJ

*+(2317) and Ds1

*+(2457).

3) What we are reconsidering. (This is a story in progress…)

Ted BarnesPhysics Div. ORNLDept. of Phys. and Astro., U.Tenn.

HQL2004

Small qq separation

Large qq separation

basic physics of QCD

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)

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.

3D3 (3810)

3D2 (3803)

3D1 (3787)

1D2 (3802)

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oops… cc has been withdrawn.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.

J

DD*MeV

Accidental agreement?X = cc (2 or 2 or …),or a DD* molecule?

MeV

Alas the known = 3D1 cc.

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

n.b.DD*MeV

MeV

Belle Collab. K.Abe et al, hep-ex/0308029;S.-K.Choi et al, hep-ex/0309032, PRL91 (2003) 262001.X(3872) from

KEK

X(3872) confirmation (from Fermilab)

G.Bauer, QWG presentation, 20 Sept. 2003.

n.b. most recent CDF II: M = 3871.3 pm 0.7 pm 0.4 MeV

CDF II Collab. D.Acosta et al, hep-ex/0312021, PRL to appear

OK, it’s real…n.b. molecule.ne.multiquark

X(3872) also confirmed by D0 Collab. at Fermilab. Perhaps also seen by BaBar

The trouble with multiquarks: “Fall-Apart Decay” (actually not a decay at all: no H

I)

Multiquark models found thatmost channels showed short distance repulsion:

E(cluster) > M1 + M

2.

Thus no bound states.

Only 1+2 repulsive scattering.

nuclei and hypernuclei

weak int-R attraction allows “molecules”

E(cluster) < M1 + M

2,

bag model:

u2d2s2 H-dibaryon, MH - M

= 80 MeV.

n.b.

hypernuclei exist, so this H was wrong.

Exceptions:

VNN

(R)

2mN

R R

“V

(R)”

2m

Q2q2 (Q = b, c?)

2)

1)

3) Heavy-light

X(3872)

Belle Collab. K.Abe et al, hep-ex/0308029;S.-K.Choi et al, hep-ex/0309032, PRL91 (2003) 262001.

J

DD*MeV

Accidental agreement?X = cc 2 or 2 or …,or a molecular (DD*) 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

Charm in nuclear physics???

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

2 3( 3D

2 is a typo)2

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

A more conventional possibility: X(3872) = cc?

Charmonium Options for the X(3872) T.Barnes and S.Godfrey, hep-ph/0311169, PRD69 (2004) 054008. (n.b. Eichten, Lane and Quigg have similar results.)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.

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

0.6 [MeV]

3D2

-

3D1

43 [MeV]

1D2

-

DD 23.6(2.7) [MeV]

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

X(3872)

(New strong and EM decay results from Barnes, Godfrey and Swanson, in prep.)

Strong Widths: 3P0 Decay Model

1F3F

4 9.0 [MeV]

3F3

87 [MeV]

3F2

165 [MeV]

1F3

64 [MeV]

DDDD*D*D*D

sD

s

X(3872)

Strong Widths: 3P0 Decay Model

33S1

74 [MeV]

31S0

67 [MeV]

3S

DDDD*D*D*D

sD

s

X(3872)

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 = 1P

1

5F1

= 0

std. cc and D meson SHO wfn. length scale

Strong Widths: 3P0 Decay Model

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 1P

1

5F1 = 0.141

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)

If X = 1D cc: Total width eliminates only 3D

1.

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% radiative 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:23P

1 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.)

Concl: We cannot yet exclude 5 of the 8 1D and 2P cc assignments. However, we do see how to proceed.

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, PLB578, 119 (2004).C.Y.Wong, hep-ph/0311088. E.Braaten and M.Kusunoki, hep-ph/0311147, PRD69, 074005 (2004).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.)

n.b.2 Could the signal simply be a cusp due to new DD* channelsopening? (A.Bacher query.) No one has considered this.

Interesting prediction of molecule decay modes:

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

J“”J

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

Very characteristic mix of isospins: comparable J andJ“”decay 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, CDF and DZERO.

It is seen 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 the X is a deuteronlike DoD*o-molecule.

Naïvely, this suggests a narrow total X width of ca. 50 keV

and 3:2 bfs to DoDo and DoDo.

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

This predicts (X) = 2 MeV and remarkable, comparable “isospin violating” b.f.s to Jand J.

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).

Where it all started. BABAR: D*sJ

(2317)+ in Ds+

0

D.Aubert et al. (BABAR Collab.), PRL90, 242001 (2003).

M = 2317 MeV (2 Ds channels),

< 9 MeV (expt. resolution)

(Theorists expected L=1 cs states, e.g. JP=0+, but with a LARGE width and at a much higher mass.) …

“Who ordered that !?”

I.I.Rabi (about the - )

Since confirmed by CLEO, Belle and FOCUS.

And another! CLEO: D*sJ

(2463)+ in Ds*+

0

Since confirmed by BABAR and Belle. M = 2457 MeV.

D.Besson et al. (CLEO Collab.), PRD68, 032002 (2003).

M = 2463 MeV,

< 7 MeV (expt. resolution)

A JP=1+partner of the possibly 0+ D*

sJ(2317)+ cs ?

(Godfrey and Isgur potential model.) Prev. (narrow) expt. states in gray.

DK threshold

Experimental D states (PDG 2002) vs Godfrey-Isgur potential model.

Is the same discrepancy evident in the cn sector?

The new broad D states. The 1+ states are not especially low wrt QM. However the status of the 0+ is unclear. (2 expts. differ by 100 MeV.)

Theorists’ responses to the new DsJ* states

Approx. 80 theoretical papers have been published since

the discovery. There are two general schools of thought:

1) They are cs quark model mesons, albeit at a much lower mass than expected by the usual NRQPMs. [Fermilab]

2) They are “multiquark” states.

(“DK molecules”) [UT,Oxon,Weiz.]

3) They are somewhere between 1) and 2). [reality]

M.A.Nowak, M.Rho and I.Zahed,PRD48, 4370 (1993).W.A.Bardeen and C.T.Hill,PRD49, 409 (1994)BEH, PRD68, 054024 (2003).

2. Multiquark states (DK molecules) [UT,Oxon,Weiz.] 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)

L’oops

Future: “Unquenching the quark model”

Virtual meson decay loop effects,qq <-> M1 M2 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.

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

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

[ 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!

Summary and conclusions:1) Three new narrow mesons containing at least cc and cs have been reported:

X(3872) D*sJ(2317)+ D*

sJ(2457)+

2) Theorists expected similar (?) states but at rather different masses. The cs states were expected to have very broad strong decay widths.The interpretation of the new states (qq / two-meson molecules / lin.comb.) is being discussed. Decay loops determine mixing.

Radiative transitions should allow definitive tests of qq assignments.

There are E1 rate predictions for D*sJ Ds

+ andDs* + assuming cs,

analogous to the X(3872) rates we discussed.(e.g. S.Godfrey, hep-ph/0305122, PLB568, 254 (2003).)D*

sJ(2457)+ Ds+ reported recently by Belle; strongly favors J=1, as expected.

3) Useful future measurements: A. Precise E1 cc (CLEO; ’ , (3770) and ) and D*

sJ radiative rates;

B. Strong decay model checks (4040, 4159 DD, DD*; D*D* PWA) (BES,CLEO).

n.b(4415 + ) (at ca. 4440 MeV) a D*sJ source?

(expect few % BFs to D*s0(2317) D*

s and D*s1(2457) Ds)