1. The XYZs of cc: 1. Charmonium reminder. 2. The new states:
T.Barnes
ORNL / U.Tenn.
Charm2006 Beijing
7 June 2006
The XYZs of cc:
Charmonium reminder.
The new states:
X(3943) Y(3943) Z(3931) Y(4260)
cc? cc hybrids!?
How to test these possibilities.
(My) theor. numbers are from
T.Barnes, S.Godfrey and E.S.Swanson, PRD72, (2005).
For BABAR, BELLE, BES, CLEO, GSI, … :
All 40 cc states expected to 4.42 GeV, all 139 of their open-charm strong modes and partial widths,
all 231 open-charm strong decay amplitudes, all 153 E1 and (some) M1 EM widths.

2. Charmonium (cc) A nice example of a QQ spectrum.
Expt. states are shown with the usual L classification.
Above 3.73 GeV:
Open charm strong decays
(DD, DD* …):
broader states
except 1D2 2- +, 2- -
3.73 GeV
Below 3.73 GeV:
Annihilation and EM decays.
(rp, KK* , gcc, gg, l+l-..):
narrow states.

3. Minimal quark potential model physics:
OGE + linear scalar confinement;
Schrödinger eqn (often relativized) for wfns.
Spin-dep. forces, O(v2/c2), treated perturbatively.
Here…
Contact S*S from OGE;
Implies S=0 and S=1 c.o.g.
degenerate for L > 0.
(Not true for vector confinement.)

4. Fitted and predicted cc spectrum
Coulomb (OGE) + linear scalar conft. potential model
black = expt, red = theory.
Y(4260) JPC = 1- -
Z(3931), X(3943), Y(3943) C = (+)
states fitted
S*S OGE

5. cc and cc–H from LGT <- 1- + exotic cc-H at 4.4 GeV
A LGT cc-sector spectrum e.g.: X.Liao and T.Manke,
hep-lat/ (quenched – no decay loops)
Broadly consistent with the cc potential model.
No LGT cc radiative or strong decay predictions yet.
cc and cc–H from LGT
< exotic cc-H at 4.4 GeV
n.b. The flux-tube model of hybrids
has a lightest multiplet with 8 JPCs;
3 exotics and 5 nonexotics, roughly
degenerate: (0,1,2) +- /-+, 1++,, 1- -.
Y(4260)?
Small
L=2 hfs.

6. Comparing expt. with theory, especially for 2P cc states, through:
The main theme:
Comparing expt. with theory,
especially for 2P cc states, through:
1st Strong decays
2nd EM (g and gg transitions)

7. Trivial observations for 2P cc open-charm strong decays:
Thresholds
DD GeV
DD* GeV
(Ds Ds GeV - small)
J PC-allowed D, D* modes (M < D*D*)
c2’ P DD, DD*
c1’ P DD*
c0’ P DD
hc’ P DD* but C = ( -)
Looking for both DD and DD* is a good filter!
n.b. JP = 1+ DD* final states have both S and D amps.
Detailed 2P cc predictions…

8. Open-charm strong decays: 3P0 decay model (Orsay group, 1970s)
qq pair production with vacuum quantum numbers.
L I = g y y .
A standard for light hadron decays. It works for D/S in b1 -> wp.
The relation to QCD is obscure.

9. One success of strong decay models
An historical SLAC puzzle explained:
the weakness of y(4040) -> DD
e.g. D*D* molecule?
After restoring this “p3 phase space factor”, the BFs are:
D0D : D0D* : D*0D*0
0.12 +/ / [1] +/- 0.31

10. Y(4040) Y(4040) partial widths [MeV] Y(4040) -> D*D* amplitudes
(3P0 decay model):
DD = 0.1
DD* = 32.9
D*D* = 33.4 [multiamp. mode]
DsDs = 7.8
Y(4040) -> D*D* amplitudes
(3P0 decay model):
1P1 =
5P1 = = - 2 * 51/2 * 1P1
5F = 0
famous nodal suppression
of a 33S1 Y(4040) cc -> DD
std. cc and D meson SHO wfn. length scale

11. Expt. preview, M, G and modes, X(3943), Y(3943), Z(3931):
J/y

12. 2P cc Strong Widths: 3P0 Decay Model
(assuming NR cc
potential model masses) DD
DD*
DsDs 2P
23P [MeV]
23P [MeV]
23P [MeV]
21P [MeV]

13. An interesting new charmonium
production mechanism!
Allows access to C=(+) cc states
in e+e- w/o using gg.
X(3943)
hc’
X(3943) hc c0
No c1 or c2 !?
n.b. Eichten: X(3943) may be the 31S0 cc hc’’.
[ref] = P.Pakhlov et al. (Belle), hep-ex/ , 8 Jul 2005.

14. Strong Widths: 3P0 Decay Model
X(3943)
Maybe not 2P?
X(3943) = 31S0 hc” ?
(Eichten)
33S [MeV]
31S [MeV] 3S DD
DD*
D*D*
DsDs
52(10) MeV
X(3872)
Is the narrow expt width a problem for X(3943) = 31S0 hc” ?
Let’s recalculate with M = 3943 MeV and see …

15. X(3943) Gthy = 70 MeV vs Gexpt = 15(10) MeV
Yes the total width is a problem for X(3943) = 31S0 hc”.
Gthy = 70 MeV vs Gexpt = 15(10) MeV
X(3943) 2
thy.
expt.

16. B -> KY(3943), Y -> w J/y
[ref] = S.-K. Choi et al. (Belle), PRL94, (2005).

17. Y(3943) Gtot Y(3943) = 23P1 cc? (Too light for cc-H.) theory expt.
Expt for Y(3943): B -> KY(3943),
Y -> wJ/y
G = 87 +/- 22 MeV
1++ cc -> wJ/y is unusual;
cc -> virtual DD* e.g. -> wJ/y ?
n.b. c1 IS seen in B decays
theory
expt.
Theory for 23P1(3943):
G = 135 MeV
A strong DD* mode $ ?
The only open-charm mode?

18. Z(3931) gg -> Z(3931) -> DD [ JPC(gg) .ne. 1++ ]
[ref] = S.Uehara et al. (Belle), hep-ex/ , 8 Jul 2005.

19. Z(3931) Gtot Z(3931) = 23P2 cc ? (suggested by Belle)
Expt for Z(3931): gg -> Z(3931) -> DD
G = 20 +/- 8 +/- 3 MeV
Ggg * BDD = / / keV
Theory for 23P2(3931):
G = 47 MeV DD*/DD = 0.35
Ggg * BDD = 0.47 keV
(Ggg from T.Barnes, IXth Intl. Conf.
on gg Collisions, La Jolla, 1992.)
The crucial test of
Z(3931) = 23P2 cc :
DD* mode $ ?
Gtot
thy
expt
Ggg in

20. (How one might make 2P cc states.)
EM transitions
(How one might make 2P cc states.)
What radiative partial widths do we expect
from various initial 1- - cc states to 2P cc states?

21. E1 Radiative Partial Widths
3S -> 2P
33S1 -> 23P [keV]
33S1 -> 23P [keV]
33S1 -> 23P [keV]
31S0 -> 21P [keV]
3S -> 1P
33S1 -> 3P [keV]
33S1 -> 3P [keV]
33S1 -> 3P [keV]
31S0 -> 1P [keV]
blue = known states
red = unknown

22. E1 Radiative Partial Widths
2D -> 2P
23D3 -> 23P [keV]
23D2 -> P [keV]
23P [keV]
23D1 -> P [keV]
23P [keV]
23P [keV]
21D2 -> 21P [keV]
2D -> 1F
23D3 -> 3F [keV]
-> 3F [keV]
-> 3F [keV]
23D2 -> 3F [keV]
3F [keV]
23D1 -> 3F [keV]
21D2 -> 1F [keV]
2D -> 1P
23D3 -> 3P [keV]
23D2 -> 3P [keV]
3P [keV]
23D1 -> 3P [keV]
3P [keV]
3P [keV]
21D2 -> 1P [keV]

23. y(3770) y(3770) -> g ccJ y(3770) -> g cc2
Ref: R.A.Briere et al. (CLEO),
hep-ex/ (May 2006).
y(3770) -> g ccJ
y(3770) -> g cc2
is very sensitive to the 23S1 <-> 3D1 mixing angle q.
With q approx -15o, both the e+e- and strong 3770 widths = theor predictions.
This q is very interesting: what drives 23S1 <-> 3D1 mixing?

24. y(3770) Experiment and theory [assuming y(3770) = pure 3D1 cc ].
Ref: R.A.Briere et al. (CLEO),
hep-ex/ (May 2006).
Experiment and theory [assuming y(3770) = pure 3D1 cc ].

25. y(3770) Ref: Y.-B.Ding, D.-H.Qin and K.-T.Chao, PRD44, 3562 (1991).
new
CLEO
rad
widths:
172 (30)
70 (17)
< 21
n.b. ratios of versus J are the most reliable theor predictions.
y(3770) -> g ccJ

26. Y(4260)

27. e+e- -> Y(4260)ISR, Y -> p+p-J/y
[ref] = BaBar, PRL95, (2005).
Not seen
in R.
Hmmm?!
log scale

28. Y(4260) CLEO: Evidence for Y(4260) in J/y p+ p- and J/y p0p0
channel s [pb]
J/y p+ p /- 4
J/y p0p /- 1
(approx. 2:1 ratio expected for I=0)
J/y K+ K /- 1
+12
-10
+12
- 8
+ 9
- 5
Ref: T.E.Coan et al. (CLEO), PRL96, (2006);
hep-ex/ v2.

29. cc spectrum, potential models (dashed: nonrel L, Godfrey-Isgur R) vs data
Possible 1- - state Y(4260).
Note no plausible cc
assignment exists.
A 1- - charmonium hybrid??

30. cc and cc–H from LGT <- 1- + exotic cc-H at 4.4 GeV
A LGT cc-sector spectrum e.g.: X.Liao and T.Manke,
hep-lat/ (quenched – no decay loops)
Broadly consistent with the cc potential model.
No LGT cc radiative or strong decay predictions yet.
cc and cc–H from LGT
< exotic cc-H at 4.4 GeV
n.b. The flux-tube model of hybrids
has a lightest multiplet with 8 JPCs;
3 exotics and 5 nonexotics, roughly
degenerate: (0,1,2) +- /-+, 1++,, 1- -.
Y(4260)?
Small
L=2 hfs.

31. Characteristics of cc-hybrids.
(folklore, mainly abstracted from models, some LGT)
States
(flux-tube model):
The lightest hybrid multiplet should be a roughly degenerate set containing
3 exotic and 5 nonexotic JPC;
0+-, 1-+, 2+-, 0-+, 1+-, 2-+, 1++, 1--
Mass ca. 4.0 – 4.5 GeV, with LGT preferring the higher range.
The 1-- should be visible in e+e- but with a suppressed width.
(Hybrid models for different reasons predict ycc (r=0) = 0, suppressing Gee .)
Decays
(flux-tube model and f-t decay model):
Dominant open-charm decay modes are of S+P type, not S+S. (e.g. DD1 not DD or DD*).
n.b. p1(1600) -> p h’ argues against this model.
LGT(UKQCD):
Closed-charm modes like cc-H -> cc + light mesons are large!
(Shown for bb-H; (bb) is preferentially P-wave, and “light mesons” = scalar pp.)

32. p-p -> p-h’ p p1(1600) p1(1600) S+S, not S+P !
E.I.Ivanov et al. (E852)
PRL86, 3977 (2001).
p1(1600)
The (only) strong JPC-exotic H candidate signal.
p-p -> p-h’ p
p1(1600)
1-+ exotic reported in p-h’
S+S, not S+P !
ph’is a nice channel because nn couplings
are weak for once (e.g. the a2(1320) noted here). The reported exotic P-wave is dominant!

33. Strong Widths: 3P0 Decay Model
43S [MeV]
41S [MeV]
43(15) [MeV]
A warning about hybrid = S+P modes:
Theor. decay BFs of the 43S1 cc y(4415). DD
DD*
D*D*
DD0*
DD1
DD1’
DD2*
D*D0*
DsDs
DsDs*
Ds*Ds*
DsDs0*

34. (As for all states above open-charm thresholds.)
Y(4415)
A cc state, but the
main mode (thy.) is
S+P, not S+S !
n.b. PDG says the 4415
decays mainly to
“hadrons”.
Expt BFs needed!
(As for all states above
open-charm thresholds.)
Y(4415) partial widths [MeV]
(3P0 decay model):
DD =
DD* = 2.3
D*D* = 15.8 [multiamp.]
DsDs =
DsDs* =
Ds*Ds* = [m]
New S+P mode calculations:
DD1 = 30.6 [m] <- MAIN MODE!!!
DD1’ = [m]
DD2* = 23.1
D*D0* = 0.0
Y(4415) - > DD1 amplitudes:
(3P0 decay model):
3S1 = <- !!! (HQET)
3D1 =

35. An “industrial application” of the y(4415).
Sit “slightly upstream”, at ca MeV, and you should have
a copious source of D*s0(2317). (Assuming it is largely cs 3P0.)

36. Summary, conclusions, suggestions, re expt:
X(3943), Y(3943), Z(3931) and Y(4260) …
1. X(3943) as 31S0 hc’’, cc ? DD*-only checks, G may be a bit small..
Just measure J P !!! (also for Y and Z!)
2. If Y(3943) is the 23P1 c1’, one expects a large DD* mode, and no DD.
3. gg -> Z(3931) -> DD and DD* if c2’. …

37. Summary, conclusions, suggestions, re expt:
4. Y(4260) as hybrid? No new cc expected near this mass:
if it exists it’s already something unusual.
Theory folklore says hybrids prefer S+P modes,
UKQCD says c + light meson(s) may be large.
Best approach would be to search for it in all accessible
open charm and closed charm modes.
e+e- -> DD, DD*, D*D*, DD0*, DD1*; J/y pp,
any other (cc) + light meson mode.
(Close and Page, hep-ph/ v2, PLB628, 215 (2005) gives a detailed list of modes)

38. The End Summary, conclusions, suggestions, re expt (cont.):
X(3943), Y(3943), Z(3931) …
5. E1 radiative transitions from 1- - cc states:
You can find all three 23PJ cc states using
y(4040) and y(4160) -> gDD, gDD*.
e.g. All three E1 rad BFs of the y(4040) are ca. few * 10-4.
These could show whether the X,Y,Z (3.9) are 2P cc as speculated.
The End