Exotica and CLEO 1) A short reminder about cc -> exotica 2) Spectrum, higher charmonia 3) Strong decays (main topic) 4) EM decays (in paper – tiny bit here) 5) L’oops (F.Y.A.) Ted Barnes Physics Div. ORNL Dept. of Physics, U.Tenn. CLEO seminar 6 May )-4) abstracted from T.Barnes, S.Godfrey and E.S.Swanson, hep-ph/ : All 40 cc states expected to 4.42 GeV, all 139 of their open flavor strong modes and partial widths, all 231 o.f. strong decay amplitudes, all 153 E1 and (some) M1 EM widths. Phew.

The canonical, ca method to search for glueballs. Expected J PC = 0 , 0 , 2 . Found some qq states plus the previously unknown   and   . Latter is now the f   scalar glueball candidate. C =  1  C =  But first, a short reminder…

1  C =  A 2 nd, sometimes better approach for exotica searches. “Flavor-tagging” J/ hadronic decays. (mid-late 1980s, after J/ radiative.) You can access the same states but also see what flavors they preferentially couple to. (Need not be J/’are also interesting.)

Flavor-tagging J/   V f hadronic decays, an e.g.: f = K + K - Against , you see the f 0 (1710). No f 2 ’ (1525) (ss). Against , you see the f 2 ’ (1525) (ss). Weak f 0 (1710) shoulder claimed. Against  you see both. No nn / ss flavor discrimination. J.J.Becker et al. (MarkIII) SLAC-PUB-4243 (Feb.1987) DEAR CLEO, PLEASE DON’T FORGET:  The usual mixed-flavor J/    f Flavor tagged J/    f Flavor tagged J/    f

Higher Charmonia (above 3.73 GeV)

2. 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 states except 1D 2 2   2  3.73 GeV Below 3.73 GeV: Annihilation and EM decays. , KK*,  cc, , l  l ..): narrow states.

 s = b = [GeV 2 ] m c = [GeV]  = [GeV] Fitted and predicted cc spectrum Coulomb (OGE) + linear scalar conft. potential model blue = expt, red = theory. S*S OGE L*S OGE – L*S conft, T OGE

1P -> 1S 3 P 2  3 S [keV] 3 P 1  3 S [keV] 3 P 0  3 S [keV] 1 P 1  1 S [keV] 426(51) [keV] 288(48) [keV] 119(19) [keV] - E1 Radiative Partial Widths 2S -> 1P 2 3 S 1  3 P 2 38 [keV] 2 3 S 1  3 P 1 54 [keV] 2 3 S 1  3 P 0 63 [keV] 2 1 S 0  1 P 1 49 [keV] 18(2) [keV] 24(2) [keV] - Same model, wfns. and params as the cc spectrum. Standard | | 2 E1 decay rate formula. Expt. rad. decay rates from PDG 2002

Fitted and predicted cc spectrum Coulomb (OGE) + linear scalar conft. potential model Left = NR model, right = GI model.. S*S OGE 2P 1F

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/ (quenched – no decay loops) Broadly consistent with the cc potential model spectrum. No radiative or strong decay predictions yet.

3. Strong decays (open flavor)

R and the 4 higher 1 -- states (plot from Yi-Fang Wang’s online BES talk, 16 Sept 2002)

Experimental R summary (2003 PDG) Very interesting open experimental question: Do strong decays use the 3 P 0 model decay mechanism or the Cornell model decay mechanism or … ?  br  vector confinement??? controversial e  e , 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 3 P 0 decay model: qq pair production with vacuum quantum numbers. L I = g  A standard for light hadron decays. It works for D/S in b 1 . 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: 3 P 0 Decay Model 1D 3 D [MeV] 3 D D 1 43 [MeV] 1 D 2 - 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 3 D 3  3 P [keV] 3 D 2  3 P 2 64 [keV] 3 P [keV] 3 D 1  3 P 2 5 [keV] 3 P [keV] 3 P [keV] 1 D 2  1 P [keV] X(3872)

Strong Widths: 3 P 0 Decay Model 1F 3 F [MeV] 3 F 3 84 [MeV] 3 F [MeV] 1 F 3 61 [MeV] DD DD* D*D* D s X(3872)

E1 Radiative Partial Widths 1F -> 1D 3 F 4  3 D [keV] 3 F 3  3 D 3 41 [keV] 3 D [keV] 3 F 2  3 D 3 2 [keV] 3 D 2 62 [keV] 3 D [keV] 1 F 3  1 D [keV]

Strong Widths: 3 P 0 Decay Model 3 3 S 1 74 [MeV] 3 1 S 0 80 [MeV] 3S DD DD* D*D* D s X(3872) 52(10) MeV

After restoring this “p 3 phase space factor”, the BFs are: D 0 D 0 : D 0 D* 0 : D* 0 D* 0 

 partial widths [MeV] ( 3 P 0 decay model): DD = 0.1 DD* = 32.9 D*D* = 33.4 [multiamp. mode] D s D s = 7.8 Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 DD DD* D*D* famous nodal suppression of a 3 3 S 1  (4040) cc  DD  D*D* amplitudes ( 3 P 0 decay model): 1 P 1 =  P 1 =  =    1 P 1 5 F 1 = 0 std. cc and D meson SHO wfn. length scale 

E1 Radiative Partial Widths 3S -> 2P 3 3 S 1  2 3 P 2 14 [keV] 3 3 S 1  2 3 P 1 39 [keV] 3 3 S 1  2 3 P 0 54 [keV] 3 1 S 0  2 1 P [keV] 3S -> 1P 3 3 S 1  3 P [keV] 3 3 S 1  3 P [keV] 3 3 S 1  3 P [keV] 3 1 S 0  1 P [keV]

Strong Widths: 3 P 0 Decay Model 2P 2 3 P 2 80 [MeV] 2 3 P [MeV] 2 3 P 0 30 [MeV] 2 1 P 1 87 [MeV] DD DD* D s

Strong Widths: 3 P 0 Decay Model 2D 2 3 D [MeV] 2 3 D 2 92 [MeV] 2 3 D 1 74 [MeV] 2 1 D [MeV] DD DD* D*D* D s D s D s * 78(20) [MeV]

std. cc SHO wfn. length scale  D*D* amplitudes: ( 3 P 0 decay model): 1 P 1 =  P 1 =     1 P 1 5 F 1 =   partial widths [MeV] ( 3 P 0 decay model): DD = 16.3 DD* = 0.4 D*D* = 35.3 [multiamp. mode] D s D s = 8.0 D s D s * = 14.1  Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 DD DD* D*D*

E1 Radiative Partial Widths 2D -> 1P 2 3 D 3  3 P 2 29 [keV] 2 3 D 2  3 P 2 7 [keV] 3 P 1 26 [keV] 2 3 D 1  3 P 2 1 [keV] 3 P 1 14 [keV] 3 P 0 27 [keV] 2 1 D 2  1 P 1 40 [keV] 2D -> 1F 2 3 D 3  3 F 4 66 [keV]  3 F 3 5 [keV]  3 F 2 14 [keV] 2 3 D 2  3 F 3 44 [keV] 3 F 2 6 [keV] 2 3 D 1  3 F 2 51 [keV] 2 1 D 2  1 F 3 54 [keV] 2D -> 2P 2 3 D 3  2 3 P [keV] 2 3 D 2  2 3 P 2 52 [keV] 2 3 P [keV] 2 3 D 1  2 3 P 2 6 [keV] 2 3 P [keV] 2 3 P [keV] 2 1 D 2  2 1 P [keV]

Strong Widths: 3 P 0 Decay Model 4S 4 3 S 1 78 [MeV] 4 1 S 0 61 [MeV] DD DD* D*D* DD 0 * DD 1 DD 1 ’ DD 2 * D*D 0 * D s D s D s * D s *D s * D s D s0 * 43(15) [MeV]

Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 DD DD* D*D*  DD 1 amplitudes: ( 3 P 0 decay model): 3 S 1 =  0   !!! (HQET) 3 D 1 =   partial widths [MeV] ( 3 P 0 decay model): DD = 0.4 DD* = 2.3 D*D* = 15.8 [multiamp.] New mode calculations: DD 1 = 30.6 [m]  MAIN MODE!!! DD 1 ’ = 1.0 [m] DD 2 * = 23.1 D * D 0 * = 0.0 D s D s = 1.3 D s D s * = 2.6 D s *D s * = 0.7 [m] 

An “industrial application” of the  (4415). Sit “slightly upstream”, at ca MeV, and you should have a copious source of D* s0 (2317). (Assuming it is largely cs 3 P 0.)

5. L’oops Future: “Unquenching the quark model” Virtual meson decay loop effects, qq M 1 M 2 mixing. D sJ * 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).

| D sJ *+ (2317,2457)> = DK molecules? T.Barnes, F.E.Close and H.J.Lipkin, hep-ph/ , PRD68, (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 D s B and B s flavor mesons. 3 P 0 “flux tube” decay model. The L=1 0 + and 1 + cs “D s ” mesons are predicted to Have rather large total widths, MeV. (= broad to unobservably broad). Charmed meson decays (God91) How large are decay loop mixing effects?

J P = 1 + (2457 channel) J P = 0 + (2317 channel) The 0 + and 1 + channels are predicted to have very large DK and D*K decay couplings. This supports the picture of strongly mixed | D sJ *+ (2317,2457)> = |cs> + |(cn)(ns)> states. Evaluation of mixing in progress. Initial estimates for cc …

L’oops evaluated [ J/  - M 1 M 2 - J/  3 P 0 decay model, std. params. and SHO wfns. M 1 M 2  M [J/  ] P M 1 M 2 [J/  ] DD  MeV DD*  MeV D*D*  MeV D s D s  MeV D s D s *  MeV D s *D s *  MeV famous 1 : 4 : 7 ratio DD : DD* : D*D* Sum = MeV P cc = 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 D s D s : D s D s * : D s *D s *

L’oops [ cc - M 1 M 2 - cc  3 P 0 decay model, std. params. and SHO wfns. Init. Sum  M P cc J/  MeV 0.65  c MeV 0.71  MeV 0.43  1  MeV 0.46  0  MeV 0.53 h c  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 be recalculated, including transitions within the continuum. Apparently we CAN expect D sJ -sized (100 MeV) relative mass shifts due to decay loops in extreme cases. cs system to be considered. Beware quenched LGT!

1) Please don’t forget J/  (or other cc) flavor-tagging hadronic decays! May be better than J/  -rad for producing exotica. 2) Spectrum The known states agree well with a cc potential model, except: small multiplet splittings for L.ge.2 imply that the X(3872) is implausible as a “naive” cc state. 3) Strong decays (main topic) Some cc states above 3.73 GeV are expected to be rather narrow (in addition to 2 - states), notably 3 D 3 and 3 F 4. Of the known states,  (4040),  (4159) and  (4415) all have interesting decay modes: 1 st 2, D*D* relative amps, and for  (4415) we predict DD 1 dominance; also a D* s0 (2317) source. 4) L’oops Virtual meson decay loops cause LARGE mass shifts and cc M 1 M 2 mixing. (Perhaps explaining the D * sJ masses?) These effects are under investigation.