1. Higher Charmonium 1) Spectrum 2) Strong decays (main topic) 3) L’oops Ted Barnes Physics Div. ORNL Dept. of Physics, U.Tenn. GHP2004 Fermilab, 24-26 Oct. 2004 abstracted from T.Barnes, S.Godfrey and E.S.Swanson, in prep.

2. 1. Spectrum

3. 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.

4.  s = 0.5538 b = 0.1422 [GeV 2 ] m c = 1.4834 [GeV]  = 1.0222 [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

5. 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.

6. 2. Strong decays (open flavor)

7. 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!

8. 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.

9. 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)

10. Strong Widths: 3 P 0 Decay Model 1D 3 D 3 0.5 [MeV] 3 D 2 - 3 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)

11. E1 Radiative Partial Widths 1D -> 1P 3 D 3  3 P 2 305 [keV] 3 D 2  3 P 2 70 [keV] 3 P 1 342 [keV] 3 D 1  3 P 2 5 [keV] 3 P 1 134 [keV] 3 P 0 443 [keV] 1 D 2  1 P 1 376 [keV] X(3872)

12. Strong Widths: 3 P 0 Decay Model 1F 3 F 4 8.3 [MeV] 3 F 3 84 [MeV] 3 F 2 161 [MeV] 1 F 3 61 [MeV] DD DD* D*D* D s X(3872)

13. 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

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

15.  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* 4159 4415 famous nodal suppression of a 3 3 S 1  (4040) cc  DD  D*D* amplitudes ( 3 P 0 decay model): 1 P 1 =  0.056 5 P 1 =  0.251 =    1 P 1 5 F 1 = 0 std. cc and D meson SHO wfn. length scale 

16. Strong Widths: 3 P 0 Decay Model 2D 2 3 D 3 148 [MeV] 2 3 D 2 92 [MeV] 2 3 D 1 74 [MeV] 2 1 D 2 111 [MeV] DD DD* D*D* D s D s D s * 78(20) [MeV]

17. 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: ( 3 P 0 decay model): 1 P 1 =  0.081 5 P 1 =  0.036    1 P 1 5 F 1 =  0.141  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 

18. 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]

19. Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 DD DD* D*D* 4159 4415  DD 1 amplitudes: ( 3 P 0 decay model): 3 S 1 =  0   !!! 3 D 1 =  + 0.110  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] 

20. 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 3 P 0.)

21. 3. 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).

22. | D sJ *+ (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)

23. 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, 140 - 990 MeV. (= broad to unobservably broad). Charmed meson decays (God91) How large are decay loop mixing effects?

24. 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 …

25. 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  - 30. MeV 0.027 DD*  - 108. MeV 0.086 D*D*  - 173. MeV 0.123 D s D s  - 17. MeV 0.012 D s D s *  - 60. MeV 0.041 D s *D s *  - 97. MeV 0.060 famous 1 : 4 : 7 ratio DD : DD* : D*D* Sum = - 485. 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 *

26. L’oops [ cc - M 1 M 2 - cc  3 P 0 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 h c  - 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 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!

27. 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) is implausible 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 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. 3) L’oops Virtual meson decay loops cause LARGE mass shifts and cc M 1 M 2 mixing. These effects are under investigation.