Higher Charmonium 1) Spectrum 2) Strong decays (main topic) 3) L’oops Ted Barnes Physics Div. ORNL Dept. of Physics, U.Tenn. GHP2004 Fermilab, Oct 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 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

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.

2. Strong decays (open flavor)

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 70 [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)

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 

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]

Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 DD DD* D*D* 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 

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   !!! 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.)

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).

| 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) 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.