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Higher Charmonium

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

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Higher Charmonium

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  1. Ted Barnes Physics Div. ORNL Dept. of Physics, U.Tenn. GHP2004 Fermilab, 24-26 Oct. 2004 Higher Charmonium • Spectrum • Strong decays (main topic) • L’oops 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 1D2 2- +, 2- - 3.73 GeV Below 3.73 GeV: Annihilation and EM decays. (rp, KK* , gcc, gg, l+l-..): narrow states.

  4. Fitted and predicted cc spectrum Coulomb (OGE) + linear scalar conft. potential model blue = expt, red = theory. L*S OGE – L*S conft, T OGE as = 0.5538 b = 0.1422 [GeV2] mc = 1.4834 [GeV] s = 1.0222 [GeV] S*S OGE

  5. 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. cc from LGT <-1- + exotic cc-H at 4.4 GeV Small L=2 hfs. 1+ - cc has returned.

  6. 2. Strong decays (open flavor)

  7. g0 g0 br vector confinement??? controversial Experimental R summary (2003 PDG) How do open-flavor strong decays happen at the QCD (q-g) level? Very interesting open experimental question: Do strong decays use the3P0model decay mechanism orthe Cornell model decay mechanism or … ? e+e-, hence 1-- cc states only. “Cornell” decay model: (1980s cc papers) (cc) <-> (cn)(nc) coupling from qq pair production by linear confining interaction. Absolute norm of G is fixed!

  8. The 3P0 decay model: qq pair production with vacuum quantum numbers. LI = g y y . A standard for light hadron decays. It works for D/S in b1-> wp. 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.) 43(15) MeV 78(20) MeV 52(10) MeV < 2.3 MeV X(3872) 23.6(2.7) MeV PDG values

  10. Strong Widths: 3P0 Decay Model 1D 3D30.5 [MeV] 3D2 - 3D1 43 [MeV] 1D2 - DD Parameters are g = 0.4 (from light meson decays), meson masses and wfns. X(3872) 23.6(2.7) [MeV]

  11. E1 Radiative Partial Widths 1D -> 1P 3D3 -> 3P2305 [keV] 3D2-> 3P270 [keV] 3P1342 [keV] 3D1->3P2 5 [keV] 3P1134 [keV] 3P0443 [keV] 1D2->1P1376 [keV] X(3872)

  12. Strong Widths: 3P0 Decay Model 3F48.3[MeV] 3F3 84 [MeV] 3F2 161 [MeV] 1F3 61 [MeV] 1F DD DD* D*D* DsDs X(3872)

  13. Strong Widths: 3P0 Decay Model 3S 33S1 74 [MeV] 31S0 80 [MeV] DD DD* D*D* DsDs 52(10) MeV X(3872)

  14. After restoring this “p3 phase space factor”, the BFs are: D0D0 : D0D*0 : D*0D*0 0.12 +/- 0.06 0.95 +/- 0.19 [1] +/- 0.31

  15. Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4415 4040 4159 D*D* DD* DD Y(4040) Y(4040) partial widths [MeV] (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 = +0.056 5P1 = -0.251 = - 2 * 51/2 *1P1 5F1 = 0 famous nodal suppression of a 33S1Y(4040) cc-> DD std. cc and D meson SHO wfn. length scale

  16. Strong Widths: 3P0 Decay Model 23D3 148 [MeV] 23D2 92 [MeV] 23D1 74 [MeV] 21D2 111 [MeV] 2D DD DD* D*D* DsDs DsDs* 78(20) [MeV]

  17. Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 D*D* DD* DD Y(4159) 4415 4159 Y(4159) partial widths [MeV] (3P0 decay model): DD = 16.3 DD* = 0.4 D*D* = 35.3 [multiamp. mode] DsDs= 8.0 DsDs*= 14.1 Y(4159) ->D*D* amplitudes: (3P0 decay model): 1P1 = +0.081 5P1 = -0.036 = - 5 -1/2 *1P1 5F1 = -0.141 std. cc SHO wfn. length scale

  18. Strong Widths: 3P0 Decay Model 43S1 78 [MeV] 41S0 61 [MeV] 4S 43(15) [MeV] DD DD* D*D* DD0* DD1 DD1’ DD2* D*D0* DsDs DsDs* Ds*Ds* DsDs0*

  19. Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 Y(4415) 4415 4159 Y(4415) partial widths [MeV] (3P0 decay model): DD = 0.4 DD* = 2.3 D*D* = 15.8 [multiamp.] New mode calculations: DD1= 30.6 [m] <- MAIN MODE!!! DD1’= 1.0 [m] DD2*=23.1 D*D0*= 0.0 DsDs= 1.3 DsDs*= 2.6 Ds*Ds*= 0.7 [m] D*D* DD* DD Y(4415) - >DD1 amplitudes: (3P0 decay model): 3S1 = 0 <- !!! 3D1 = + 0.110

  20. An “industrial application” of the y(4415). Sit “slightly upstream”, at ca. 4435 MeV, and you should have a copious source of D*s0(2317). (Assuming it is largely cs3P0.)

  21. 3. 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 in QCD. Also LGT-relevant (they are usually quenched too).

  22. T.Barnes, F.E.Close and H.J.Lipkin, hep-ph/0305025, PRD68, 054006 (2003). |DsJ*+(2317,2457)> =DK molecules? 3. reality (loop effects now being evaluated) Reminiscent of Weinstein and Isgur’s “KK molecules”.

  23. How large are decay loop mixing effects? Charmed meson decays(God91) 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 to unobservably broad).

  24. JP = 0+ (2317 channel) JP = 1+ (2457 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 |DsJ*+(2317,2457)> = |cs> + |(cn)(ns)> states. Evaluation of mixing in progress. Initial estimates for cc …

  25. L’oops evaluated [ J/y - M1M2 - J/y ] 3P0 decay model, std. params. and SHO wfns. M1M2 DM [J/y] PM1M2[J/y] DD- 30. MeV 0.027 DD*- 108. MeV 0.086 D*D*- 173. MeV 0.123 famous 1 : 4 : 7 ratio DD :DD* : D*D* DsDs - 17. MeV 0.012 DsDs*- 60. MeV 0.041 Ds*Ds*- 97. MeV 0.060 1/2 : 2 : 7/2 DsDs : DsDs*:Ds*Ds* Sum =- 485. MeVPcc = 65.% VERY LARGEmass shift and large non-cc component! Can the QM really accommodate such large mass shifts??? Other “cc” states?

  26. L’oops Init.SumDM Pcc [ cc - M1M2 - cc ] 3P0 decay model, std. params. and SHO wfns. J/y - 485. MeV 0.65 hc - 447. MeV 0.71 c2 - 537. MeV 0.43 c1 - 511. MeV 0.46 c0- 471. MeV 0.53 hc -516. MeV 0.46 Aha? The large mass shifts are all similar; the relative shifts are “moderate”. 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! Continuum components are large; transitions (e.g. E1 radiative) will have to be recalculated, including transitions within the continuum.

  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 3D3 and 3F4. Of the known states, y(4040), y(4159) and y(4415) all have interesting decay modes: 1st 2, D*D* relative amps, and for y(4415) we predict DD1 dominance; also a D*s0(2317) source. 3) L’oops Virtual meson decay loops cause LARGE mass shifts and cc <-> M1M2 mixing. These effects are under investigation.

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