Charmonium Ted Barnes Physics Div. ORNL Dept. of Physics, U.Tenn.

1) Basic physics 2) Theoretical spectrum versus known states 3) NEW: open-flavor strong widths 4) E1 transitions 5) X(3872) The numbers quoted in 2-4) will appear in T.Barnes, S.Godfrey and E.S.Swanson (in prep.) I will mainly quote cc potential model results, which provide a useful intuitive picture of charmonium. LGT (C.Morningstar) is not yet competitive for higher mass cc states but is of course the preferred technique and will eventually solve everything. Charmonium

e g Small qq separation Large qq separation

The QCD flux tube (LGT, G.Bali et al; hep-ph/ ) LGT simulation showing the QCD flux tube QQ R = 1.2 [fm] “funnel-shaped” V QQ (R) Coul. (OGE) linear conft. (str. tens. = 16 T)

Physically allowed hadron states (color singlets) qq q3q3 Conventional quark model mesons and baryons. q 2 q 2, q 4 q,… multiquarks g 2, g 3,… glueballs maybe 1 e.g. qqg, q 3 g,… hybrids maybe 1-3 e.g.s 100s of e.g.s ”exotica” : ca e.g.s of (q 3 ) n, maybe 1-3 others (q 3 ) n, (qq)(qq), (qq)(q 3 ),… nuclei / molecules (q 2 q 2 ),(q 4 q),… multiquark clusters controversial e.g.  _ Basis state mixing may be very important in some sectors.

cc mesons states and spectrum The nonrelativistic quark model treats conventional charmonia as cc bound states. Since each quark has spin-1/2, the total spin is S qq = ½ x ½ = Combining this with orbital angular momentum L qq gives states of total J qq = L qq spin singlets J qq = L qq +1, L qq, L qq -1 spin triplets tot. xxxxx

Parity P qq = (-1) (L+1) C-parity C qq = (-1) (L+S) cc mesons quantum numbers 1S: 3 S 1 1   ; 1 S 0 0   2S: 2 3 S 1 1   ; 2 1 S 0 0   … 1P: 3 P 2 2  ; 3 P 1 1  ; 3 P 0 0  ; 1 P 1 1    2P … 1D: 3 D 3 3  ; 3 D 2 2  ; 3 D 1 1  ; 1 D 2 2    2D … J PC forbidden to qq are called “J PC -exotic quantum numbers”. 0   ; 0  ; 1  ; 2  ; 3  … Plausible J PC -exotic candidates = hybrids, glueballs (high mass), maybe multiquarks (fall-apart decays). The resulting cc NL states N 2S+1 L J have J PC =

Charmonium Theoretical spectrum versus known states

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.

Fitting cc potential model parameters.  s, b, m c,  fixed from 1P c.o.g. and all 1S and 2S masses. blue = expt, red = theory.  s = b = [GeV 2 ] m c = [GeV]  = [GeV]

Predicted spin-dependent cc 1P multiplet splittings (sensitive test of OGE) Parameters  s, b, m c,  fixed from 1 3 P J c.o.g. and all 1S, 2S masses, prev slide. blue = expt, red = theory.  s = b = [GeV 2 ] m c = [GeV]  = [GeV] OGE + lin. scalar conft. 1 P 1 (not shown) is 8 MeV below the 3 P J c.o.g. Scalar conft. gives neg. L*S

2 3 S 1 (3672) 2 1 S 0 (3635) 3 3 S 1 (4073) 3 1 S 0 (4047) 4 3 S 1 (4407) 4 1 S 0 (4387) 3 3 P 2 (4320) 3 3 P 1 (4272) 3 3 P 0 (4202) 3 1 P 1 (4281) 2 3 P 2 (3976) 2 3 P 1 (3927) 2 3 P 0 (3853) 2 1 P 1 (3936) 3 P 2 (3560) 3 P 1 (3507) 3 P 0 (3424) 1 P 1 (3517) 2 3 D 3 (4170) 2 3 D 2 (4161) 2 3 D 1 (4144) 2 1 D 2 (4160) 3 D 3 (3810) 3 D 2 (3803) 3 D 1 (3787) 1 D 2 (3802) 2 3 F 4 (4351) 2 3 F 3 (4355) 2 3 F 2 (4353) 2 1 F 3 (4353) 3 F 4 (4025) 3 F 3 (4032) 3 F 2 (4032) 1 F 3 (4029) 3 S 1 (3087) 1 S 1 (2986) Fitted and predicted cc spectrum blue = expt, red = theory.  s = b = [GeV 2 ] m c = [GeV]  = [GeV] Previous fit (1S,2S,1P cog.):  s = b = [GeV 2 ] m c = [GeV]  = [GeV]

cc from the “standard” potential model S.Godfrey and N.Isgur, PRD32, 189 (1985).

Godfrey-Isgur model cc spectrum (SG, private comm.)

cc from LGT   exotic cc-H at 4.4 GeV oops…   cc has been withdrawn. Small L=2 hfs. What about LGT??? An 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.

Charmonium Open-flavor strong decays

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 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.

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

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

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.

Strong Widths: 3 P 0 Decay Model 3 3 S 1 74 [MeV] 3 1 S 0 67 [MeV] 3S DD DD* D*D* D s 52(10) MeV

 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 =  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 93 [MeV] 2 3 D 1 74 [MeV] 2 1 D [MeV] DD DD* D*D* D s D s D s * 78(20) [MeV]

 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* std. cc SHO wfn. length scale  D*D* amplitudes: ( 3 P 0 decay model): 1 P 1 =  P 1 =  F 1 =  0.141

Strong Widths: 3 P 0 Decay Model 2P 2 3 P 2 83 [MeV] 2 3 P [MeV] 2 3 P 0 29 [MeV] 2 1 P 1 86 [MeV] DD DD* D s

Strong Widths: 3 P 0 Decay Model 1F 3 F [MeV] 3 F 3 87 [MeV] 3 F [MeV] 1 F 3 64 [MeV] DD DD* D*D* D s

Charmonium Radiative transitions n.b. I will discuss only E1 because of time limitations. Yes, M1 is interesting too! J/    c and ’  ’ c give m c, and ’   c tests S*S corrections to orthog. 1S-2S wfns.

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 39 [keV] 2 3 S 1  3 P 1 57 [keV] 2 3 S 1  3 P 0 67 [keV] 2 1 S 0  1 P 1 74 [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

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]

E1 Radiative Partial Widths 3S -> 2P 3 3 S 1  2 3 P 2 12 [keV] 3 3 S 1  2 3 P 1 38 [keV] 3 3 S 1  2 3 P 0 10 [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 1 11 [keV]

E1 Radiative Partial Widths 2D -> 1P 2 3 D 3  3 P 2 35 [keV] 2 3 D 2  3 P 2 8 [keV] 3 P 1 30 [keV] 2 3 D 1  3 P 2 1 [keV] 3 P 1 17 [keV] 3 P 0 32 [keV] 2 1 D 2  1 P 1 48 [keV] 2D -> 1F 2 3 D 3  3 F 4 67 [keV]  3 F 3 5 [keV]  3 F 2 15 [keV] 2 3 D 2  3 F 3 46 [keV] 3 F 2 6 [keV] 2 3 D 1  3 F 2 49 [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 54 [keV] 2 3 P 1 319[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]

E1 Radiative Partial Widths 1F -> 1D 3 F 4  3 D [keV] 3 F 3  3 D 3 43 [keV] 3 D [keV] 3 F 2  3 D 3 2 [keV] 3 D 2 66 [keV] 3 D [keV] 1 F 3  1 D [keV]

X (3872 ) Belle Collab. S.-K.Choi et al, hep-ex/ ; K.Abe et al, hep-ex/         J   D   D*   MeV Accidental agreement? X = cc 2  or 2  or …, or a molecular state?  MeV  = 3 D 1 cc. If the X(3872) is 1D cc, an L-multiplet is split much more than expected assuming scalar conft. n.b.  D   D*   MeV MeV

X (3872) from CDF G.Bauer, QWG presentation, 20 Sept n.b. most recent CDF II: D.Acosta et al, hep-ex/ , 5 Dec M = pm 0.7 pm 0.4 MeV

cc from the “standard” potential model S.Godfrey and N.Isgur, PRD32, 189 (1985).     ( 3 D 2 is a typo)   The obvious guess if cc is 2  or 2 . No open-flavor strong decays – narrow.

Charmonium Options for the X(3872) T.Barnes and S.Godfrey, hep-ph/ Our approach: Assume all conceivable cc assignments for the X(3872): all 8 states in the 1D and 2P cc multiplets. Nominal Godfrey-Isgur masses were 3 D 3 (3849) 2 3 P 2 (3979) 3 D 2 (3838) 2 3 P 1 (3953) 3 D 1 (3.82) [  (3770)] 2 3 P 0 (3916) 1 D 2 (3837) 2 1 P 1 (3956) We assigned a mass of 3872 MeV to each state and calculated the resulting strong and EM partial widths.

If X = 1D cc: Total width eliminates only 3 D 1. Large, ca. 300 – 500 keV E1 radiative partial widths to  J and  h c are predicted for 1D assignments ( 3 D 3, 3 D 2 ) and 1 D 2. If  tot = 1 MeV these are 30% - 50% b.f.s! The pattern of final P-wave cc states you populate identifies the initial cc state. If X = 1 D 2 cc, you are “forced” to discover the h c ! If X = 2P cc: 2 3 P 1 and 2 1 P 1 are possible based on total width alone. These assignments predict weaker but perhaps accessible radiative branches to J, ’ and  c  c ’ respectively. NOT to  J states. (E1 changes parity.) We cannot yet exclude 5 of the 8 1D and 2P cc assignments.

DD* molecule options This possibility is suggested by the similarity in mass, N.A.Tornqvist, PRL67, 556 (1991); hep-ph/ F.E.Close and P.R.Page, hep-ph/ C.Y.Wong, hep-ph/ E.Braaten and M.Kusunoki, hep-ph/ E.S.Swanson, hep-ph/ n.b. The suggestion of charm meson molecules dates back to 1976:  (4040) as a D*D* molecule; (Voloshin and Okun; deRujula, Georgi and Glashow).  X MeV D  D*  MeV (I prefer this assignment.)

Interesting prediction of molecule decay modes: E.Swanson, hep-ph/ : 1  D o D* o molecule with additional comps. due to rescattering. J   J    Predicted total width ca. = expt limit (2 MeV). Very characteristic mix of isospins: J     and  J   decay modes expected. Nothing about the X(3872) is input: this all follows from O  E and C.I. !!!

X(3872) summary: The X(3872) is a new state reported by Belle and CDF in only one mode: J   . It is very narrow,  < 2.3 MeV. The limit on   is comparable to the observed J   . The mass suggests that X is a deuteronlike D o D* o -molecule. Naïvely, this suggests a narrow total X width of ca. 50 keV and 3:2 b.f.s to D o D o   and D o D o . However, internal rescatter to (cc)(nn) may be important. This predicts  (X) = 2 MeV and remarkable, comparable b.f.s to J   and J [ E.S.Swanson, hep-ph/ ]. The bleedin’ obvious decay mode J    should be searched for, to test C(X) and establish whether     =    Possible “wrong-mass” cc assignments to 1D and 2P levels can be tested by their (often large) E1 radiative transitions to (cc).

Charmonium: Summary 1) The spectrum fits a OGE + linear scalar conft. potential model reasonably well. More cc states will be useful to test this. (Pt. 4.) 2) Some cc states above 3.73 GeV in addition to 2     and 2   are expected to be relatively narrow, notably 3 D 3 3 F 4 3 D 3 (  = 0.6 MeV ) and 3 F 4 (  = 9 MeV ). 3) The multiamplitude strong decays   D*D* can be used to establish the dom. strong decay mechanism. b.f.s to DD, DD*, D s D s … will be useful too. [ 3) is my favorite new-age cc topic.] 4) E1 rad:    2 tests S-wave comp. ,    DD search for new C=(+) cc states. 5) The X(3872) is likely a D o D* o molecule. J     and  J   decay modes? X = cc options predict large E1 b.f.s to   + P-wave cc.