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

Charmonium 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.

e Small qq separation g Large qq separation

LGT simulation showing the QCD flux tube R = 1.2 [fm] “funnel-shaped” VQQ(R) Coul. (OGE) linear conft. (str. tens. = 16 T) The QCD flux tube (LGT, G.Bali et al; hep-ph/010032)

Physically allowed hadron states (color singlets) _ Conventional quark model mesons and baryons. qq q3 100s of e.g.s ca. 106 e.g.s of (q3)n, maybe 1-3 others (q3)n, (qq)(qq), (qq)(q3),… nuclei / molecules Basis state mixing may be very important in some sectors. ”exotica” : g2, g3,… glueballs maybe 1 e.g. qqg, q3g,… hybrids maybe 1-3 e.g.s q2q2, q4q,… multiquarks (q2q2),(q4q),… multiquark clusters controversial e.g. Q(1542)

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 Sqq = ½ x ½ = 1 + 0 Combining this with orbital angular momentum Lqq gives states of total Jqq = Lqq spin singlets Jqq = Lqq+1, Lqq, Lqq-1 spin triplets xxxxx tot.

cc mesons quantum numbers Parity Pqq = (-1) (L+1) C-parity Cqq = (-1) (L+S) The resulting cc NL states N2S+1LJ have JPC = 1S: 3S1 1- - ; 1S0 0 - + 2S: 23S1 1- - ; 21S0 0 - + … 1P: 3P2 2+ + ; 3P1 1+ + ; 3P0 0+ + ; 1P1 1+ - 2P … 1D: 3D3 3- - ; 3D2 2- - ; 3D1 1- - ; 1D2 2- + 2D … JPC forbidden to qq are called “JPC-exotic quantum numbers”. 0 - - ; 0 + - ; 1 - + ; 2 + - ; 3 - + … Plausible JPC-exotic candidates = hybrids, glueballs (high mass), maybe multiquarks (fall-apart decays).

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 1D2 2- +, 2- - 3.73 GeV Below 3.73 GeV: Annihilation and EM decays. (rp, KK* , gcc, gg, l+l-..): narrow states.

Fitting cc potential model parameters. as, b, mc, s fixed from 1P c.o.g. and all 1S and 2S masses. blue = expt, red = theory. as = 0.5111 b = 0.1577 [GeV2] mc = 1.4439 [GeV] s = 1.1667 [GeV]

Predicted spin-dependent cc 1P multiplet splittings (sensitive test of OGE) Parameters as, b, mc, s fixed from 13PJ c.o.g. and all 1S, 2S masses, prev slide. blue = expt, red = theory. as = 0.5111 b = 0.1577 [GeV2] mc = 1.4439 [GeV] s = 1.1667 [GeV] OGE + lin. scalar conft. 1P1 (not shown) is 8 MeV below the 3PJ c.o.g. Scalar conft. gives neg. L*S

Fitted and predicted cc spectrum blue = expt, red = theory. 23F4 (4351) 23F3 (4355) 23F2 (4353) 21F3 (4353) 43S1 (4407) 41S0 (4387) 33P2 (4320) 33P1 (4272) 33P0 (4202) 31P1 (4281) 23D3 (4170) 23D2 (4161) 23D1 (4144) 21D2 (4160) 33S1 (4073) 31S0 (4047) 3F4 (4025) 3F3 (4032) 3F2 (4032) 1F3 (4029) 23P2 (3976) 23P1 (3927) 23P0 (3853) 21P1 (3936) 3D3 (3810) 3D2 (3803) 3D1 (3787) 1D2 (3802) 23S1 (3672) 21S0 (3635) 3P2 (3560) 3P1 (3507) 3P0 (3424) 1P1 (3517) Previous fit (1S,2S,1Pcog.): as = 0.5111 b = 0.1577 [GeV2] mc = 1.4439 [GeV] s = 1.1667 [GeV] as = 0.5538 b = 0.1422 [GeV2] mc = 1.4834 [GeV] s = 1.0222 [GeV] 3S1 (3087) 1S1 (2986)

cc from the “standard” potential model S. Godfrey and N 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 <- 1- + exotic cc-H at 4.4 GeV What about LGT??? An 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. oops… 1+ - cc has been withdrawn.

Charmonium Open-flavor strong decays

Experimental R summary (2003 PDG) How do strong decays happen at the QCD (q-g) level? Experimental R summary (2003 PDG) Very interesting open experimental question: Do strong decays use the 3P0 model decay mechanism or the 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! g0 br vector confinement??? controversial

The 3P0 decay model: qq pair production with vacuum quantum numbers. L I = g y y . A standard for light hadron decays. It works for D/S in b1 -> wp. The relation to QCD is obscure.

R and the 4 higher 1-- states 3770 4040 4160 4415 (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.) 43(15) MeV 78(20) MeV 52(10) MeV < 2.3 MeV 23.6(2.7) MeV PDG values

Strong Widths: 3P0 Decay Model Parameters are g = 0.4 (from light meson decays), meson masses and wfns. 1D 3D3 0.6 [MeV] 3D2 - 3D1 43 [MeV] 1D2 - DD 23.6(2.7) [MeV]

Strong Widths: 3P0 Decay Model 33S1 74 [MeV] 31S0 67 [MeV] 3S DD DD* D*D* DsDs 52(10) MeV

Y(4040) partial widths [MeV] (3P0 decay model): DD = 0.1 DD* = 32.9 Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 DD DD* D*D* 4159 4415 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 5F1 = 0 famous nodal suppression of a 33S1 Y(4040) cc -> DD std. cc and D meson SHO wfn. length scale

Strong Widths: 3P0 Decay Model 23D3 148 [MeV] 23D2 93 [MeV] 23D1 74 [MeV] 21D2 112 [MeV] DD DD* D*D* DsDs DsDs* 78(20) [MeV]

Y(4159) -> D*D* amplitudes: (3P0 decay model): 1P1 = + 0.081 Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 DD DD* D*D* 4159 4415 Y(4159) -> D*D* amplitudes: (3P0 decay model): 1P1 = + 0.081 5P1 = - 0.036 5F1 = - 0.141 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 std. cc SHO wfn. length scale

Strong Widths: 3P0 Decay Model 23P2 83 [MeV] 23P1 162 [MeV] 23P0 29 [MeV] 21P1 86 [MeV] DD DD* DsDs

Strong Widths: 3P0 Decay Model 1F 3F4 9.0 [MeV] 3F3 87 [MeV] 3F2 165 [MeV] 1F3 64 [MeV] DD DD* D*D* DsDs

Charmonium n.b. I will discuss only E1 because of time limitations. Yes, M1 is interesting too! J/y -> ghc and y’ -> gh’c give mc, and y’ -> ghc tests S*S corrections to orthog. 1S-2S wfns. Radiative transitions

E1 Radiative Partial Widths Same model, wfns. and params as the cc spectrum. Standard |<yf | r |yi >|2 E1 decay rate formula. Expt. rad. decay rates from PDG 2002 2S -> 1P 23S1 -> 3P2 39 [keV] 23S1 -> 3P1 57 [keV] 23S1 -> 3P0 67 [keV] 21S0 -> 1P1 74 [keV] 18(2) [keV] 24(2) [keV] - 1P -> 1S 3P2 -> 3S1 472 [keV] 3P1 -> 3S1 353 [keV] 3P0 -> 3S1 166 [keV] 1P1 -> 1S0 581 [keV] 426(51) [keV] 288(48) [keV] 119(19) [keV] -

E1 Radiative Partial Widths 1D -> 1P 3D3 -> 3P2 305 [keV] 3D2 -> 3P2 70 [keV] 3P1 342 [keV] 3D1 -> 3P2 5 [keV] 3P1 134 [keV] 3P0 443 [keV] 1D2 -> 1P1 376 [keV]

E1 Radiative Partial Widths 3S -> 2P 33S1 -> 23P2 12 [keV] 33S1 -> 23P1 38 [keV] 33S1 -> 23P0 10 [keV] 31S0 -> 21P1 114 [keV] 3S -> 1P 33S1 -> 3P2 0.8 [keV] 33S1 -> 3P1 0.6 [keV] 33S1 -> 3P0 0.3 [keV] 31S0 -> 1P1 11 [keV]

E1 Radiative Partial Widths 2D -> 2P 23D3 -> 23P2 246 [keV] 23D2 -> 23P2 54 [keV] 23P1 319[keV] 23D1 -> 23P2 6 [keV] 23P1 173 [keV] 23P0 515 [keV] 21D2 -> 21P1 355 [keV] 2D -> 1F 23D3 -> 3F4 67 [keV] -> 3F3 5 [keV] -> 3F2 15 [keV] 23D2 -> 3F3 46 [keV] 3F2 6 [keV] 23D1 -> 3F2 49 [keV] 21D2 -> 1F3 54 [keV] 2D -> 1P 23D3 -> 3P2 35 [keV] 23D2 -> 3P2 8 [keV] 3P1 30 [keV] 23D1 -> 3P2 1 [keV] 3P1 17 [keV] 3P0 32 [keV] 21D2 -> 1P1 48 [keV]

E1 Radiative Partial Widths 1F -> 1D 3F4 -> 3D3 351 [keV] 3F3 -> 3D3 43 [keV] 3D2 375 [keV] 3F2 -> 3D3 2 [keV] 3D2 66 [keV] 3D1 524 [keV] 1F3 -> 1D2 409 [keV]

X(3872) M = 3872.0 +- 0.6 +- 0.5 MeV M( Do + D*o) = 3871.5 +- 0.5 MeV Belle Collab. S.-K.Choi et al, hep-ex/0309032; K.Abe et al, hep-ex/0308029. X(3872) B+ / - -> K+ / - ( p+p- J /Y ) y(3770) = 3D1 cc. If the X(3872) is 1D cc, an L-multiplet is split much more than expected assuming scalar conft. G < 2.3 MeV Accidental agreement? X = cc 2- + or 2- - or …, or a molecular state? M = 3872.0 +- 0.6 +- 0.5 MeV M( Do + D*o) = 3871.5 +- 0.5 MeV n.b. M( D+ + D*-) = 3879.5 +- 0.7 MeV

X(3872) from CDF G.Bauer, QWG presentation, 20 Sept. 2003. n.b. most recent CDF II: D.Acosta et al, hep-ex/0312021, 5 Dec 2003. M = 3871.3 pm 0.7 pm 0.4 MeV

The obvious guess if cc is 2 - + or 2 - -. cc from the “standard” potential model S.Godfrey and N.Isgur, PRD32, 189 (1985). 2- + 2- - 3- - (3D2 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/0311169. 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 3D3(3849) 23P2(3979) 3D2(3838) 23P1(3953) 3D1(3.82) [y(3770)] 23P0(3916) 1D2(3837) 21P1(3956) We assigned a mass of 3872 MeV to each state and calculated the resulting strong and EM partial widths.

We cannot yet exclude 5 of the 8 1D and 2P cc assignments. If X = 1D cc: Total width eliminates only 3D1. Large, ca. 300 – 500 keV E1 radiative partial widths to gcJ and ghc are predicted for 1D assignments ( 3D3, 3D2 ) and 1D2. If Gtot = 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 = 1D2 cc, you are “forced” to discover the hc! If X = 2P cc: 23P1 and 21P1 are possible based on total width alone. These assignments predict weaker but perhaps accessible radiative branches to g J/y, gy’ and ghc, ghc’ respectively. NOT to gcJ states. (E1 changes parity.)

DD* molecule options M(X) = 3872.0 +- 0.6 +- 0.5 MeV (I prefer this assignment.) This possibility is suggested by the similarity in mass, M(X) = 3872.0 +- 0.6 +- 0.5 MeV M( Do + D*o) = 3871.5 +- 0.5 MeV N.A.Tornqvist, PRL67, 556 (1991); hep-ph/0308277. F.E.Close and P.R.Page, hep-ph/0309253. C.Y.Wong, hep-ph/0311088. E.Braaten and M.Kusunoki, hep-ph/0311147. E.S.Swanson, hep-ph/0311229. n.b. The suggestion of charm meson molecules dates back to 1976: Y(4040) as a D*D* molecule; (Voloshin and Okun; deRujula, Georgi and Glashow).

Interesting prediction of molecule decay modes: E.Swanson, hep-ph/0311299: 1+ + DoD*o molecule with additional comps. due to rescattering. J/yro J/yw Predicted total width ca. = expt limit (2 MeV). Very characteristic mix of isospins: J/yro and J/yw decay modes expected. Nothing about the X(3872) is input: this all follows from OpE and C.I. !!!

X(3872) summary: The X(3872) is a new state reported by Belle and CDF in only one mode: J/y p+ p- . It is very narrow, G < 2.3 MeV. The limit on gc1 is comparable to the observed J/y p+ p-. The mass suggests that X is a deuteronlike DoD*o-molecule. Naïvely, this suggests a narrow total X width of ca. 50 keV and 3:2 b.f.s to DoDopo and DoDog. However, internal rescatter to (cc)(nn) may be important. This predicts G(X) = 2 MeV and remarkable, comparable b.f.s to J/yro and J/yw [E.S.Swanson, hep-ph/0311299]. The bleedin’ obvious decay mode J/y po po should be searched for, to test C(X) and establish whether p+ p- = ro. Possible “wrong-mass” cc assignments to 1D and 2P levels can be tested by their (often large) E1 radiative transitions to g(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 3D3 ( G = 0.6 MeV) and 3F4 ( G = 9 MeV). 3) The multiamplitude strong decays y(4040), y(4159) -> D*D* can be used to establish the dom. strong decay mechanism. b.f.s to DD, DD*, Ds Ds … will be useful too. [ 3) is my favorite new-age cc topic.] 4) E1 rad: y(3770) -> gc2 tests S-wave comp. y(4040), y(4159) -> gDD search for new C=(+) cc states. 5) The X(3872) is likely a Do D*o molecule. J/yro and J/yw decay modes? X = cc options predict large E1 b.f.s to g + P-wave cc.