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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 Q Q R = 1.2 [fm] “funnel-shaped” VQQ(R) linear conft. (str. tens. = 16 T) Coul. (OGE) The QCD flux tube (LGT, G.Bali et al; hep-ph/010032)
(q2q2),(q4q),… (q3)n, (qq)(qq),(qq)(q3),… multiquark clusters nuclei / molecules controversial e.g. Q(1542) ca. 106 e.g.s of (q3)n, maybe 1-3 others g2, g3,… qqg, q3g,… q2q2, q4q,… glueballs hybrids multiquarks maybe 1 e.g. maybe 1-3 e.g.s Physically allowed hadron states (color singlets) _ Conventional quark model mesons and baryons. qq q3 100s of e.g.s Basis state mixing may be very important in some sectors. ”exotica” :
cc mesonsstates 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 Lqqgives states of total Jqq = Lqqspin singlets Jqq = Lqq+1, Lqq, Lqq-1spin triplets xxxxx tot.
cc mesonsquantum numbers ParityPqq = (-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, sfixed 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 multipletsplittings (sensitive test of OGE) Parameters as, b, mc, sfixed 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) 3F4 (4025) 3F3 (4032) 3F2 (4032) 1F3 (4029) 33S1 (4073) 31S0 (4047) 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 modelS.Godfrey and N.Isgur, PRD32, 189 (1985).
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
g0 g0 br vector confinement??? controversial Experimental R summary (2003 PDG) How do 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!
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.
4040 4160 3770 4415 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.) 43(15) MeV 78(20) MeV 52(10) MeV < 2.3 MeV 23.6(2.7) MeV PDG values
Strong Widths: 3P0 Decay Model 1D 3D30.6 [MeV] 3D2 - 3D1 43 [MeV] 1D2 - DD Parameters are g = 0.4 (from light meson decays), meson masses and wfns. 23.6(2.7) [MeV]
Strong Widths: 3P0 Decay Model 3S 33S1 74 [MeV] 31S0 67 [MeV] DD DD* D*D* DsDs 52(10) MeV
Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4415 4040 4159 D*D* DD* DD 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 33S1Y(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] 2D DD DD* D*D* DsDs DsDs* 78(20) [MeV]
Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4415 4040 4159 D*D* DD* DD 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 5F1 = -0.141 std. cc SHO wfn. length scale
Strong Widths: 3P0 Decay Model 2P 23P2 83 [MeV] 23P1 162 [MeV] 23P029 [MeV] 21P1 86 [MeV] DD DD* DsDs
Strong Widths: 3P0 Decay Model 3F49.0[MeV] 3F3 87 [MeV] 3F2 165 [MeV] 1F3 64 [MeV] 1F 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 18(2) [keV] 24(2) [keV] 24(2) [keV] - 23S1->3P239 [keV] 23S1->3P157 [keV] 23S1->3P067 [keV] 21S0->1P174 [keV] 2S -> 1P 1P -> 1S 3P2->3S1472 [keV] 3P1->3S1353 [keV] 3P0->3S1166 [keV] 1P1->1S0581 [keV] 426(51) [keV] 288(48) [keV] 119(19) [keV] - 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
E1 Radiative Partial Widths 1D -> 1P 3D3 -> 3P2305 [keV] 3D2-> 3P2 70 [keV] 3P1342 [keV] 3D1->3P2 5 [keV] 3P1134 [keV] 3P0443 [keV] 1D2->1P1 376 [keV]
E1 Radiative Partial Widths 3S -> 2P 33S1->23P212 [keV] 33S1->23P138 [keV] 33S1->23P010 [keV] 31S0->21P1114 [keV] 3S -> 1P 33S1->3P2 0.8 [keV] 33S1->3P1 0.6 [keV] 33S1->3P0 0.3 [keV] 31S0->1P111 [keV]
E1 Radiative Partial Widths 23D3 -> 23P2246 [keV] 23D2->23P2 54 [keV] 23P1319[keV] 23D1->23P2 6 [keV] 23P1173 [keV] 23P0515 [keV] 21D2->21P1 355 [keV] 2D -> 2P 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] 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] 2D -> 1P
E1 Radiative Partial Widths 1F -> 1D 3F4 -> 3D3351 [keV] 3F3-> 3D3 43 [keV] 3D2375 [keV] 3F2->3D3 2 [keV] 3D2 66 [keV] 3D1524 [keV] 1F3->1D2 409 [keV]
X(3872) Belle Collab. S.-K.Choi et al, hep-ex/0309032; K.Abe et al, hep-ex/0308029. 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 < 2.3MeV 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 +- 0.7MeV
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
cc from the “standard” potential modelS.Godfrey and N.Isgur, PRD32, 189 (1985). 2- - 3- -(3D2 is a typo) 2- + 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 = 1D2cc, 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 (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/yroandJ/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/yroand J/yw [E.S.Swanson, hep-ph/0311299]. The bleedin’ obvious decay mode J/y po poshould 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).
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*, DsDs … 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/yroandJ/ywdecay modes? X = cc options predict large E1 b.f.s to g+ P-wave cc. Charmonium: Summary