Update on Charmonium Theory T.Barnes ORNL/U.Tenn. HADRON09 11/30/09 criteria: some recent theory likely of relevance to cc expt. please me about papers I have missed

Update on Charmonium Theory Topics: 1)double charmonium production 2)LQccD (vy. short: a coming attraction) 3)loops; unquenching the quark model 4)cc production cross sections at PANDA 5)charm molecules 6)charmiscelleny T.Barnes ORNL/U.Tenn. HADRON09 11/30/09

Double charmonium production The traditional approach, s-channel e  e  annihilation, but … now we can make C=(+) charmonia! J/  C=(+) cc J PC = J P 

c’c’ 00 cc X(3943) An interesting new charmonium production mechanism! Allows access to C=(+) cc states in e  e  w/o using . No   or    !? X(3943) [ref] = Belle, hep-ex/ , 8 Jul n.b. Eichten: X(3943) may be the 3 1 S 0 cc  c ’’.

Updated expt refs: K. Abe et al. [Belle Collaboration], Phys. Rev. D 70, (2004) [arXiv:hep-ex/ ]; Phys. Rev. Lett. 98, (2007) [arXiv:hep-ex/ ]; B. Aubert et al. [BABAR Collaboration], Phys. Rev. D72, (2005) [arXiv:hep-ex/ ]. (Belle)

cc spectrum, potential models (dashed: nonrel L, Godfrey-Isgur R) vs data Possible C=(+) cc states from e  e  2P or not 2P?

If we can understand the mechanism, we can use the observed cross sections to identify new cc states observed in this process. What is the mechanism? (i.e. How is the 2 nd cc pair produced?) J/  C=(+) cc Best known previous study: OGE pair production, NRQCD E.Braaten and J.Lee, PRD67, (2003), err. D72, (2005), arXiv:hep-ph/ : Large   amplitude from OGE.  ( J    J    J    approx  A rather complicated calculation. Confirmation?

2nd study, OGE pair production model K.-Y. Liu, Z.-G. He and K.-T. Chao, PRD77, (2008), arXiv: [hep-ph] Search for excited charmonium states in e + e - annihilation at sqrt(s) = 10.6 GeV. 1. Confirms Braaten and Lee OGE results analytically (w/err); more complete treatment of QED diagrams. 2. Also finds that the scale of the predicted NRQM cross sections is an order of magnitude smaller than experiment. (n.b. follow-on study finds that NLO corrections considerably reduce the expt/thy discrepancy; Zhang, Ma and Chao, PRD78, (2008), ). 3. Many interesting new dbl cc channels predicted…

Liu, He and Chao predictions for relative intensities of various e  e   (cc)(cc) channels relative to J/  +  c. e.g.s: 1) h c ; 2) the unknown narrow J P =2  states. h c +  c h c +  c1 J/  +  c2  c1 +  2 J/  c reference  2 (1P)

New study: OGE and 3P0 (factorizable) pair production models F.E.Close and C.Downum, PRD79, (2009), arXiv: [hep-ph] Charmonium production in e + e - -> psi + X(cc) and e + e - -> Y(4260) -> psi pi pi. 1. Confirms Braaten and Lee OGE results analytically. 2. Also considers 3 P 0 type pair prod amplitudes (actually factorizable decay models generally*); in this case J    doesn’t dominate. Consistent with light meson expt? e.g. e  e    f 2 dominant. *see also T.J.Burns, F.E.Close and C.E.Thomas, PRD77, (2008), arXiv: [hep-ph]. Next step needed: attach realistic wfns and predict absolute cross sections. (Improved scale?)

LQccD (A brief mention: see plenary talk by C.Thomas.) Of course we have had LQCD predictions for the meson and baryon spectrum for some time (which are mainly for low-lying states and basically confirm experiment and quark models. In spectroscopy these LQCD predictions have been most useful for exotica such as glueballs (preferred approach) and hybrids (mass scale otherwise uncertain). An e.g. of previous LQCD calculations for cc:

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. No cc radiative or strong decay predictions from LGT yet.

What’s new in LQccD? Primarily work by members of the JLAB LQCD group, J.Dudek, R.Edwards, D.Richards, C.Thomas: 1. Detailed spectrum calculations for cc and cc-hybrids. 2. Use of operator LCs to determine the compositions of states (L; hybrid). JD,RE,DR,CT, “Highly excited and exotic meson spectrum from dynamical lattice QCD.” arXiv: v2 [hep-ph]. 3. Radiative matrix elements, including multipole decompositions. JD,RE,CT, “Exotic and excited-state radiative transitions in charmonium from lattice QCD.” PRD79, (2009), arXiv: [hep-ph]. [3.] Also for hybrids! Q: Is the 12 GeV upgrade justified by large hybrid photocouplings? A: Yes. (Nice to know…) The results are often reminiscent of quark model predictions, but should be much less subject to systematic uncertainties. However still using the quenched approximation for cc. Just how important are hadron loops (quenched approximation) in cc?

J.J.Dudek, R.G.Edwards and C.E.Thomas, Exotic and excited-state radiative transitions in charmonium from lattice QCD PRD79, (2009), arXiv: [hep-ph]. Paper quotes  c     exotic  J  keV. A typical “robust” cc radiative width. JLAB is justified. non-exotic   hybrid rad. trans.

Loops The loop conundrum: 1.Quark models that ignore loops find a nice fit to the “classic” cc spectrum (States in 1S, 1P, 2S; 1D, 3S, 4S). RMS error typically ca. 20 MeV. However… 2. If you actually calculate a loop diagram (2 nd order virtual strong decay process) with 1 intermediate, e.g. J/   DD*  J/  you find a large negative mass shift, typically ca MeV. How can these be consistent? Don’t the assorted “random” ca MeV loop effects destroy the nice pattern of quark model cc J,L,S multiplets and multiplet splittings? One example of an explicit cc loop calculation: (cc)  (cn)(nc)  (cc) (’)

 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 Potential model cc spectrum w/o loops.

L’oops [ 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 = 69.% VERY LARGE mass shift and large non-cc component! Can the QM really accommodate such large mass shifts??? Other “cc” states? explicit e.g. from TB and ESS ref.

L’oops [ cc - M 1 M 2 - cc  3 P 0 decay model, std. params. and SHO wfns. Loops produce a roughly state-independent overall negative mass shift ! explicit e.g. from TB and ESS ref.

General Loop Theorems! Derived assuming 3 P 0 strong vertices and initially degenerate J,L,S multiplets, ident. space wfns, calculate the effects of intermediate J,L,S, open-flavor multiplets. e.g. J/  -> (DD,DD*,D*D*) -> J/ , with M(D) = M(D*). Thus loops give (1 st approx) a large overall multiplet shift. This is how the loop effects can be individually large and yet be “hidden” in the detailed spectrum. Corrections (violations) of the 3 laws arise from preexisting multiplet splittings (of external and virtual states) (hence phase space differences) and decay model effects. How large are these corrections? t.b.d. The 3 laws of loopotics: 1.No splittings (within an N,L,S (qq generally) multiplet, e.g. 1P) 2. No mixing (qq J,L,S J,L’,S’ through loops = 0.) (e.g. 3 S 1 3 D 1.) 3. Equal strong op. flav. widths (in an (N,L,S) mult. e.g. 2 3 D J ; Im(loop) ->  o.f. )

Refs: The 3 laws: T.Barnes and E.S.Swanson, PRC77, (2008) [arXiv: [hep-ph]]; extended by F.E.Close and C.E.Thomas, PRC79, (2009) [arXiv: [hep-ph]]; loop degeneracies (law 1) noted earlier by N.Tornquist, Ann. Phys. 179, 1 (1979). also recent cc loop studies by Kalashnikova and by van Beveren and Rupp.

Hopes for loops: 1. The degeneracy theorem is badly violated if the « initial » qq state is close to the continuum threshold of one specific intermediate state (i.e. the « initially degenerate JLS multiplets » assumption is badly broken). In such cases one might see clear discrepancies between the expected and observed positions of states, such as the « cs » D* s0 (2317) and D s1 (2460). 2. The large loop mass shifts also imply large « continuum components » in hadron state vectors. It would be nice to identify a « smoking gun » signature for these continuum components, e.g. in radiative transitions. 3. Loops = « unquenching the quark model ». These effects should also be present in LQCD cc when unquenched.

Where it all started. BABAR: D * s0 (2317) + in D s +  0 D.Aubert et al. (BABAR Collab.), PRL90, (2003). M = 2317 MeV (2 D s channels),  < 9 MeV (expt. resolution) (Theorists expected L=1 cs states, e.g. J P =0 +, but with a LARGE width and at a much higher mass.) … “Who ordered that !?”  I.I.Rabi, about the  - Since confirmed by CLEO, Belle and FOCUS.

And another! CLEO: D s1 (2460) + in D s * +  0 Since confirmed by BABAR and Belle. M = 2457 MeV. D.Besson et al. (CLEO Collab.), PRD68, (2003). M = 2463 MeV,  < 7 MeV (expt. resolution) A J P =1 + partner of the 0 + D * s0 (2317) + cs ?

(Godfrey and Isgur potential model.) Prev. (narrow) expt. states in gray. DK threshold What caused large downwards mass shifts? Mixing with 2 meson continuum states? (Believed true.)

PANDA PANDA (GSI) plans to produce cc sector J PC -exotics (presumably hybrids) using the associated process pp  light meson(s) + “cc”-exotic Crucial question for this n*10 8 Euro facility: just how large or small are these near-threshold cross sections? Very little relevant data exists. There is some data on the hopefully similar associated charmonium production reaction pp  J/    from E760/835 at Fermilab. I will show all the world’s data and all the theoretical attempts to predict these cross sections.

Evidently ca. 0.1–0.2 [nb] near threshold for J/ . Other states, other energies??? Nada. all the world’s data on  pp  m J/  our calc. All the world’s (published) data on pp  cc + meson (exclusive) processes near threshold.  ( pp    J/  ) E760

Approximate low to moderate-E cross sections for pp   + meson(s) = ? Four theor. references to date: 1. M.K.Gaillard. L.Maiani and R.Petronzio, PLB110, 489 (1982). PCAC W  pp  J   ) 2. A.Lundborg, T.Barnes and U.Wiedner, PRD73, (2006). Crossing estimates for  ( pp  m  ) from  (   p p m) (  ‘ ; m = several) 3. T.Barnes and X.Li, hep-ph/ , PRD75, (2007). PCAC-like model W   ( pp   ),  c      ‘ 4. T.Barnes, X.Li and W.Roberts, arXiv: , PRD77, (2008). [3] model, e  e   J/   pp (for BES), pp  J   W and . Dirac and Pauli strong ppJ  FFs. Polarization.

1 st approx, just assume a constant amplitude: p we know … we want … J/   p p A p A 

our calc. Not bad for a first rough “phase space” estimate. Improved cross section estimates require a model of the reaction dynamics (next). const. amp. model all the world’s published data (E760)

Assume simple pointlike hadron vertices; g   5 for the NN  vertex,   = g  (  5, -i  , -i, -i    5 ) for    c  J/  and  ’      Use the 2 tree-level Feynman diagrams to evaluate d  /dt and . g5g5  PCAC-like model of pp   +  0 : T.Barnes and X.Li, hep-ph/ ; PRD75, (2007). +

To predict numerical pp   +  0 production cross sections in this model, we know g pp  ~ 13.5 but not the { g pp  }. Fortunately we can get these new coupling constants from the known   pp partial widths: Our formulas for  (   pp ): Resulting numerical values for the { g pp  } coupling constants: (Uses PDG total widths and pp BFs.) g5g5  !! !

 ( pp  J/   ), PCAC-like model versus “phase space” model:  (J/    pp) input “phase space”  (J/   pp) and g NN  =13.5 input “real dynamics”

And the big question… Are any other cc states more easily produced than J/  ? ANS: Yes, by 1-2 orders of magnitude!

Final result for cross sections. (All on 1 plot.) Have also added two E835 points (open) from a PhD thesis. gg quant. nos. all data is for J/ 

Molecules (cc… sector) A quick reminder, then an amusing new suggestion.

        J   D   D*   MeV Accidental agreement? X = cc (2  or 2  or …), or a DD* molecule?  MeV Alas the known  = 3 D 1 cc. If the X(3872) is 1D cc, an L-excited multiplet is split much more than expected assuming scalar confinement. n.b.  D   D*   MeV MeV Belle Collab. K.Abe et al, hep-ex/ ; S.-K.Choi et al, hep-ex/ , PRL91 (2003) X(3872) from KEK Charm in nuclear physics???

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/ , PLB578, 119 (2004). C.Y.Wong, hep-ph/ E.Braaten and M.Kusunoki, PRD69, (2004). E.S.Swanson, PLB588, 189 (2004); PLB589, 197 (2004). 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

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

The usual scenario: The X(3872) D 0 D* 0 is S-wave 1 ++ bound mainly by attractive t-channel one pion exchange. Note this involves P -wave pion emission AND absorption (hence doubly suppressed), D*  D  …so… DD*  D(D   (D   D   D*D        x (L P    Channels with attractive one-pion exchange and S-wave pion emission might form more deeply bound (Qq)(qQ) molecules. What states and quantum numbers are likely? This has been studied recently by Close and Downum, who suggest deep charm molecules with E B ca. 100 MeV below the threshold of 4430 MeV.  J  P  yes. One obvious case is D*D 1. (Implicit cn nc flavor.) New suggestion: Deep Charm Molecules? PPP

Close and Downum result for E B of D*D 1 states from t-channel pion exchange. (I=0 states; J P         , degenerate in the one pion exchange V S.) Conjecture: The Y(4260) and Y(4360) are 1S and 2S D*D 1 molecule states! (Decay to (cc)  is by internal constituent interchange.) Test: Search for large DD  (constituent) decay modes. E B (MeV) axes are two (D*D 1 )-wfn. var. params.    

Ref: F.E.Close and C.Downum, On the possibility of Deeply Bound Hadronic Molecules from single Pion Exchange. PRL102, (2009). arXiv: [hep-ph] and others cited therein.

Charmiscelleny 1. Z(3930) (if 2 3 P 2 cc) decay modes  (4415) (if 4 3 S 1 cc) decay modes

 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

Z(3930) a 2 3 P 2 charmonium state?

e  e  collisions (2): “Two-photon collisions”. Forms positive C-parity charmonia. (esp. J PC = 0 , 0  , 2   ). Quite small cross sections,  = O(  4 ), so requires high intensity e  e  beams.

Z(3931)  Z(3931)  DD [ref] = Belle, hep-ex/ , 8 Jul 2005.

Z(3931) = 2 3 P 2 cc ? (suggested by Belle) Expt for Z(3931):  > Z(3931) -> DD = 20 +/- 8 +/- 3 MeV   * B DD = / / keV thy expt  tot Theory for 2 3 P 2 (3931):  = 47 MeV DD*/DD = 0.35   * B DD = 0.47 keV (   from T.Barnes, IX th Intl. Conf. on  Collisions, La Jolla, 1992.) Z(3931) = 2 3 P 2 cc predicts a large DD* mode, BF ca. 25%.   ?   in Z(3931)

 (4415) decay modes Until recently the highest mass cc candidate. Potential models find the mass consistent with 4 3 S 1 cc, although other assignments are speculated. Strong decays a smoking gun? The predicted dominant decay modes for a 4 3 S 1 cc are very unusual (next 2 slides). The PDG has for decades stated that it decays dominantly to “hadrons”. Now we finally have an exclusive hadronic mode, from BELLE. Predicted decay modes and widths:

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]; now BELLE 77(20) (stat.) [MeV] A warning about hybrid = S+P modes: Theor. decay BFs of a   S  cc

 partial widths [MeV] ( 3 P 0 decay model): DD = 0.4 DD* = 2.3 D*D* = 15.8 [multiamp.] D s D s = 1.3 D s D s * = 2.6 D s *D s * = 0.7 [m] New S+P mode calculations: DD 1 = 30.6 [m]  MAIN MODE!!! DD 1 ’ = 1.0 [m] DD 2 * = 23.1 D * D 0 * = 0.0   DD 1 amplitudes: ( 3 P 0 decay model): 3 S 1 =  0   !!! (HQET) 3 D 1 =  A cc state, but the main mode (thy.) is S+P, not S+S ! n.b. PDG says the 4415 decays mainly to “hadrons”. Expt BFs needed! (As for all states above open-charm thresholds.) T.Barnes, S.Godfrey and E.S.Swanson, PRD72, (2005).

BELLE Collab, G.Pakhlova et al., PRL100, (2008), arXiv: v2 [hep-ex]. Evidence for  D 2 *(2460)D, BF probably ca %. (Using D 2 *(2460) -> D  / D*  ~ 2.) Observation of  D 2 *(2460)D in D 0 D    

 (4415) decay modes … A large DD 2 * mode has now been reported as predicted, expt. BF probably ca %. A check of the 3 P 0 model prediction of a leading D-wave DD 1 mode would be very interesting!

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.) An industrial application of the  and finally…

Summary; where we have been: 1)dbl.ch.: mech. known, OGE; search for narrow 2  states? 2)LQccD: cc spec, comp and  coupls. (vy. short: coming attr.) 3)loops: exch. full o.f. multiplets -> 3 (broken) theorems 4)pp -> cc prod. PANDA. estimates exist. needs more theorists. 5)c. mols: Y(4260,4360) = deeply bound, S-wave  ex? test by DD  search. 6)cmisc.: confirm modes in expt.? Z(3940) -> DD* and  (4415) -> [D 1 D] D (main mode) suggested. T.Barnes ORNL/U.Tenn. HADRON09 11/30/09

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