Recent developments in charm meson spectroscopy: Chaos, confusion and craziness. Basic hadronics Making charmonium Spectrum of charmonium Exciting new developments (2003-present): D * s0, D s1, X(3872),…(X,Y,Z), Y(4260), Z(4430). Theory abstracted from T.Barnes, S.Godfrey and E.S.Swanson, PRD72, (2005). For BABAR, BELLE, BES, CLEO, GSI, … : All 40 cc states expected to 4.42 GeV, all 139 of their open flavor strong modes and partial widths, all 231 o.f. strong decay amplitudes, all 153 E1 and (some) M1 EM widths. Phew. Ted Barnes BNL Seminar 18 Mar. 2008

1. Basic hadronics.

QCD flux tube (LGT, G.Bali et al.; hep-ph/010032) 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) Color singlets and QCD exotica “confinement happens”.

Physically allowed hadron states (color singlets) (naïve, valence) 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 X(3872) = DD*! (q 3 ) n, (qq)(qq), (qq)(q 3 ),… nuclei / molecules (q 2 q 2 ),(q 4 q),… multiquark clusters dangerous e.g.  _ Basis state mixing may be very important in some sectors.

qq mesons states The quark model treats conventional mesons as qq bound states. Since each quark has spin-1/2, the total spin is S qq tot = 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

Parity P qq = (-1) (L+1) C-parity C qq = (-1) (L+S) qq 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” :       … Plausible J PC -exotic candidates = hybrids, glueballs (high mass), maybe multiquarks (fall-apart decays). The resulting qq NL states N 2S+1 L J have J PC =

2. Making charmonium.

How to make charmonium? Hit things together. e  e  collisions (as in Beijing, Cornell, SLAC) “clean” theoretically but small cross sections and restricted quantum numbers hadron-hadron collisions e.g. pp Fermilab (past), GSI/Darmstadt (start 2013 AD) messy theoretically, large backgrounds, less restricted quantum numbers …some Feynman diagrams:

e  e  collisions (1): The traditional approach: s-channel annihilation. Restricted to J PC = 1 .  = O(  2 ). (May then use hadronic or radiative transitions to reach other states.) ee ee   hadrons

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.

e  e  collisions (3): Surprisingly effective for making charmonia. The source of several recent discoveries in this field. “B factories” b

pp collisions : Used at Fermilab (E760 and E835). Planned for GSI/Darmstadt (PANDA facility).

Pre-dawn, a lava field near Carrizozo, New Mexico. 3. The spectrum of charmonium.

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.

Minimal quark potential model physics: OGE + linear scalar confinement; Schrödinger eqn (often relativized) for wfns. Spin-dep. forces, O(v 2 /c 2 ), treated perturbatively. Here… Contact S*S from OGE; Implies S=0 and S=1 c.o.g. degenerate for L > 0. (Not true for vector confinement.)

 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

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 Two narrow states are expected, with J PC = 2  and 2 . The 1D multiplet is theoretically close to degenerate, near the  D   (3770).

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.

Best recent LQCD ref for ccbar and cc-H spectroscopy: “Charmonium excited state spectrum in lattice QCD.” J.J.Dudek, R.G.Edwards, N.Mathur and D.G.Richards, arXiv: [hep-lat], Phys.Rev.D77:034501,2008. Results for cc still rather difficult to distinguish from quark model. Ambiguity in the 1  exotic noted. (However other exotics again appear around 4.5 GeV.) (J  spectrum) M [MeV]

End of Introduction to cc

4. The new “XYZ” states: 2P cc? 3S cc? Molecules? cc hybrids? Nonresonant enhancements? Experimental errors? How to test these possibilities? Recommended reading: “The New Heavy Mesons: A Status Report” E.S.Swanson, Phys. Reports 429, (2006). “What’s new with the XYZ mesons?” S.L.Olsen, arXiv: v3 [hep-ex]13 Feb “The Exotic XYZ Charmonium-like Mesons.” S.Godfrey and S.L.Olsen, arXiv: [hep-ph] Jan submitted to Ann. Rev. Nucl. Part. Phys.

“Selections from…” (Godfrey and Olsen review, list of new states):

cc spectrum, potential models (dashed: nonrel L, Godfrey-Isgur R) vs data Possible new cc states at these masses! Z;X,Y;Y 2P or not 2P? Reminder: Three as yet unknown 1D states. Predicted to have  < 1 MeV! BGS, hep-ph/ , PRD72, (2005).

D * s0 (2317) and D s1 (2457) cs mesons or DK molecules? (or both) … but first, the first of the new discoveries: new, unexpected, very long-lived mesons in the cs sector!

e  e  collisions (3): Surprisingly effective for making charmonia. The source of several recent discoveries in this field. “B factories”

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.)

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?

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 !

L’oops [ cc - M 1 M 2 - cc  3 P 0 decay model, std. params. and SHO wfns. Loop mass shifts of states within L,S cc multiplets are analytically identical if the initial masses are equal, if you sum over multiplets of loop spin states! (A theorem in:) “Hadron Loops: General Theorems and Application to Charmonium” T.Barnes and E.S.Swanson, arXiv: [hep-ph] (Nov.2007)

X(3872) a charmed meson molecule?

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 Two narrow states are expected, with J PC = 2  and 2 . The 1D multiplet is theoretically close to degenerate, near the  D   (3770).

        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

X(3872) confirmation (from Fermilab) n.b. most recent CDF II: M = pm 0.7 pm 0.4 MeV CDF II Collab. D.Acosta et al, hep-ex/ , PRL. OK, it’s real… n.b. molecule.ne.multiquark X(3872) also confirmed by D0 Collab. at Fermilab. Perhaps also seen by BaBar

The trouble with multiquarks: “Fall-Apart Decay” (actually not a decay at all: no H I ) Multiquark models found that most channels showed short distance repulsion: E(cluster) > M 1 + M 2. Thus no bound states. Only 1+2 repulsive scattering. nuclei and hypernuclei weak int-R attraction allows “molecules” E(cluster) < M 1 + M 2, bag model: u 2 d 2 s 2 H-dibaryon, M H - M  =  80 MeV. n.b.   hypernuclei exist, so this H was wrong. Exceptions: V NN (R)  2m N RR “V  (R)”  2m  Q 2 q 2 (Q = b, c?) 2) 1) 3) Heavy-light

X(3872 ) Belle Collab. K.Abe et al, hep-ex/ ; S.-K.Choi et al, hep-ex/ , PRL91 (2003)         J   D   D*   MeV Accidental agreement? X = cc 2  or 2  or …, or a molecular (DD*) 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 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 n.b.2 Could the signal simply be a cusp due to new DD* channels opening?

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.

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  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.) The crucial test of Z(3931) = 2 3 P 2 cc : DD* mode   ?   in Z(3931)

X(3940) and double charmonium production

e  e  collisions (5): Double charmonium production. The traditional approach, s-channel annihilation, but can now make C=(+) charmonia! J PC = J P  J/  C=(+) cc

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 ’’.

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

Y(4260) a charmonium hybrid?

     p    ’  p E.I.Ivanov et al. (E852) PRL86, 3977 (2001).  1 (1600)   exotic reported in   ’ ’ is a nice channel because nn couplings are weak for once (e.g. the a 2 (1320) noted here). The reported exotic P-wave is dominant! The (only) strong J PC -exotic H candidate signal.

e  e  collisions (6): Initial state radiation (ISR) The traditional approach, s-channel annihilation, but can use higher energy beams. Still restricted to J PC = 1 . J/ 

Y(4260) e  e   Y(4260) ISR, Y     J /  log scale Not seen in R. Hmmm?! [ref] = BaBar, PRL95, (2005). closed-flavor decay mode !?

cc spectrum, potential models (dashed: nonrel L, Godfrey-Isgur R) vs data Possible 1  state Y(4260). Note no plausible cc assignment exists. A 1  charmonium hybrid??

cc and cc – H from LGT   exotic cc-H at 4.4 GeV Small L=2 hfs. A LGT cc-sector spectrum e.g.: X.Liao and T.Manke, hep-lat/ (quenched – no decay loops) Broadly consistent with the cc potential model. No LGT cc radiative or strong decay predictions yet. n.b. The flux-tube model of hybrids has a lightest multiplet with 8 J PC s; 3 exotics and 5 nonexotics, roughly degenerate: (0,1,2) , 1 ,  1    Y(4260)?

How to test a cc-hybrid assignment, esp. for Y(4260) : 1. Confirm existence 2. Establish the multiplet, including J PC exotics! 3. Unusual decays (if not exotic)

Y(4360), Y(4660) Y(4260) Prev.      state in e  e       J New     states in e  e       ’ X.L.Wang et al, PRL99, (2007). BaBar; Belle, CLEO Belle shown

Z  (4430) charged charmonium??? The latest craziness…

BELLE Collab v1 (14 Aug. 2007) Z(4430)  charge requires ccud quark content. Not cc! n.b. At D*(2010) D 1 (2420) threshold.

We discussed some of the exciting new discoveries: D * s0, D s1 light, long-lived cs + … mesons X(3872) DD* molecule Z(3940) new 2P 2 ++ cc in  X(3930) new 2P or 3S C=(+) cc (?) state Y(4260), Y(4350), Y(4660) charmonium hybrids? Z(4430) “charged charmonium”?? D * D 1 molecule? …and new production techniques: ISR and double cc production. This is an exciting time for charm spectroscopy, with many topics for both experimenters and theorists to study! The End… Thank you! Conclusions

END / EXTRAS

3.b. Strong decays

Strong decays of charmonia There are two main types of cc strong decays. Neither is well understood. I. cc annihilation. (cc)  gluons (?)  light hadrons II. Open flavor decays. (Dominant if allowed.) (cc)  (cq) + (qc) Theorists have simple ideas about these strong decays and rough models for them but not much more. Some simple ideas like pQCD fail dramatically. This is a wide open field for the smart young theorist.

Some brief comments about cc-annihilation strong decays. These are secondary strong decay processes that are only dominant for states below open-charm threshold. (M < 2M D = 3.73 GeV.) Estimating total annihilation widths by counting gluon vertices is a standard rough guide:  tot (MeV):  c  25.5 (3.4)   10.4 (0.7)    2.06 (0.12)  c ’  14. (7.) J  (0.0021)  ’  (0.013)

Strong decays (open flavor)

Total widths of cc resonances…

What are the total widths of cc states above 3.73 GeV? (These are dominated by open-flavor decays.) < 2.3 MeV 80(10) MeV 62(20) MeV 103(8) MeV 2007 PDG values X(3872) 26.3(1.9) MeV

Experimental R summary (2003 PDG) Very interesting open theoretical 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 open-flavor 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!

An alternative strong decay model 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.

S.Godfrey and R.Kokoski, PRD43, 1679 (1991). Decays of S- and P-wave D D s B and B s flavor mesons. 3 P 0 “flux tube” decay model. The L=1 0 + and 1 + cs “D s ” mesons are predicted to have large total widths, MeV. (= broad to unobservably broad). Charmed meson decays How large are decay loop mass shifts and mixing effects? 1. What cs mesons are predicted to have exceptionally large strong decay amps?

J P = 1 + (2460 channel) J P = 0 + (2317 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 | D sJ *+ (2317,2460)> = |cs> + |(cn)(ns)> states. Evaluation of loops: Initial results for cc …

cc-hybrids, theory

Characteristics of cc-hybrids. (folklore, mainly abstracted from models, some LGT) Hybrid Multiplets (flux-tube model): The lightest hybrid multiplet should be a roughly degenerate set containing 3 exotic and 5 nonexotic J PC ; 0 , 1 , 2 , 0 , 1 , 2 , 1 , 1  Mass ca. 4.0 – 4.5 GeV, with LGT preferring the higher range. The 1  should be visible in e  e  but with a suppressed width. (Hybrid models for different reasons predict  cc  (r=0) = 0, suppressing  ee.) Unusual Decays (flux-tube model and f-t decay model): Dominant open-charm decay modes are of S+P type, not S+S. (e.g. DD 1 not DD or DD*). n.b.  1 (1600)   ’ argues against this model. LGT(UKQCD): Closed-charm modes like cc-H  cc + light mesons are large! (Shown for bb-H; (bb) is preferentially P-wave, and “light mesons” = scalar .)

QQ-hybrid closed-flavor decays predicted by LGT: We are hoping that closed-flavor decays are a signature for charmonium hybrids (and not charmonia). If so, nature has been kind. This is a nice experimental signature. Searches for other decay modes of the Y(4260) are in progress…