Recent developments in cc, cn and cs spectroscopy: X(3872), D sJ *(2317) + and D s1 *(2457) +. 1) Basic physics. How well qq worked (charmonium e.g.) 2) The X(3872), D sJ * + (2317) and D s1 * + (2457). 3) What we are reconsidering. (This is a story in progress…) Ted Barnes Physics Div. ORNL Dept. of Phys. and Astro., U.Tenn. HQL2004

Small qq separation Large qq separation basic physics of QCD

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

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.

 s = b = [GeV 2 ] m c = [GeV]  = [GeV] Fitted and predicted cc spectrum Coulomb (OGE) + linear scalar conft. potential model blue = expt, red = theory. 3 D 3 (3810) 3 D 2 (3803) 3 D 1 (3787) 1 D 2 (3802)

cc from LGT   exotic cc-H at 4.4 GeV oops…   cc has been withdrawn.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.

        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) G.Bauer, QWG presentation, 20 Sept n.b. most recent CDF II: M = pm 0.7 pm 0.4 MeV CDF II Collab. D.Acosta et al, hep-ex/ , PRL to appear 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???

cc from the “standard” potential model S.Godfrey and N.Isgur, PRD32, 189 (1985). 2  3   ( 3 D 2 is a typo) 2  The obvious guess, if cc, is 2  or 2 . No open-flavor strong decays: narrow states. A more conventional possibility: X(3872) = cc?

Charmonium Options for the X(3872) T.Barnes and S.Godfrey, hep-ph/ , PRD69 (2004) (n.b. Eichten, Lane and Quigg have similar results.) 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.

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 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!

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.

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 X(3872)

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. X(3872) (New strong and EM decay results from Barnes, Godfrey and Swanson, in prep.)

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 X(3872)

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 X(3872) 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 =  =    1 P 1 5 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 =     1 P 1 5 F 1 =  0.141

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] X(3872)

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% radiative 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.) Concl: We cannot yet exclude 5 of the 8 1D and 2P cc assignments. However, we do see how to proceed.

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, hep-ph/ , PRD69, (2004). 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.) n.b.2 Could the signal simply be a cusp due to new DD* channels opening? (A.Bacher query.) No one has considered this.

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: comparable 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, CDF and DZERO. It is seen 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 the X is a deuteronlike D o D* o -molecule. Naïvely, this suggests a narrow total X width of ca. 50 keV and 3:2 bfs 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 “isospin violating” b.f.s to J   and J. 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).

Where it all started. BABAR: D * sJ (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 * sJ (2463) + 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 possibly 0 + D * sJ (2317) + cs ?

(Godfrey and Isgur potential model.) Prev. (narrow) expt. states in gray. DK threshold

Experimental D states (PDG 2002) vs Godfrey-Isgur potential model. Is the same discrepancy evident in the cn sector?

The new broad D states. The 1+ states are not especially low wrt QM. However the status of the 0+ is unclear. (2 expts. differ by 100 MeV.)

Theorists’ responses to the new D sJ * states Approx. 80 theoretical papers have been published since the discovery. There are two general schools of thought: 1) They are cs quark model mesons, albeit at a much lower mass than expected by the usual NRQPMs. [Fermilab] 2) They are “multiquark” states. (“DK molecules”) [UT,Oxon,Weiz.] 3) They are somewhere between 1) and 2). [reality]

M.A.Nowak, M.Rho and I.Zahed, PRD48, 4370 (1993). W.A.Bardeen and C.T.Hill, PRD49, 409 (1994) BEH, PRD68, (2003).

2. Multiquark states (DK molecules) [UT,Oxon,Weiz.] T.Barnes, F.E.Close and H.J.Lipkin, hep-ph/ , PRD68, (2003). 3. reality Reminiscent of Weinstein and Isgur’s “KK molecules”. (loop effects now being evaluated)

L’oops

Future: “Unquenching the quark model” Virtual meson decay loop effects, qq M1 M2 mixing. D sJ * states (mixed cs DK …, how large is the mixing?) Are the states close to |cs> or |DK>, or are both basis states important? A perennial question: accuracy of the valence approximation. Also LGT-relevant (they are usually quenched too).

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 rather large total widths, MeV. (= broad to unobservably broad). Charmed meson decays (God91) How large are decay loop mixing effects?

J P = 1 + (2457 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 *+ (2317,2457)> = |cs> + |(cn)(ns)> states. Evaluation of mixing in progress. Initial estimates for cc …

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 = 65.% VERY LARGE mass shift and large non-cc component! Can the QM really accommodate such large mass shifts??? Other “cc” states? 1/2 : 2 : 7/2 D s D s : D s D s * : D s *D s *

L’oops [ cc - M 1 M 2 - cc  3 P 0 decay model, std. params. and SHO wfns. Init. Sum  M P cc J/  MeV 0.65  c MeV 0.71  MeV 0.43  1  MeV 0.46  0  MeV 0.53 h c  MeV 0.46 Aha? The large mass shifts are all similar; the relative shifts are “moderate”. Continuum components are large; transitions (e.g. E1 radiative) will have to be recalculated, including transitions within the continuum. Apparently we CAN expect D sJ -sized (100 MeV) relative mass shifts due to decay loops in extreme cases. cs system to be considered. Beware quenched LGT!

Summary and conclusions: 1) Three new narrow mesons containing at least cc and cs have been reported: X(3872) D * sJ (2317) + D * sJ (2457) + 2) Theorists expected similar (?) states but at rather different masses. The cs states were expected to have very broad strong decay widths. The interpretation of the new states (qq / two-meson molecules / lin.comb.) is being discussed. Decay loops determine mixing. Radiative transitions should allow definitive tests of qq assignments. There are E1 rate predictions for D * sJ  D s +  and  D s * +  assuming cs, analogous to the X(3872) rates we discussed. (e.g. S.Godfrey, hep-ph/ , PLB568, 254 (2003).) D * sJ (2457) +  D s +  reported recently by Belle; strongly favors J=1, as expected. 3) Useful future measurements: A. Precise E1 cc (CLEO;  ’,  (3770) and  ) and D * sJ radiative rates; B. Strong decay model checks (4040, 4159  DD, DD*; D*D* PWA) (BES,CLEO). n.b  (  ) (at ca MeV) a D * sJ source? (expect few % BFs to D * s0 (2317) D * s and D * s1 (2457) D s )