Strong Decays (open flavor) 1) Big Questions 2) Strong Decays: Historical introduction 3) Status and prospects in quarkonia + exotica 4) Future: Unquenching the quark model Ted Barnes Physics Div. ORNL Dept. of Physics, U.Tenn. … q and g decay models. Mesons almost exclusively.

1.) The Big Questions: We know L QCD … but what does it predict? What types of hadrons exist (as resonances)? Isn’t that just color singlets? No! (Beware multiquark systems.) What are their masses and quantum numbers? State composition? What are their social properties? GOALS: 1. Establish and understand the spectrum. Requires: observe and analyze decays (esp. strong; maybe radiative) 2. Interactions

Historical Introduction (1969) The model used for strong decays now in current use ( 3 P 0 ) is due to L.Micu, Nucl. Phys. B10, (1969) “Decay Rates of Meson Resonances in a Quark Model” In this pre-QCD model, Micu suggested that the simplest possible quantum numbers be assumed for the J PC of the qq pair produced in two-body open-flavor decays of quark model mesons and baryons, J PC = 0 ++ = vacuum quantum numbers. With no knowledge of the qq pair production mechanism this is simplest assumption. 2.) Strong Decays (open flavor):

(No QM spatial wfns: reduced m.e.s and expt. input.)

Historical Introduction ( ) The ORSAY group (LeYaouanc et al.) attached explicit wfns to the 3 P 0 model, which put it in essentially the form used today. LeYaouanc, L.Oliver, O.Péne and J.C.Raynal, PRD 8, 2223 (1973) [formalism; NN  NN  and  ; b 1 -> , a 1 ->  D/S ratios] PRD 9, 1415 (1974) [ca. 40 u,d,s baryon decays] PRD 11, 1272 (1975) [ca nonstrange B*->Bm decay amps. (  )]. PLB 71, 397 (1977) [  (4040) as a 3S cc radial excitation.] 

Open-charm strong decays: 3 P 0 decay model (Orsay group, 1970s) 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. (Feynman rules from E.S.Ackleh et al., PRD54, 6811 (1996).)

= 0.4 GeV = typical light qq meson SHO length scale Ref.: Ackleh et al. (1996). 3 P 0 model widths. “The world we know” selects  GeV fairly strongly! SHO wfn. inverse length scale

The famous D/S test which led to the acceptance of the 3 P 0 decay model. Ref.: Ackleh et al (1996). b 1  and a 1 

M. Nozar et al. (E852), Phys. Lett. B541, 35 (2002). A study of the reaction  - p   - p at 18 GeV/c: The D and S decay amplitudes for b 1 (1235)  . A novel application of decays to scattering expt. Often one assumes subamplitudes in a decay are relatively real. (e.g. S and D in b 1     ). This is not correct. Distinct decay channels with different quantum numbers have different FSI phases. (We assume the FSIs are diagonal.) The relative S-D phase of the   system in b 1  has been extracted by E852. Is this our first measurement of VPs scat? MANY more similar opportunities exist. b1b1   S,D b 1  revisited! FSI

M. Nozar et al. (E852), Phys. Lett. B541, 35 (2002). A study of the reaction  - p -->  - p at 18 GeV/c: The D and S decay amplitudes for b 1 (1235) --> . The usual amplitude ratio measurement. |D/S| = 0.269(9) The novel  scattering phase measurement.   D  S | M b 1 = o +/- 2.4 o b1b1  

Regarding    b  ... a very important test of decay models. However it will occur, even if the intrinsic decay amplitude = 0! 1) Hybrid   b   is predicted to be large. Is |    qq    H basis state mixing VERY small??? 2) Off-diagonal FSI, e.g.   f  b  . HH b1b1    b1b1   Allowed by general quantum number considerations. Forbidden in 3 P 0, f.t., OGE, instanton, … decay models. S qq =0  S qq =0 + S qq =0. Experimentally tightly constrained: BF < 0.19% 97.7% c.l. D.V.Amelin et al. (VES), Phys. At. Nucl. 62, 445 (1999). Consistent with E852 (A.Popov, HADRON01; M.Lu et al., Bull. Am. Phys. Soc. 47, 33 (2002).) S qq =0 = 0 3P03P0

Two principal lines of research on strong decays: 1. Try to understand what’s going on in terms of QCD. (less common) 2. Just assume a decay model and calculate every partial width and amplitude of interest.

Mechanism ( s ) of strong decays L.Micu ( 3 P 0 ) E.Eichten et al. (linear vector conft.) P.Geiger and E.S.Swanson ( 3 P 0 and flux tube vs. 3 S 1 ) PRD50, 6855 (1994). E.S.Ackleh, T.Barnes and E.S.Swanson (OGE and linear scalar conft.) PRD54, 6811 (1996). Numerical evaluation of OGE and linear scalar conft. meson decay amplitudes (8 test decays). P.Page, E.S.Swanson and A.Szczepaniak, PRD59, (1999). Models of H decays. S.Capstick and P.R.Page, hep-ph/ , PLB566, 108 (2003). Discuss various models;      b  . R.Ricken, M.Koll, D.Merten, B.C.Metsch, hep-ph/ , EPJA18, 667 (2003). nn decays, B-S eqn with ‘t Hooft instanton decay model. (a few refs i know of; not systematic)

Mechanism(s) of strong decays (cont.) E.vanBeveren and G.Rupp, ca. 35 refs. hep-ph/ ,… Mainly 3 P 0 model, iterated coupling to qq. “Unquenching the QM.” (many other refs exist, this is just a sample) LGT: Very few refs. Work is needed here! J.Sexton, A.Vaccarino and D.Weingarten, NPB (PS) 42, 279 (1995); PRL75, 4563 (1995). Glueball decay violations of flavor symm. C.McNeile, C.Michael and P.Pennanen (UKQCD), PRD65, (2002). Heavy-Q Hybrids may decay significantly into closed-flavor QQ mesons. C.McNeile and C.Michael (UKQCD), PLB556, 177 (2003). One e.g. of a LGT study of a light meson decay.

Cornell decay model E.Eichten, K.Gottfried, T.Kinoshita, K.D.Lane, T.-M.Yan, PRD 17, 3090 (1978) qq pair production from a timelike linear vector confining potential br  

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!

Typically, pair production from the confining interaction dominates the OGE terms. An exception: OGE dominates in f 0 ->  E.S.Ackleh, T.Barnes and E.S.Swanson PRD54, 6811 (1996). “Cornell type” decay model albeit with standard OGE + linear scalar confinement interactions.

LGT studies of strong decays LGT has been applied to strong decays of glueballs, conventional light mesons, and heavy-quark hybrids. The results are all “to be confirmed”, and some LGT practitioners are skeptical. Nonetheless here are some references and results:

Strong M Ps dependence of the G-PsPs coupling reported in an early LGT study. This complicates nn-ss-G mixing angle determinations from f 0 (1500) decays that assume flavor-blind G decay amplitudes. J.Sexton, A.Vaccarino and D.Weingarten, NPB (PS) 42, 279 (1995); PRL75, 4563 (1995). G decays

C.McNeile, C.Michael and P.Pennanen (UKQCD), PRD65, (2002). Very interesting prediction for experimenters: Heavy-quark hybrids have large closed-flavor decay modes! H ->  + S. (estm. 61(14) MeV for b) Leads to very nice experimental signatures, however it’s a surprise, recall  ’  J  is very small, 10s of keV. Needs confirmation. Relevant to Y(4260) and Y(4354)??? H decays

Extracting    decay couplings on the lattice C.McNeile and C.Michael (UKQCD), PLB556, 177 (2003).  transition  3-pt. function Q decays

Two principal lines of research on strong decays: 1. Try to understand what’s going on in terms of QCD. (less common) 2. Just assume a decay model and calculate every partial width and amplitude of interest. some e.g.s from s (HallD) and c mesons (CLEO,SLAC,BES,GSI)

The  (2230) = ssbar brou ha ha  Originally reported by Mark III at SLAC; R.M.Baltrusaitis et al., PRL56, 107 (1986). Not seen by DM2 with better statistics. Claimed by BES but status unclear. Perhaps a tensor glueball?  (1440) f J (1710) S.Godfrey, R.Kokoski and N.Isgur “spoiler” paper, PLB141, 439 (1984): Widths of L=3 ss states 3 F 2 and 3 F 4 are accidentally small, assuming domination by KK, KK*, K*K*. GKI concluded the state was consistent with F 2 ss. J/   KK ?

 It’s prudent to calculate all decay modes  3 F 2 ss(2230)  K 1 (1273) K. oops. A higher “S+P” mode neglected by Godfrey, Kokoski and Isgur is actually dominant in the 3 P 0 model ! We cannot assume the simple S+S modes are dominant. Subsequent more detailed study of L=3 ss decays. H.G.Blundell and S.Godfrey, PRD53, 3700 (1996).

Extensive decay tables ( ca present ) S.Godfrey and N.Isgur, PRD32, 189 (1985). T.Barnes, F.E.Close, P.R.Page and E.S.Swanson, PRD55, 4157 (1997). [u,d mesons] T.Barnes, N.Black and P.R.Page, PRD68, (2003) “BBP paper” [s mesons] [43 states, all 525 modes, all 891 amps.] qq meson decays: qqq baryon decays: S.Capstick and N.Isgur, PRD34, 2809 (1986). S.Capstick and W.Roberts, PRD49, 4570 (1994); nucl-th/ , Prog.Part.Nucl.Phys. 45 (2000) S241-S331 (91 pp. review article). [BPs, BV modes of u,d baryons] Mainly light (u,d,s) hadrons in f.-t. or 3 P 0 models. A few references:

3 F 2 ss -> K 1 (1273) K confirms Blundell and Godfrey. 3 F 3 ss -> K 2 * K dominant 3 F 4 ss (max J) typically ARE dominated by the lowest few allowed modes. (Cent. barrier.) The five narrowest unknown (?) ssbar states below 2.2 GeV: state  tot Favored modes [expt?]      D   2 (1850)  129 MeV KK* [WA102  2 (1617)-  2 (1842): nn ss mixing?] 2)     F   f  (2200) 156 MeV K*K*, KK, KK* [LASS 2209; Serp. E ] 3)   3 1 S 0  s (1950) 175 MeV K*K*, KK* 4)   2 1 P 1 h 1 (1850) 193 MeV KK*, K*K*, [ss filter] 5)   1 3 D 2  2 (1850) 214 MeV KK*,  Some results for strange meson decays (BBP paper):

The strangest state in the strange spectrum. K*(1414). (< K(1460) ???) (Mass and decays.) Mass: recall nn 1  states  (1465),  (1419). Decays: Expt.  K  B.F.  6% (LASS) Mixing with “      ” K-hybrid state?

|K 1 (1273)> = cos(  ) |1 1 P 1 > + sin(  ) |1 3 P 1 > |K 1 (1402)> = -sin(  ) |1 1 P 1 > + cos(  ) |1 3 P 1 > HQET  The same problem as why we have narrow and broad D 1 states. Crucial for understanding the 1 + D s1 system. Mixing mechanism unknown. L*S? Coupling through decay channels? Lipkin’s rules for B decays with ’: PLB415, 186 (1997); 433, 117 (1998); 494, 248 (2000).

The amusing  ’ excited kaon decay modes. (2/3 are “Lipkin’s rules.”)

New Millennium: Charm and Charmonium decays

Where it all started: The BABAR state 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! The CLEO state D * s1 (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 ?

         J   D   D*   MeV Accidental agreement? X = cc (   or   or …), or a molecular (multiquark) state?  MeV Alas the known  = 3 D 1 cc. If the X(3872) is 1 D 2 or 3 D 2 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

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:         Y(4260), 4354?

S*S OGE Z(3931), X(3943), Y(3943) C = (+) Fitted and predicted cc spectrum Coulomb (OGE) + linear scalar conft. potential model black = expt, red = theory. states fitted Y(4260), 4350 J PC = 1 - -

A series of papers by the Cornell group addressed open-charm strong decays of charmonium states above 3.73 GeV. They assumed an unusual non- 3 P 0 decay model, qq pair production from linear, timelike vector confinement. The absolute decay rates predicted (they actually extracted R) were reasonably close to experiment. The  (4040) decay branching fractions in particular were explained as due to nodes in the 3 3 S 1 radial wavefunction. E.Eichten, K.Gottfried, T.Kinoshita, K.D.Lane, T.-M.Yan, PRL 36, 500 (1976) PRD 17, 3090 (1978) PRD 21, 203 (1980). Charmonium decays ( )

R and the 4 higher 1 -- states (plot from online Y.-F. Wang BES talk, 16 Sept 2002)

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 Parameters are  = 0.4 (from light meson decays), meson masses and wfns. X(3872) 1D DD 3 D [MeV] 3 D D 1 43 [MeV] 1 D (2.7) [MeV]

E1 Radiative Partial Widths 1D -> 1P 3 D 3  3 P [keV] 3 D 2  3 P 2 64 [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)

Strong Widths: 3 P 0 Decay Model X(3872) 3 3 S 1 74 [MeV] 3 1 S 0 80 [MeV] 3S DD DD* D*D* D s 52(10) [MeV]

After restoring this “p 3 phase space factor”, the BFs are: D 0 D 0 : D 0 D* 0 : D* 0 D* 0  One success of strong decay models An historical SLAC puzzle explained: the weakness of  DD e.g. D*D* molecule?

famous nodal suppression of a 3 3 S 1  (4040) cc  DD std. cc and D meson SHO wfn. length scale   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  D*D* amplitudes ( 3 P 0 decay model): 1 P 1 =  P 1 =  =    1 P 1 5 F 1 = 0

2D 2 3 D [MeV] 2 3 D 2 92 [MeV] 2 3 D 1 74 [MeV] 2 1 D [MeV] DD DD* D*D* D s D s D s * 78(20) [MeV] Strong Widths: 3 P 0 Decay Model

std. cc SHO wfn. length scale  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  D*D* amplitudes: ( 3 P 0 decay model): 1 P 1 =  P 1 =     1 P 1 5 F 1 =  

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] X(3872) 

 DD 1 amplitudes: ( 3 P 0 decay model): 3 S 1 =  0   !!! (HQET) 3 D 1 =  BGS results ( 3 P 0 decay model):  partial widths [MeV] 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  Theor R from the Cornell model. Eichten et al, PRD21, 203 (1980): 4040 DD DD* D*D*

An “industrial application” of the   (4415). 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.) 

X(3872) X(3943) Y(3943) Z(3931) Y(4260) Y(4354) cc? cc hybrids!? charm molecules? Testing these possibilities through strong decays. Our recent ref: 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-charm strong modes and partial widths, all 231 open-charm strong decay amplitudes, all 153 E1 and (some) M1 EM widths. today… …just 1 quick example.

Z(3931) [ref] = S.Uehara et al. (Belle), hep-ex/ , 8 Jul  DD [ J PC .ne ]

Z(3931) = 2 3 P 2 cc ? (suggested by Belle) Expt for Z(3931):  DD       MeV     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)

Is GSI suitable for cc and cc-H? Energies… KE p = 0.8 – 14.5 [GeV] Invariant mass formed in pp collision in s-channel. J/  X(3872)   c  cc-H 4.4 [GeV] Production cross sections?

Example: what is the cross section for pp  J/    ? we know… J/   p p A p p A we extrapolate to… These processes are actually not widely separated kinematically: J/   A.Lundborg, T.Barnes and U.Wiedner; Charmonium production in p anti-p annihilation: Estimating cross sections from decay widths. hep-ph/ , Phys. Rev. D73, (2006).

 dt

Zeroth-order (constant A ) estimate; ca. 0.3 nb at 3.5 GeV: our calc. all the world’s data on  pp  m J/  our calc. Improved estimates will require a more detailed study of the reaction dynamics (work planned for this summer at GSI).

Hybrids Gluonic Excitations Of Mesons: Why They Are Missing And Where To Find Them N.Isgur, R.Kokoski and J.Paton, PRL 54, 869 (1985). Considers J PC -exotic hybrids (0 +-, 1 -+, 2 +- ) in the lightest f.-t. multiplet. S+P decay modes dominant in f.-t. decay model.    b   a nice case for experiment.  ’ etc should be small. The Production and Decay of Hybrid Mesons by Flux-Tube Breaking F.E.Close and P.R.Page, NPB443, 233 (1995). “IKP-2” Confirms prev. results and also considers nonexotics (0 -+, 1 +-, 2 -+,1 ++,1 - - ) in the lightest f.-t. multiplet. Some special cases of nonexotics predicted to be rather narrow if M H = 1.6 GeV; extra  and   notable. The f.-t. hybrid   decays strongly to b   in the f.-t. decay model. ( = hadrons with excited glue.)

Hybrid Meson Decays: flux-tube model N.Isgur, R.Kokoski and J.Paton, PRL54, 869 (1985). Gluonic Excitations of Mesons: Why They Are Missing and Where to Find Them.   b  f   not’   S+P 72 hybrids in lowest flavor-nonet multiplet. A rich spectrum! Where are they??? Ans: 1.9 GeV. Many broad. Obscure S+P decay modes. 3 P 0 decay model qq vertex !

 hybrid    hybrid; b   mode    hybrid I    exotics narrow nonexotic hybrids … and much narrower if M H  1750 MeV ! Close and Page: some notable nonexotic hybrids in the flux tube model I 

The famous claimed and disputed E852 broad, weak, exotic P-wave    in    near 1.4 GeV. Crystal Barrel sees a similar effect in pp   near 1.4 GeV… It grows curiouser and curiouser. S.U.Chung et al. (E852) PRD60, (1999).   p    p a 2 (1320) A.Abele et al. (CBar), PLB446, 349 (1999).    S+S, not S+P !

E.I.Ivanov et al. (E852) PRL86, 3977 (2001).      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. S+S, not S+P !      p   ’   p

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

Unquenching the quark model Reconciling The OZI Rule With Strong Pair Creation P.Geiger, PRD44, 799 (1991). How the OZI Rule Evades Large Loop Corrections P.Geiger and N.Isgur, PRL67, 1066 (1991). When Can Hadronic Loops Scuttle The OZI Rule? P.Geiger, PRD47, 5050 (1993). Strange Hadronic Loops of the Proton: A Quark Model Calculation P.Geiger and N.Isgur, PRD55, 299 (1997). Baryon-Meson Loop Effects on the Spectrum of Nonstrange Baryons D.Morel and S.Capstick, nucl-th/ (unpublished?) Complex Meson Spectroscopy (HADRON2005) E.vanBeveren, F.Kleefeld and G.Rupp, hep-ph/ , AIP Conf. Proc. 814,143 (2006). (most successful to date?) n.b. the importance of meson loops in spectroscopy has been stressed by N.Tornqvist for many years.

“DK molecules”? DK  csbar mixing. A conjecture. T.Barnes, F.E.Close, H.J.Lipkin, hep-ph/ , PRD68, (2003). (reality = mixed, not either/or) Reminiscent of Weinstein and Isgur’s KKbar molecules, bound by level repulsion of the KKbar continuum against higher mass qqbar 0+ scalars at ca. 1.3 GeV. Test by comparing quenched vs unquenched LGT csbar masses? (also van Beveren and Rupp)

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 in progress for cc.

|state> = c 0 |cc> +  i c i |open charm mesons> Table I shows P cc = |c 0 | 2. E.Eichten et al., PRL 36, 500 (1976). c cncn ncnc Closer to |cc > in E.Eicten et al, PRD21, 223 (1980); P  = 0.88, P ’ = However they warn that their intermediate states are truncated at D,D*.

Summary and conclusions FIN