Charmonium Production at PANDA 1. Estimates of associated charmonium cross sections at PANDA  ( pp c + m )  ( pp   cc + m ) 2. Comments re vector charmonium strong decays:  and  Ted Barnes Physics Div. ORNL and Dept. of Physics, U.Tenn. Hirschegg 18 Jan. 2007

1. Estimates of associated charmonium cross sections at PANDA  ( pp c + m )  ( pp   cc + m )

PANDA at GSI… pp  cc + m, cc-H + m (ProtonAntiprotonaNnihilationexperimentatDArmstadt) p beam energies… KE p = 0.8 – 14.5 [GeV]: “m” = light meson(s); needed to allow cc-H = J PC exotics  c  Invariant mass formed in pp collision in s-channel. J/  X(3872)  cc-H 4.3 [GeV] Production cross sections??

What PANDA needs to know: What are the approximate low-E cross sections for pp   + meson(s) ? (  is a generic charmonium or charmonium hybrid state.) Recoil against meson(s) allows access to J PC -exotic . The actual processes are obscure at the q+g level, so “microscopic” models will be problematic. We just need simple “semiquantitative” estimates. Three 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/ PCAC-like model W   ( pp   ),  c      ‘

1. M.K.Gaillard. L.Maiani and R.Petronzio, PLB110, 489 (1982). PCAC W  pp  J   ) Soft Pion Emission in pp Resonance Formation Motivated by CERN experimental proposals. Assumes low-E PCAC dynamics with the pp system in a definite J,S,L channel. (Hence not immediately useful for total cross section estimates for PANDA.) Quite numerical, gives W(  ) at a specific E  (cm) = 230 MeV as the only example. Implicit analytic results completed in Ref.2.

Crossing estimates: We have experimental results for several decays of the type    ppm. These have the same amplitude as the desired  ( pp   m  ). Given a sufficiently good understanding of the decay Dalitz plot, we can usefully extrapolate from the decay to the production cross section. n.b. Also completes the derivation of some implicit results for cross sections in the Gaillard et al. PCAC paper. 0 th -order estimate: assume a constant amplitude, then  ( pp  m  ) is simply proportional to    ppm ). Specific example,  pp  J   ): 2. A.Lundborg, T.Barnes and U.Wiedner, hep-ph/ , PRD73, (2006). “summer in Uppsala, c/o U.Wiedner” Charmonium Production in pp Annihilation: Estimating cross sections from decay widths.

These processes are actually not widely separated kinematically: p we know … we want … J/   p p A p A 

 dt

For a 0 th -order (constant A ) cross section estimate we can just swap 2-body and 3-body phase space to relate a generic cc  ( pp     ) to  (   pp    Result: where A D is the area of the decay Dalitz plot: Next, an example of the numerical cross sections predicted by this simple estimate, compared to the only (published) data on this type of reaction…  ( pp  J/    ) from  ( J/    pp    compared to the E760 data points:

our calc. Not bad for a first rough “phase space” estimate. Improved cross section estimates will require a detailed model of the reaction dynamics. …but is that really ALL the data? all the world’s data on  pp  m J/  const. amp. model all the world’s published data (E760)

 pp  J/  +  0 from continuum M. Andreotti et al., PRD 72, (2005) Expt… Only 2 E760 points published. This is E835 (D.Bettoni, yesterday) Physical cross sec is ca. 100x this.

Other channels may be larger, however the constant Amp approx is very suspect. N* resonances?

Calculates the differential and total cross sections for pp   using the same PCAC type model assumed earlier by Gaillard et al., but for incident pp plane waves, and several choices for  c      ‘  The a priori unknown  pp couplings are taken from the (now known) pp widths. 3. T.Barnes and Xiaoguang Li, hep-ph/ “summer in Darmstadt, c/o K.Peters” Associated Charmonium Production in Low Energy pp Annihilation

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 model of pp   +  0 : (T.Barnes and X.Li, hep-ph/ ) +

m  = 0 limit, fairly simple analytic results… unpolarized differential cross sections: (in the analytic formulas) simplifications M = m  m = m p x = (t - m 2 ) / m 2 y = (u - m 2 ) / m 2 f = -(x+y) = (s - m  2 - M 2 ) / m 2 also, in both d<  /dt and < , r i = m i / m

(analytic formulas) m  = 0 limit, fairly simply analytic results… unpolarized total cross sections:

However we would really prefer to give results for physical masses and thresholds. So, we have also derived the more complicated m .ne. 0 formulas analytically. e.g. of the pp   J/   0 unpolarized total cross section: Values of the {   } coupling constants?

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: Freshly derived formulas for  (   pp ): Resulting numerical values for the { g pp  } coupling constants: (Uses PDG2004 total widths and pp BFs.) g5g5  !! !

Now we can calculate NUMERICAL total and differential cross sections for pp  any of these cc states +  . We can also answer the big question, Are any cc states more produced more easily in pp than J/  ? (i.e. with significantly larger cross sections)

 ( pp  J/    ), PCAC-like model versus “phase space” model:

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 from a PhD thesis (open pts.).

An interesting observation: The differential cross sections have nontrivial angular dependence. e.g. This is the c.m. frame (and m  =0) angular distribution for pp   c   at E cm = 3.5 GeV: Note the (state-dependent) node, at t = u. Clearly this and the results for other quantum numbers may have implications for PANDA detector design. beam axis

Predicted c.m. frame angular distribution for pp   c   normalized to the forward intensity, for E cm = 3.2 to 5.0 GeV by 0.2. spiderman plot

Predicted c.m. frame angular distribution for pp  J    normalized to the forward intensity, for E cm = 3.4 to 5.0 GeV.

Next steps using this model: 1. Publish this paper! (hep-ph/ ) 2. Polarization predictions are nontrivial. 3. Extend to other baryon resonances, e.g. N*(1535). This is important e.g. for  production.

2. Comments re vector charmonium strong decays:  and  Most results shown here are abstracted from T.Barnes, S.Godfrey and E.S.Swanson, PRD72, (2005).

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  (4260),  (4320) J PC = 1 - -

What are the total widths of cc states above 3.73 GeV? (These are dominated by open-flavor decays.) 23.0(2.7) [MeV] 80(10) [MeV] 62(20) [MeV] 103(8) [MeV] PDG2006 values X(3872)

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).)

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 80(10) [MeV]

Recall J.Napolitano (CLEO) yesterday:

After restoring this “p 3 phase space factor”, the expt BFs were: 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 * 103(8) [MeV] Strong Widths: 3 P 0 Decay Model

Recall J.Napolitano (CLEO) yesterday:

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 * 62(20) [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.) 

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