1. Y -> ppm Two reasons why are these decays are interesting:
Ted Barnes
Physics Div. ORNL
Phys. Dept. U.Tenn.
DOE/NP
北 京
23 Oct. 2010
Y -> ppm
Two reasons why are these decays are interesting:
Relating BES <-> PANDA
NNm couplings and NN forces from Y -> ppm?
Predictions for Y -> ppm
Experiment (some)
Future (models discussed are incomplete)

2. Interest in Y -> ppm
N* spectroscopy; Y -> N* N -> NNm (will not discuss here)
PANDA assist: use BES Y -> ppm data to estimate the cross section
for the PANDA associated Y production process
pp -> Y m
3-hadron vertices: extract NNm couplings from Y -> ppm to
1) Test meson exchange models of NN forces
(NNm couplings = ?. Normally are just fitted to NN scat. data).
Is NN scat. REALLY due to meson exchange?
2) Test predictions of standard baryon strong decay models such
as 3P0 (predicts NNm as well as N* -> Nm). Any good?

3. Relating BES <-> PANDA

4. PANDA pp -> light meson(s) + “cc”-exotic
PANDA (GSI) plans to produce cc sector JPC-exotics (presumably hybrids)
using the associated process
pp -> light meson(s) + “cc”-exotic
Crucial question for PANDA: just how large or small are these near-threshold
associated production cross sections?
Very little relevant data exists. There is some data on the hopefully similar
associated charmonium production reaction pp -> J/y p0 from E760/835
at Fermilab.
I will show all the world’s data and all the theoretical attempts to predict these
cross sections.

5. Why associated production? ( pp -> cc + m, (cc)H + m )
Problem:
You can’t make JPC-exotics in s-channel pp annihilation (as in
E760/835 at Fermilab), since pp only accesses conventional meson
(qq) quantum numbers. To make J PC- exotic hybrids you have
to make something else to recoil against (associated production): p
qq quant. nos. only p
All JPC quant. nos.,
including cc-hybrids
with exotic JPC
something else
e.g. typically p 0
New Problem: Just how big are these cross sections?
Let’s look at all the world’s data.

6. s ( pp -> p0 J/y ) E760 All the world’s (published) data on
our calc.
All the world’s (published) data on
pp -> cc + meson
(exclusive) processes near threshold.
s ( pp -> p0 J/y ) E760
Evidently ca. 0.1–0.2 [nb] near threshold for J/y . Other states, other energies??? Nada.

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

8. The idea: PANDA predictions from BES data
we know …
we want …
J/y p0 A

9. Extrapolation from J/y -> pp p0 to pp -> J/y p0.
ò dt
(DP drawn with funny axes, sorry!)

10. Approximate low to moderate-E cross sections for pp -> Y + meson(s) = ?
Four theor. references to date:
1. M.K.Gaillard. L.Maiani and R.Petronzio, PLB110, 489 (1982).
PCAC W(q) (pp -> J/y + p 0 )
2. A.Lundborg, T.Barnes and U.Wiedner, PRD73, (2006).
Crossing estimates for s( pp -> Y m ) from G( Y -> ppm)
(Y = y, y‘ ; m = several)
3. T.Barnes and X.Li, hep-ph/ , PRD75, (2007).
Hadron pole model W(q), s ( pp -> Y + p 0 ), Y = hc, y, c0, c1, y ‘
4. T.Barnes, X.Li and W.Roberts, arXiv: , PRD77, (2008).
[3] model, e+e- -> J/y -> pp (for BES), pp -> J/y + p 0
W and s. Dirac and Pauli strong ppJ/y FFs. Polarization.

11. … and one new paper, specifically about Y -> ppm :
5. T.Barnes, X.Li and W.Roberts, arXiv: , PRD81, (2010).
Hadron pole model of Y -> pp m
Y = hc, y, c0, c1, y’ ; m = p0 , f0, w
topics:
Theor. Dalitz plot distributions, G( Y -> ppm) decay widths.
Estimation of NNm couplings from Y -> ppm Dalitz plots.

12. 1st approx, just assume a constant amplitude:
A.Lundborg, T.Barnes and U.Wiedner,
PRD73, (2006).
Const. amp. model of pp -> Y + p0:
1st approx, just assume a constant amplitude: p
we know …
we want …
J/y p0 A

13. Not bad for a first rough “phase space” estimate.
const. amp. model
all the world’s published data (E760)
our calc.
Not bad for a first rough “phase space” estimate.
Improved cross section estimates require a model of the reaction dynamics (next).
Better yet, extrapolate Dalitz plot DATA for Y -> ppm to get s (pp -> Y m) !
(Some high stats. DP data now exists from BES and CLEO. This needs a volunteer.)

14. Hadron pole model of pp -> Y + p0:
T.Barnes and X.Li,
PRD75, (2007).
Assume simple pointlike hadron vertices;
gpg5 for the NNp vertex, GY = gY (g5, -i gm, i, -i gm g5) for
Y = (hc, J/y and y’, c0, c1)
Use the 2 tree-level Feynman diagrams to evaluate ds/dt and s.
gpg5 GY +

15. To predict numerical pp -> Y + p0 production cross sections in this model,
we know gppp ~ but not the { gppY }. Fortunately we can get these new
coupling constants from the known
Y -> pp partial widths:
gpg5 GY
Our formulas for G( Y -> pp ):
Resulting numerical values for the { gppY } coupling constants:
(Uses PDG total widths and pp BFs.) !! !

16. s( pp -> J/yp0 ), hadron pole model versus “phase space” model:
G(J/y -> pp)
and gNNp=13.5
input
“real dynamics”
G(J/y -> p0pp) input
“phase space”

17. The BIG question for PANDA…
Are any other cc states more easily produced in pp -> Ym than J/y?
ANS: Yes, by 1-2 orders of magnitude!

18. Final result for PANDA cross sections, hadron pole model
Final result for PANDA cross sections, hadron pole model. (All on 1 plot.)
Have also added two E835 points (open) from a PhD thesis. gg
quant.
nos.
all data is for J/y

19. Extracting NNm couplings from Y -> ppm

20. Interest in Y -> ppm 3-hadron vertices: extract NNm couplings
Test meson exchange models of NN forces
(NNm couplings are normally fitted to NN scat. data)
Is meson exchange the real NN scat. mechanism?

21. Traditional NN force model; t-channel meson exchange.
Form factors and
gNNm coupling consts, normally
treated as free params. A C D B
e.g. for NN scat:
p, r, w, “s”, …
Easy to calculate (Feynman diagrams) but the vertices are obscure.
MANY free NNm couplings, usually just fitted to NN scattering data.
Is “vector exchange really the right physics at small r_NN? [r _NN~ 1/m_V ~ 0.2 [fm]]
Can we test this with BES data ?! [Extract these NNm couplings independently?]

22. The main ingredients are the p, s , and w.
A selection of fitted NNm couplings in the NN meson-exchange-model literature.
The main ingredients are the p, s , and w.
Note especially the NNw,r Pauli couplings kw,r.
NNw,r Pauli couplings kw,r
(fm. QCDSRs) also discussed by
Shi-Lin Zhu,
PRC59, 435 and 3455 (1999).
C.Downum, T.Barnes, J.R.Stone and E.S.Swanson,
PLB638, 455 (2006).

23. We can predict the Dalitz plot distributions in Y -> ppm with this hadronic model.
Hopefully this will let us extract ppm meson-baryon couplings “directly” from data.
J/y p0 p A

24. The idea:
1) The Y -> pp measured partial width gives g_Ypp p
g_ppp0 p0
g_Ypp Y p
2) This measured partial width gives |g_ppp0 x g_Ypp |2, if this decay model is close to reality. (TBD from the expt DP in all cases.) The ratio G_ppp0 / G_pp then tells us the “ppm” coupling (here g_ppp0 ) Does this work?

25. Trial estimate of g_NNp from expt (J/y –> pp and ppp0) BFs + thy:
(Does this work at all?)
Reasonable! Can we extract other ppm strong couplings from Y -> ppm in this way?

26. An e.g. Dalitz plot calculation: hc -> pp p0
All theor. results for DPs from Barnes, Li and Roberts, PRD81, (2010).
So what do the Dalitz plot distributions actually look like?

27. hc -> pp p0 Dalitz plot.
Predicted way cool
hc -> pp p0 Dalitz plot.
A t=u node in
pp -> hcp0
maps into a diagonal
DP node in
hc -> pp p0.
Mpp2
[GeV2 ]
Mpp2 [GeV2 ]

28. Hadron pole model J/y -> pp p0 Dalitz plot event density.

29. Note the local diagonal minimum in the DP
Predicted
J/y -> pp p0
Dalitz plot.
Note the local diagonal minimum in the DP
(at t = u in pp -> J/yp0 ).
Mpp2
[GeV2 ]
Mpp2 [GeV2 ]

30. Predicted J/y -> pp p0 Dalitz plot. (event density contours).
Expt? …

31. Predicted J/y -> pp p0 Dalitz plot. (event density contours).
BES J/y -> pp p0
M.Ablikim et al. (BES),
PRD80, (2009).
N* resonance bands evident,
no clear relation to the model. (PAW warning)
However … next look at projection in M_(ppi), no free parameters:

32. Predicted (pole model, no free params) and
observed (BES) Mpp- projected event density.
= A background due to the nucleon pole, with N* resonances superimposed ?
J/y -> pp p0
BES data c/o Shu-Min Li
and Xiaoyan Shen

33. Note the enhancement in the low-pp-mass region.
Not included in this model.
Predicted J/y -> pp p0 Dalitz plot.
(event density contours).
CLEO y’ -> pp p0
J.P.Alexander et al.,
arXiv: v2 (10/12/2010)
Sides actually attributed to N*(1440);
N pole terms not included in fit.

34. cc0, c1 -> p p p0
P.U.E.Onyisi et al. (CLEO), PRD82, (R) (2010)
This “new” decay mechanism dominates these chi-cJ decays !
(BFs 3x and 10x hadron pole model: a dominant low-pp-mass enhancement.)
Y -> mm’, m’ -> pp ? FSI? This mechanism is needed in the decay model.
Beware of the Blob!

35. What is the new Y -> ppm decay mechanism? Perhaps …
Figure from: A.Sibirtsev, J.Haidenbauer, S.Krewald,U.-G.Meissner, A.W.Thomas
PRD71, (2005).
We have assumed (N*=N only) ->
Dominant (?) process for
c 0,1c -> ppp =>
(or pp FSI?)

36. (could be used to estimate NNw couplings)
Final example,
J/y -> ppw :
(could be used to estimate NNw couplings)
J/y -> ppw Dalitz plot density, with w Pauli terms (note the kw dependence):
(Reqd traces, each having ca. 200 terms.)

37. Predicted
J/y -> ppw
Dalitz plot.
(With no w Pauli terms.)

38. kw = -3/2 Predicted J/y -> pp w Dalitz plot. With w Pauli term,
(quark model prediction).
How does this compare
with data?
Low-pp mass region?
What does a fit give for
g_NNw and k_NNw?
To be determined.

39. Expt. BES-II Dalitz plot for J/y -> ppw.
M.Ablikim et al., Eur.Phys.J.C53, 15 (2008).
(c/o Beijiang Liu and Xiaoyan Shen)
Not immediately
clear how well this
compares to the
theor. DPs just shown.
This is candidate events;
acceptance?
At least
“No significant enhancement
near the pp mass threshold
is observed…”
Fig. 3. The Dalitz plot for J/ψ →ωpp candidate events

40. Summary: 1. BES <-> PANDA:
For studies of JPC-exotics in pp collisions, PANDA plans to exploit
associated exotic-Y production, pp -> Y m.
Even the basic “benchmark” reaction
pp -> J/y p0
is poorly constrained experimentally. BES (& CLEO) data on Y -> ppm
can be used to estimate these cross sections. (Esp. given
new fits to the expt. Dalitz plot event densities, e.g. of y’ -> ppp0 ).
2. Meson-baryon (NNm) couplings from Y -> ppm:
NN forces as meson exchange? This can be tested through an indep.
check of their fitted NNm couplings, using BES data on Y -> ppm.
(ppm Dalitz plot event densities -> NNm couplings.)
An improved Y -> ppm decay model is likely needed to do this.
(A low-mass pp enhancement is often important. “Beware of the Blob.”)