1. Charmonium decays to pp and ppm final states
Ted Barnes
Physics Div. ORNL and
Dept. of Physics, U.Tenn.
IHEP Beijing 14 June 2007
Charmonium decays to pp and ppm final states
Why are these interesting? The reasons include…
I. They allow estimates of associated charmonium
production cross sections for PANDA at GSI/Darmstadt
s ( pp -> cc + m )
II. They allow novel estimates of light ppm coupling constants, e.g. gNNw.
(discussion at end…)
(Test NN nuclear force models! Do we really understand the nuclear force?)

2. I. Estimates of associated charmonium cross sections for PANDA
s ( pp -> cc + m ) = ?

3. PANDA at GSI… pp -> cc + m, cc-H + m (ProtonAntiprotonaNnihilationexperimentatDArmstadt) p beam energies… KEp = 0.8 – 14.5 [GeV]:
“m” = light meson(s); needed
to allow cc-H = JPC exotics
hc(2980)
Invariant mass formed in pp collision in s-channel.
J/Y(3097)
X(3872)
Y(4415)
cc-H 4.3 [GeV]
Production
cross sections??
Planned start date
ca AD.

4. What PANDA needs to know:
What are the approximate low-E cross sections for pp -> Y + meson(s) ?
(Y is a generic charmonium or charmonium hybrid state.)
Recoil against meson(s) allows access to JPC-exotic Y.
The actual processes are obscure at the q+g level, so “microscopic” models
will be problematic. We just need simple “semiquantitative” estimates.
Three 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 -> p p m)
(Y = y, y ’ ; m = several)
3. T.Barnes and X.Li, hep-ph/ , PRD75, (2007).
PCAC-like model W(q), s ( pp -> Y + p 0 ), Y = hc, y, c0, c1, y ‘

5. Soft Pion Emission in pp Resonance Formation
1. M.K.Gaillard, L.Maiani and R.Petronzio, PLB110, 489 (1982).
PCAC W(q) (pp -> J/y + p 0 )
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,L,S channel. (Hence not immediately useful
for total cross section estimates for PANDA.) Quite numerical, gives W(q) at
a specific Epcm = 230 MeV as the only example.
Implicit analytic results completed in Ref.2.

6. 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.
Crossing estimates:
We have experimental results for several decays of the type Y -> ppm.
These have the same amplitude as the desired s( pp -> Y 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.
0th-order estimate: assume a constant amplitude, then
s( pp -> Y m ) is simply proportional to G(Y -> ppm ).
Specific example, s( pp -> J/y + p 0 ):

7. we know … we want … p0 p J/y A
These processes are actually not widely separated kinematically:

8. ò dt

9. For a rough (0th-order, constant A) cross section estimate we can just swap
2-body and 3-body phase space to relate a generic cc
s( pp -> Y p0 ) to G( Y -> pp p0 )
Result:
where AD 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…
s( pp -> J/y p0 ) from G( J/y -> pp p0 ),
compared to the E760 data points:

10. 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 will require a detailed model of the reaction dynamics.
…but is that really ALL the data?
all the world’s data on
s(pp -> mJ/y)

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

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

13. Associated Charmonium Production in Low Energy pp Annihilation
3. T.Barnes and Xiaoguang Li,
hep-ph/ ; PRD75, (2007).
“Summer in Darmstadt, c/o K.Peters”
Associated Charmonium Production in
Low Energy pp Annihilation
Calculates the differential and total cross sections for pp -> Y + p 0
using the same PCAC type model assumed earlier by Gaillard et al.,
but for incident pp plane waves, and several choices for Y: hc, y, c0, c1, y ‘.
The a priori unknown Ypp couplings are taken from the (now known)
G( Y -> pp ) widths…
- these gppY “gY” couplings are very interesting numbers!

14. PCAC-like model of pp -> Y + p0:
(T.Barnes and X.Li, hep-ph/ ,
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. mp = 0 limit, fairly simple analytic results…
unpolarized differential cross sections:
simplifications
M = mY
m = mp
r i = m i / m
a m = g2NNm / 4p
x = (t - m2) / m2
y = (u - m2) / m2
f = -(x+y)
= (s - mp2 - M 2) / m2
also, in both d<s>/dt and <s>,
(in the analytic formulas)

16. mp = 0 limit, fairly simply analytic results…
unpolarized total cross sections:
(analytic formulas)

17. However we would really prefer to give results for physical
masses and thresholds. So, we have also derived the more
complicated mp .ne. 0 formulas analytically.
e.g. of the pp -> J/y p0 unpolarized total cross section:
Values of the {aY} coupling constants?

18. 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
Freshly derived formulas for G( Y -> pp ):
Resulting numerical values for the { gppY } coupling constants:
(Uses PDG total widths and pp BFs.) !! !

19. First, revisit the only measured case, s( pp -> J/y p0 ).
PCAC-like model versus naïve “phase space” model:
1pEx Feyn diags, gNNp = 13.5,
and G( J/Y -> p p ) input
const A and
G( J/Y -> p p p0 ) input

20. Now we can calculate NUMERICAL total and differential cross sections for
pp -> any of these cc states + p0.
We can also answer the BIG question,
Are any cc states more produced more easily in pp than J/y?
(i.e. with significantly larger cross sections)

21. Are any other cc states more easily produced than J/y?
the BIG question…
Are any other cc states more easily produced than J/y?
ANS: Yes, by 1-2 orders of magnitude!
Vertical scale changed by a factor of 25 from previous J/y plot!

22. Final result for cross sections. (All on 1 plot.)
Have also added two E835 points from a PhD thesis (open pts.).

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

24. Predicted c.m. frame angular distribution for pp -> hcp0
normalized to the forward intensity, for Ecm = 3.2 to 5.0 GeV by 0.2.
spiderman plot

25. Predicted c.m. frame angular distribution for pp -> J/y p0
normalized to the forward intensity, for Ecm = 3.4 to 5.0 GeV.

26. Next steps using this model:
1. Y Polarization predictions are nontrivial. Are they interesting?
2. Extend to other baryon resonances, e.g. N*(1535).
This is especially important e.g. for pph final states.
3. Extend to other light mesons, such as the w.

27. II. Estimates of ppm couplings. (Relevant to NN nuclear force models.)

28. How hadrons interact (1 popular mechanism)
Meson exchange. (traditional nuclear)
Form factors and
gNNm coupling consts,
normally treated as free params. A C D B
e.g. for NN scat:
p, r, w, “s”, …
(In terms of hadron d.o.f.s)
Easy to calculate (Feynman diagrams) but the vertices (form factors)
are obscure. MANY free params, usually fitted to data.
Not the right physics at small r ?

29. Another scattering mechanism: NN cores from q-g forces, not w ex?
Nathan Isgur at JLAB, 1999,
suggests quark interchange
meson-meson scattering diagrams.
Isgur’s confusion theorem…

30. VNN(r) s p p exchange pp ?? w exchange
A schematic picture of NN forces s p p
“s exchange” ?
q-g forces (1gE)
p exchange
pp ??
IRA
1pE
core
rNN (fm)
VNN(r)
(MeV)
historically
considered
w exchange

31. I = 0
I = 1

32. Nucleon-meson coupling constants found in the NN meson-exchange-model literature.
The main ingredients are the p, s , and w. Note especially the NNs coupling and kw,r.
These are basically just fits to NN phase shift data.
Table from C.Downum, T.Barnes, J.R.Stone and E.S. Swanson
nucl-th/ , PLB638, 455 (2006).

33. What we have done:
All Born-order elastic phase shifts
and inelasticities in all J,L,S channels
due to 0 - , 0 + and 1-
(e.g. p, s and w) exchange…

34. Does the quark core ps resemble w exchange. (Isgur’s confusion theorem
Yes, however… a much smaller NNw coupling (gNNw = 6 shown) is required.

35. One pion exchange at least really is present in NN.

36. by extracting the ppm couplings directly from BES data on Y (= any
An idea for BES:
One can test the traditional meson exchange models of the nuclear force
by extracting the ppm couplings directly from BES data on Y (= any
convenient cc) decays, and see whether they agree with the fitted
NN meson exchange model values for the gNNm coupling constants.
If they strongly disagree, the nuclear force model may be wrong.
e.g J/y -> p p w
Since we know the coupling J/y -> p p, if this is also dominantly a
two-stage process, the ratio of BFs
B(J/y -> p p w ) / B(J/y -> p p )
alone suffices to determine g2NNw /4p.
(Theorists need to work out this relation.)
A careful study of the various Y -> p p m Dalitz plots will be necessary
to extract the N* = p “pole” contribution.
An aside: actually NNw has 2 couplings, g and k.

37. + The idea in pictures… Y m = p0, h, w, r0, h’, f, … p m g ppY
(known from G(Y -> pp ))
gppm
(to be determined) Y
N* generally; extract N*=p “pole” part
then we can check against…
gppm N N m N N

38. NNm coupling constants and form factors
Finally…
3 slides on calculating
NNm coupling constants and form factors
in the quark model.

39. Direct calculation (not fitting) of meson-baryon coupling constants and form factors in the quark model.
C.Downum, T.Barnes, J.R.Stone and E.S. Swanson
nucl-th/ , PLB638, 455 (2006). p0 g p p p
No need to guess (or fit) the vertex gBB’m(Q2) for an effective Lagrangian,
it can be calculated as a decay amplitude, given B, B’, m quark wavefunctions.
(The Orsay group did this in the 1970s for NNp. A lost art.)
Status: we have reproduced the published Orsay gNNp(Q2). Now we can calculate
the NNm coupling constants and form factors for any other exchanged meson.

40. e.g. The calculated quark model gNNp(Q2) vertex / form factor:
(TB,CD,ESS, 3 indep calcs,
confirm ORSAY.)
How does this compare numerically with the “experimental” (fitted NN scattering)
NNm coupling constants?

41. Summary of our quark model results for NNm couplings versus the NN meson-exchange-model literature.
The main ingredients are the p, s , and w. Note especially the NNs coupling and kw.
C.Downum, T.Barnes, J.R.Stone and E.S. Swanson
nucl-th/ , PLB638, 455 (2006).

42. Summary and conclusions:
BES can use charmonium decays of the generic type Y -> ppm
to extract NNm (and N*Nm) couplings.
This would allow very interesting tests of meson exchange models
of the NN force, especially of the idea that the NN core repulsion
may not be due to vector meson (w) exchange.
Related questions and comments:
NNw has both gm and smn couplings.
How can these best be separated experimentally?
Is gNNh really approx. 0 ??? (Claimed in photoproduction.)
This violates naïve flavor symmetry + gNNp.
Theorists (like me) may enjoy contributing to the study and modeling
of Y -> ppm Dalitz plots.
Is polarization interesting?

43. The End