Charmonium Production at PANDA

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Charmonium Production at PANDA
Ted Barnes Physics Div. ORNL and Dept. of
Physics, U.Tenn. Hirschegg 18 Jan. 2007

• 1. Estimates of associated charmonium cross
  sections at PANDA
• s ( pp -gt cc m )
• 2. Comments re vector charmonium strong decays
• y(4040) y(4160) and y(4415)

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1. Estimates of associated charmonium cross
sections at PANDA s ( pp -gt cc m )
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PANDA at GSI pp -gt cc m, cc-H m
(ProtonAntiprotonaNnihilationexperimentatDArms
tadt) p beam energies KEp 0.8
14.5 GeV
m light meson(s) needed to allow cc-H JPC
exotics
Production cross sections??
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What PANDA needs to know What are the
approximate low-E cross sections for pp -gt 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 qg 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(q) (pp -gt J/y p 0 ) 2.
A.Lundborg, T.Barnes and U.Wiedner, PRD73, 096003
(2006). Crossing estimates for s( pp
-gt Y m ) from G( Y -gt p p m)
(Y y,
y m several) 3. T.Barnes and X.Li,
hep-ph/0611340. PCAC-like model W(q), s (
pp -gt Y p 0 ), Y hc, y, c0, c1, y
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1. M.K.Gaillard. L.Maiani and R.Petronzio,
PLB110, 489 (1982).
PCAC W(q) (pp -gt 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,S,L channel. (Hence not immediately
useful for total cross section estimates for
PANDA.) Quite numerical, gives W(q) at a
specific Ep(cm) 230 MeV as the only example.
Implicit analytic results completed in Ref.2.
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2. A.Lundborg, T.Barnes and U.Wiedner,
hep-ph/0507166, PRD73, 096003 (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 -gt
ppm. These have the same amplitude as the
desired s( pp -gt 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 -gt Y m ) is simply
proportional to G(Y -gt ppm ). Specific
example, s( pp -gt J/y p 0 )
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These processes are actually not widely separated
kinematically
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ò dt
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For a 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 -gt Y p0 ) to G( Y
-gt 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 -gt J/y p0 ) from
G( J/y -gt pp p0 ), compared to the E760 data
points
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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 worlds data on s(pp -gt mJ/y)
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?pp ? J/? ?0 from continuum
Expt Only 2 E760 points published. This is
E835 (D.Bettoni, yesterday) Physical cross sec is
ca. 100x this.
M. Andreotti et al., PRD 72, 032001(2005)
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Other channels may be larger, however the
constant Amp approx is very suspect. N
resonances?
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3. T.Barnes and Xiaoguang Li, hep-ph/0611340.
summer in Darmstadt, c/o K.Peters Associated
Charmonium Production in Low Energy pp
Annihilation
Calculates the differential and total cross
sections for pp -gt 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) pp widths.
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PCAC model of pp -gt Y p0
(T.Barnes and X.Li, hep-ph/0611340)
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.

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mp 0 limit, fairly simple analytic
results unpolarized differential cross sections
simplifications M mY m mp x (t - m2) /
m2 y (u - m2) / m2 f -(xy) (s - mp2
- M 2) / m2
r i m i / m
also, in both dltsgt/dt and ltsgt,
(in the analytic formulas)
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mp 0 limit, fairly simply analytic
results unpolarized total cross sections
(analytic formulas)
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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 -gt J/y p0
unpolarized total cross section
Values of the aY coupling constants?
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To predict numerical pp -gt Y p0 production
cross sections in this model, we know gppp
13.5 but not the gppY . Fortunately we can
get these new coupling constants from the known
Y -gt pp partial widths
Freshly derived formulas for G( Y -gt pp )
Resulting numerical values for the gppY
coupling constants (Uses PDG2004 total widths
and pp BFs.)
!!
!
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Now we can calculate NUMERICAL total and
differential cross sections for pp -gt 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)
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s( pp -gt J/y p0 ), PCAC-like model versus
phase space model
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And the big question Are any other cc states
more easily produced than J/y? ANS Yes, by
1-2 orders of magnitude!
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Final result for cross sections. (All on 1
plot.) Have also added two E835 points from a
PhD thesis (open pts.).
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An interesting observation The differential
cross sections have nontrivial angular
dependence. e.g. This is the c.m. frame (and
mp0) angular distribution for
pp -gt hc p0
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.
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Predicted c.m. frame angular distribution for pp
-gt hcp0 normalized to the forward intensity,
for Ecm 3.2 to 5.0 GeV by 0.2.
spiderman plot
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Predicted c.m. frame angular distribution for pp
-gt J/y p0 normalized to the forward intensity,
for Ecm 3.4 to 5.0 GeV.
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Next steps using this model
1. Publish this paper! (hep-ph/0611340) 2.
Polarization predictions are nontrivial. 3.
Extend to other baryon resonances, e.g. N(1535).
This is important e.g. for h production.
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2. Comments re vector charmonium strong decays
y(4040) y(4160) and y(4415)
Most results shown here are abstracted from
T.Barnes, S.Godfrey and E.S.Swanson, PRD72,
054026 (2005).
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Fitted and predicted cc spectrum Coulomb (OGE)
linear scalar conft. potential model black
expt, red theory.
Y(4260), Y(4320) JPC 1- -
Z(3931), X(3943), Y(3943) C ()
states fitted
SS OGE
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What are the total widths of cc states above 3.73
GeV? (These are dominated by open-flavor decays.)
62(20) MeV
103(8) MeV
80(10) MeV
X(3872)
23.0(2.7) MeV
PDG2006 values
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Open-charm strong decays 3P0 decay model (Orsay
group, 1970s) qq pair production with vacuum
quantum numbers. LI g y y . A standard for
light hadron decays. It works for D/S in b1 -gt
wp. The relation to QCD is obscure.
(Feynman rules from E.S.Ackleh et al., PRD54,
6811 (1996).)
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Strong Widths 3P0 Decay Model
Parameters are g 0.4 (from light meson decays),
meson masses and wfns.
X(3872)
23.0(2.7) MeV
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E1 Radiative Partial Widths
X(3872)
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Strong Widths 3P0 Decay Model
X(3872)
80(10) MeV
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Recall J.Napolitano (CLEO) yesterday
4040
4160
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One success of strong decay models An historical
SLAC puzzle explained the weakness of y(4040) -gt
DD
e.g. DD molecule?
After restoring this p3 phase space factor, the
expt BFs were D0D0
D0D0 D0D0 0.12 /- 0.06
0.95 /- 0.19 1 /- 0.31
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Y(4040)
Y(4040) partial widths MeV (3P0 decay
model) DD 0.1 DD 32.9 DD
33.4 multiamp. mode DsDs 7.8
Y(4040) -gt DD amplitudes (3P0 decay
model) 1P1 0.034 5P1 - 0.151
- 2 51/2 1P1 5F1 0
famous nodal suppression of a 33S1 Y(4040) cc -gt
DD
std. cc and D meson SHO wfn. length scale
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Strong Widths 3P0 Decay Model
103(8) MeV
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Recall J.Napolitano (CLEO) yesterday
4040
4160
4040
4160
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Y(4159)
Y(4159) -gt DD amplitudes (3P0 decay
model) 1P1 0.049 5P1 - 0.022
- 5 -1/2 1P1 5F1 - 0.085
Y(4159) partial widths MeV (3P0 decay
model) DD 16.3 DD 0.4 DD 35.3
multiamp. mode DsDs 8.0 DsDs 14.1
std. cc SHO wfn. length scale
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Strong Widths 3P0 Decay Model
Y(4415)
62(20) MeV
X(3872)
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Y(4415)
BGS results (3P0 decay model) Y(4415)
partial widths MeV DD 0.4 DD
2.3 DD 15.8 multiamp. DsDs
1.3 DsDs 2.6 DsDs 0.7 m New
SP mode calculations DD1 30.6 m lt-
MAIN MODE!!! DD1 1.0 m DD2
23.1 DD0 0.0
Y(4415) - gt DD1 amplitudes (3P0 decay
model) 3S1 0 lt- !!! (HQET) 3D1
0.093
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Y(4415)
An industrial application of the Y (4415).
Sit slightly upstream, at ca. 4435 MeV, and you
should have a copious source of Ds0(2317).
(Assuming it is largely cs 3P0.)
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END