Diapositive 1

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The p N ? e e N process in the resonance region
insisting once more on the complementarity of
the p N ? e e N and ? N ? e e N processes
to study vector meson-nucleon transition
couplings to baryon resonances
Matthias Lutz and Madeleine Soyeur
Nucl. Phys. A 713 (2003) 97 Nucl.
Phys. A 760 (2005) 85
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Contents

• Underlying physics, kinematics,
• theory and useful comments
• 2. Expected cross sections and ?-? interference
  patterns in e e-
• 3. A couple of additional comments (hopefully
  useful)

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• Underlying physics, kinematics,
• theory and useful comments

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The issue
Coupling of vector fields to low-lying baryon
resonances ? Baryon resonance structure
studies N ? N (virtual ? or ?) ? N ee-,
link to radiative decays ? Mandatory path
towards vector meson propagation in the nuclear
medium coupling to NN-1 loops
s1/2 vector meson threshold 1.72 GeV EpLab
vector meson threshold 0.96 GeV
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p N ? ee N
Underlying Vector Meson Dominance picture
Quantum interference of the ?0- and ?- meson
amplitudes in the ee channel ? Expect sensitive
interference patterns
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p N ? e e- N studied in kinematics where
s-channel resonances dominate
Kinematics
Below and very close to the vector meson
threshold
p
e e-
p
e e-
N
N
N
N
nonresonant terms
? at energies lower than the region where
t-channel effects are expected to be important
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Baryon resonance mass range
p N ? e e N for 1.40 lt s1/2 lt 1.75
GeV
Baryon resonances involved
N states (I1/2) ? states
(I3/2) N1/2 (939) (GS) ?3/2 (1232)
(GS) N1/2 (1440) P11 ?3/2 (1600) P33
N3/2 (1520) D13 ?1/2 (1620) S31
N1/2 (1535) S11 ?3/2 (1700) S33
N1/2 (1650) S11
P-states excluded (small radiative widths)
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Theory for the pN?VN amplitudes
M. Lutz, Gy. Wolf, B. Friman, Nucl. Phys. A 706
(2002) 431.
Selfconsistent and relativistic coupled-channel
study of the pN and ?N reactions involving the
?N, pN, ?N, ?N, p?, K?, KS channels
Kinematics 1.40 lt s1/2 lt 1.75 GeV
0.4 lt EpLab lt 1 GeV Assumption Only
relative s-wave contributes in the VN final
states (near threshold
kinematics) gt only
relative s- and d-waves contribute in the
pN channel because of parity
conservation (S11,
S31, D13, D33 baryon resonances)
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Dynamics Effective meson-meson-baryon-baryon
Lagrangian Assumptions Fundamental fields
photon, mesons, nucleon, ?(1232) Baryon
resonances (S11, S31, D13, D33)
generated dynamically through Bethe-Salpeter
equation Vector Dominance Assumption
(generalized) to relate amplitudes
involving (real) photons to amplitudes involving
vector mesons Fitting procedure Use all
available data (phase shifts, inelasticity
parameters,
pion-photoproduction multipole
amplitudes, inelastic cross
sections) to fit the
effective Lagrangian parameters (56)
gt Satisfactory fit to the
data in the interval
1.40 lt s1/2 lt 1.75 GeV
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M. Lutz, Gy. Wolf, B. Friman, Nucl. Phys.
A 706 (2002) 431.
pp ? VN
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Limitations of the model
?Threshold physics s-channel dominated
vector meson production (through the
excitation of baryon resonances and
non-resonant processes) gt Excludes the
kinematic range above threshold where
t-channel, long-range exchanges (p) are
known to be important ?Vector
Dominance assumption Most general Vector
Dominance ansatz compatible with gauge
invariance (pion photoproduction amplitudes
play a crucial role in the fitting procedure)

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pp ? Vn amplitudes
pp ? ?n gtgt pp ? ?0n and opposite signs!
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pn ? Vp amplitudes
pp ? ?n gtgt pp ? ?0n and same signs!
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Vector Meson Dominance for time-like photons
Lagrangian
with
and
Experimental ee decay widths of the ?0 and ?
?
and
Assumptions the phase correlation between
isoscalar and isovector
currents (? and ?) is the same for
real and for virtual (time-like) photons
f? and f? both
positive Massive
photon in relative s-wave with respect to
the final nucleon
m ee not too far from (s1/2 MN
)
?
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2. Expected cross sections and ?-? interference
patterns in e e-
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p- p ? e e n
EpLab0.66 GeV
Destructive interference
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EpLab0.66 GeV
p n ? e e p
Constructive interference
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p- p ? e e n
EpLab0.83 GeV
Destructive interference
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EpLab0.83 GeV
p n ? e e p
Constructive interference
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Behaviour across threshold p p ? ee
n
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Behaviour across threshold p n ? ee
p
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Subconclusions

• Very strong interference effects linked to the
• presence of baryon resonances and sensitive
  to
• their couplings (in particular large
  ?-coupling)
• 2. The ?-? interference in the ee channel is
• destructive for the p p ? ee n reaction
  and constructive for the p n ? ee p reaction.

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3. A couple of additional comments (hopefully
useful)
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Comment 1 ? N ? ee N the ideal complementary
process
Bethe-Heitler ?
Vector mesons ?
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M.F.M. Lutz and M. S., Nucl. Phys. A 760 (2005) 85
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Integrated spectra gt no interference between
Bethe-Heitler and vector meson amplitudes
BH calculable
Dominance of the ?-meson contribution
Constructive interference on proton
targets Destructive interference on neutron
targets
Key question Will there ever be accurate data?

JLab (g12)? Mami?
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Comment 2 A pion in the final
state is always muddying waters
Elementary reactions a pion in the final
state means a set of processes with an
intermediate baryon resonance (?, Roper,)
decaying in the pN channel and interfering
with vector meson production. Example ? N
? ? N through ? N ? ? p0 N In nuclei
very wide spectrum of ?-meson mass shift and
broadening from ? p0 in the recent literature!
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Conclusions

• The p N ? ee N and the ? N ? ee N reactions
  are unique processes to study the couplings of
  selected
• baryon resonances to the vector meson-nucleon
  channels.
• 2. The p N ? ee N and the ? N ? ee N
  reactions are
• complementary processes to determine these
  couplings.
• ? N ? ee N very sensitive to
  N ? ?N
• p N ? ee N sensitive to both
  N ? ?N
• 
  and N ? ?N
• 3. Data are badly, badly, badly
  needed

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