Transcript Slide 1

Proton Form Factor Measurements Using Recoil
Polarization: Beyond Born Approximation
L.Pentchev
The College of
William and Mary
Charlottesville, October 9, 2008
Outline
GEp crisis: 8 years history
Experimental Status
Beyond Born Approximation: theoretical predictions
GEP-2gamma experiment at JLab: precise (1%) measurement of two
polarization quantities; test of the limits of the polarization method
Preliminary results
Reconstruction of the real part of the ep elastic amplitudes
Summary
GEp/GMp Crisis: discrepancy in the data
“The discrepancy is a serious
problem as it generates
confusion and doubt about the
whole methodology of lepton
scattering experiments”
P.A.M. Guichon and
M.Vanderhaeghen
Experimental Status
Polarization method
• Experimental errors are well understood
• Experimental errors are small and can’t explain the discrepancy between
Rosenbluth and polarization measurements; it would require significant
uncertainties in the trajectory bending angles, totally inconsistent with the optical
studies
• Consistency of different measurements:
 two experiments in HallA (GEP-1 and GEP-2) overlapping at 3.5 GeV2
 recent GEP-3/GEP-2Gamma experiments using different (HallC) detectors;
overlapping measurements at 2.5, 2.7 and 5.2 GeV2
Rosenbluth method
•JLab experiment (Super Rosenbluth) confirmed previous SLAC results:
registering proton instead of electron; different radiative corrections
• Recent JLab experiment collected data over large Q2 and e range
• The method has reduced sensitivity for Q2 > ~3 GeV2
NO EXPERIMENTAL EXPLANATION OF THE DISCREPANCY FOUND
Beyond Born Approximation
Mo and Tsai, and others:
• prescriptions for radiative
corrections commonly used
• two-photon exchange:
(e), (f) – only with one soft
photon, neglecting proton
structure
Generalized Form Factors (ep elastic amplitudes)
this experiment
Pl 
G M2
(1  e )(1  e )
d red
~


 (G M )
2
1

2

e
Y


GM
1  e 2 

~
d red
~
 (G M )
e (GE ) 
eR 2
R
2
/ GM  1 
2
 2R
 2 1   eY2


GM
G M

e+/e- x-section ratio
Rosenbluth non-linearity
~
~
 (GM )  GM (Q2 )   (GM (Q2 , e ))
~
~
 (GE )  GE (Q2 )   (GE (Q2 , e ))
~
R  GE / G M
 (1   )(1  e )  ( F3 (Q2 , e ))
Y2  0 
1 e
GM
Born Approximation
Beyond Born Approximation
P.A.M. Guichon and M.Vanderhaeghen, Phys.Rev.Lett. 91, 142303 (2003)
M.P. Rekalo and E. Tomasi-Gustafsson, E.P.J. A 22, 331 (2004)
Two-Photon Exchange: theoretical predictions
Hadronic calculations
•P.Blunden et al., Phys.Rev.C72: 034612
(2005) elastic (Figure)
•S.Kondratyuk et al., Phys.Rev.Lett. 95:
172503 (2005) including Delta reduces the
effect
• S.Kondratyuk et al., nucl-th/0701003 (2007)
including 1/2 and 3/2 resonances – no
effect
•Yu. Bystricky, E.A.Kuraev, E. Tomasi-Gustafsson
Phys. Rev. C75, 015207 (2007) structure function
method: 2 effects small, higher orders
change Rosenbluth slope (Figure)
•D.Borisuyk, A.Kobushkin arXiv:0804.4128:
proton off-shell form factors are not needed to
calculate TPE amplitudes
Two-Photon Exchange: theoretical predictions
GPD calculations
Absolute correction to FF ratio mGe/Gm:
•slow Q2 variation, strong effects at low e
• valid for high Q2 or high e
•A.Afanasev et al., Phys.Rev.D72:013008 (2005) – GPD models: Gauss on Fig., smaller effect with
Regge, or non-zero quark mass
Two-Photon Exchange: theoretical predictions
hadronic (elastic): dominated by
correction to GM
GPD (includes inelastic): dominated
by Y2 and correction to GE
Both theories describe
Rosenbluth data but have
opposite predictions for mGE/GM
.
Goal of This Experiment: e dependence of R at 2.5 GeV2
KEY IDEA OF THE METHOD: FIXED Q2
Two polarization observables are
measured: Pt/Pl and Pl separately
• same
spin transport
• same
analyzing power
e
e’
80 uA beam current
85% pol.
20cm LH target
Ee, GeV
pp
Ee’
Qp, deg
qe
e range
<Q2>
1.867
2.068
0.527
14.13
106
.130-.160
2.49
2.839
2.068
1.507
30.76
45.3
.611-.647
2.49
very small p.t.p systematics:
3.549
2.068
2.207
35.39
32.9
.765-.786
2.49
Ay , h cancel out in the Pt/Pl ratio
3.650
2.068
2.307
36.14
31.7
.772-.798
2.49
Q2 fixed, Pp fixed, spin precession fixed
precision limited only by statistics
(~ 1%), unlike Rosenbluth,
Detectors
Focal Plane Polarimeter with double Analyzer
1744 channel E.M. Calorimeter
Longitudinal transferred polarization: stability of the measurements
•open circles: this experiment
(hAyPl)meas/(Plborn Ay(q))
• filled circles – Moller measurements
of beam polarization (h)
• open boxes (connected with line):
beam polazrization predicted from
quantum efficiency measurements
(Dave Gaskell, private comm.)
• 1.873 GeV beam energy, e=0.15
• 2.846 GeV
e=0.64
• 3.549 GeV
e=0.78
•3.680 GeV
e=0.79
Preliminary results: longitudinal polarization
Uncertainties in the overall
normalization of the data
due to uncertainties in Ay
NO RADIATIVE
CORRECTIONS APPLIED,
Less than 1% (Afanasev et.al,
Phys.Rev. D64 (2001) 113009)
Beam polarization p.t.p. systematics 0.5%
Preliminary results: form factor ratio
Theoretical predictions
are with respect to the
Born approximation
NO RADIATIVE
CORRECTIONS APPLIED,
Less than 1% (Afanasev et.al,
Phys.Rev. D64 (2001) 113009)
Elastic amplitude reconstruction
Three
observables
measured at
2.5 GeV2:
• Pt/Pl
• Ay*Pl
• d
Three amplitudes (Re parts): R=mRe(GE)/Re(GM), Y2, Re(GM) and Ay unknown
Plotted: Re(GM) (d, Pt/Pl,R),
Y2g(Pt/Pl,R),
Ay(Ay*Pl,R)
CONCLUSIONS
POLARIZATION METHOD PASSED THE TEST : no evidence for effects
beyond Born approximation at 1% level in the polarization data at Q2 of 2.5 GeV2
Discrepancy between Rosenbluth and polarization method
• No experimental explanation was found
• Radiative corrections (two-photon exchange and/or higher order corrections)
are the most likely candidate but it requires further experimental and theoretical
investigation
The two polarization quantities of the present measurements and the e+p/e-p
cross-section ratio are sensitive to different amplitude combinations and
therefore, complementary in investigating the effects beyond the one-photon
exchange approximation
Measuring two polarization observables for a fixed Q2 in a wide kinematical
range with 1% precision allows to constrain the real parts of both, ratio of the
generalized electric to magnetic form factors, and the third non-Born amplitude
contribution Y2g, without model assumptions. Including precise cross-section
data will constrain also the real part of the magnetic form factor.
Preliminary results
No radiative corrections applied (<1%)
BACK-UP SLIDES
STARTING HERE


e p  ep elastic
Polarization Method
In Born (one-photon exchange) approximation:
I 0 Pt  2  (1   )GEpGMp tan
e
2
1
2
2 e
I 0 Pl 
( Ebeam  Ee )  (1   )GMp tan
Mp
2

e
2
2
I 0  GEp
 GMp
GEp
GMp
  Q / 4M
2
2
p
e
Pt ( Ebeam  Ee )
e

tan
Pl
2M p
2
1
1  2(1   ) tan2
qe
2
•Form Factor ratio can be obtained without knowing analyzing power, Ay, and beam
helicity, h, (both cancel out in the ratio), and without measuring cross-section.
•Systematic uncertainty dominated by the spin transport from the polarimeter to the
target.
A.I.Akhiezer and M.P.Rekalo, Sov.J.Part.Nucl. 3, 277 (1974)
R.Arnold, C.Carlson, and F.Gross, Phys. Rev. C 23, 363 (1981)
Analyzing Power
Polarization Method: Spin Transport
Dispersive precession
   (m 1)
Non-dispersive precession
   (m 1)

Target


Target
to Reaction Plane
Reaction Plane
m
GEp
GMp
 m
Pt ( Ebeam  Ee )

tan e
Pl
2M p
2
Longitudinal and transverse polarizations Pt and Pl are helicity dependent (transferred)
Normal polarization Pn is helicity independent; zero in Born approximation
Data analyses: elastic separation
All triggers
Inelastics
Elastics after ep
kinematical correlation
Estimated background
Circles –longitudinal
asymmetry at target
Boxes – transverse
asymmetry at target
Background contribution
max of 0.5% for e=0.15
Elastic Amplitude Reconstruction
Important note:
Elastic amplitude reconstruction is
different from full Born / non-Born
separation: need e+/e- data and triple
polarization observables (M.P.Rekalo
and E. Tomasi-Gustafsson
Nucl.Phys.A740:271-286,2004)
Still here one can constrain the
contribution from the third non-Born
amplitude Y2.
Y2 vs R=mRe(GE)/Re(GM) reconstructed from this
experiment (1 area)
GEP results
GEP preliminary results
at 2.5 and 5.2 GeV2