Transcript Proton Form Factor Measurements with Polarization Method L.Pentchev The College of William and Mary For the GEp-2g and GEp-III collaborations JLab , June 8-10, 2009

Proton Form Factor Measurements with
Polarization Method
L.Pentchev
The College of
William and Mary
For the GEp-2g and
GEp-III
collaborations
JLab , June 8-10, 2009
Outline
GEp-III (E04-108) and GEp-2g (E04-019) experiments
Polarization transfer method, experimental set-up, kinematics
Elastic/background separation
Spin transport in HMS
GEp-2g experiment: precise (1%) measurement of two polarization
quantities; test of the limits of Born approximation in polarization method
2g exchange theoretical calculations
Longitudinal transferred polarization (preliminary results), beam
polarization measurements
e-dependence of the form factor ratio (preliminary results)
Reconstruction of the real part of the ep elastic amplitudes
GEp-III: measurement of the proton form factor at high Q2
Preliminary results
Comparison with theoretical calculation, asymptotic behavior
Summary


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
e
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)
GEP-3 and GEP-2gamma experimental set-up in Hall C
e
e’
1.87- 5.71 GeV beam
80-100 mA beam current
80-85% pol.
20cm LH target
Detectors
Changes in standard HMS detector package:
•Focal Plane Polarimeter with Double Analyzer:
-> 70% increased efficiency (30% for FOM)
• Scintillator plane S0 in front of drift chambers
-> deteriorates angular resolution but
needed for triggering
1744 channel E.M. Calorimeter (BigCal):
6.8% 23%
to
• from
(due to radiation damage)
E
E
needed for triggering
• beter than 10 mm position resolution – most
important parameter for elastic separation
Goal of The Experiments
• GEp-2gamma: 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
Ee, GeV
pp
Ee’
Qp, deg
e
e range
<Q2
>
precision limited only by statistics (~ 1%),
1.867
2.068
0.527
14.49
105
.130-.160
2.5
very small p.t.p systematics:
2.839
2.068
1.507
30.98
45.3
.611-.647
2.5
Ay , h cancel out in the Pt/Pl ratio
3.549
2.068
2.207
35.39
32.9
.765-.786
2.5
Q2 fixed, Pp fixed, spin precession fixed
3.650
2.068
2.307
36.14
31.7
.772-.798
2.5
• GEp-3: high Q2 measurements
Ee, GeV
pp
Ee’
Qp,
deg
e
e
<Q2>
4.053
3.589
1.274
17.94
60.3
.377
5.2
•5.2 GeV2 point “overlapping” with GEp-II (4.0
and 5.6 GeV2)
5.714
4.464
2.090
19.10
44.2
.507
6.8
• two higher Q2 points
5.714
5.407
1.164
11.6
69.0
.236
8.5
Data analyses: elastic separation
All triggers Elastics after BigCal-HMS correlations Estimated background Range used in analyses
2.5 GeV2
e=0.15
8.5 GeV2 e=0.24
s=0.10%
s=0.11%
Background contribution: 0.5%
Correction to mR:
+0.35%
Background contribution: 13%
Absolute correction to mR: +0.10
• (PCAL-PHMS)/P0 gives better resolution then (Pp-PHMS)/P0, because of worse HMS angular resolution
•Background estimated by interpolation, dominated by g p -> p0 p
• Polarization of the background measured below the elastic peak looking at events with hits at the calorimeter
outside expected position of the elastic electron (p0 > gg)
Spin transport in HMS
QQQD type spectrometer: rotations are
additive in the quads and total precession is
sum of dispersive (main) and nondispersive precession:
Dispersive precession
  g (m 1)
  g (m 1)
Non-dispersive

precession
Allows to use simple geometrical model, giving
results very similar to COSY calculations used
for the results presented here
2.5 GeV2
e=0.15
•Non-dispersive precession – the dominant
source of systematics, because it mixes the
two polarization components in the reaction
plane
•Requires very good knowledge of nondispersive bend angle 
• uncertainty of  used for the preliminary
analyses of 1mrad
• using dedicated optical studies, we expect
to reduce the uncertainty by factor of ~3
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
GEp-2g: 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 )
ds red
~


 (G M )
2
1

2

e
Y


GM
1  e 2g 

~
ds red
~
 (G M )
e (GE ) 
eR 2
R
2
/ GM  1 
2
 2R
 2 1   eY2g


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 ))
Y2g  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 (at the 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
GPD
A.Afanasev et al., Phys.Rev.D72:013008
(2005) – GPD models: Gauss (figure), smaller
effect with Regge, or non-zero quark mass
Valid at high e region (vertical line at figure)
LO pQCD
Both theories describe
Rosenbluth data but have
opposite predictions for mGE/GM
N. Kivel and M. Vanderhaeghen
arXiv:0905.0282 [hep-ph] LO pQCD using
two different distribution amplitude models:
BLW (good agreement with lattice QCD!)
and. COZ
Valid in high e region (vertical line at figure)
Longitudinal transferred polarization: stability of the measurements
Beam polarization: dominant source of systematic error for PL measurements
•open circles: this experiment
(hAyPl)meas/(Plborn Ay())
• filled circles – Moller measurements
of beam polarization (h)
• open boxes (connected with line):
beam polarization 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
Longitudinal transferred polarization: stability of the measurements
•open circles: this experiment
(hAyPl)meas/(Plborn Ay())
• 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
NO RADIATIVE
CORRECTIONS APPLIED,
Uncertainties in the overall normalization of
the data due to uncertainties in Ay
Less than 1% (Afanasev et.al,
Phys.Rev. D64 (2001) 113009)
Beam polarization p.t.p. systematics 0.5%
Preliminary results: form factor ratio
Narrow acc.
matching all
kinematics
Theoretical predictions
are with respect to the
Born approximation
Wide acc. matching
e=0.64 and e=0.79
NO RADIATIVE CORRECTIONS APPLIED,
Less than 1% (Afanasev et.al, Phys.Rev. D64
(2001) 113009)
GEP3 preliminary results: FF ratio
•Results at 2.5 and 5.2 GeV2 agree (within one sigma) with previous Hall A results
•No zero crossing; slower decrease with Q2
GEP3 results
• No evidence for the Q2 F2/F1 scaling
• Modified (logarithmic) scaling still holds
CONCLUSIONS
GEp-2g: POLARIZATION METHOD PASSED THE TEST : no evidence for effects
beyond Born approximation at 2% level in the polarization data at Q2 of 2.5 GeV2
Slight deviations from Born approximation at two sigma level both of longitudinal
polarization and of form factor ratio require further investigations: possible “standard”
radiative corrections, not applied yet
The preliminary results do not exclude with high confidence any of existing 2gexchange theoretical models; yet high-e data favor GPD and pQCD models. Expected
reduction of systematic error and especially, knowledge of Born FF ratio (from e+/eexperiments) will greatly help in constraining theoretical predictions.
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.
GEp-III: First high Q2 proton FF ratio measurements outside Hall A confirm previous
results at one sigma level, though Hall C data possibly slightly higher
New FF ratio data up to 8.5 GeV2 exhibit slower decrease with Q2 (favoring existing
VMD, GPD models) still consistent with modified (logarithmic) scaling of F2/F1; no zero
crossing yet
Measurements above 8.5 GeV2 with 12 GeV machine are certainly very important
BACK-UP SLIDES
STARTING HERE
Elastic amplitude reconstruction
Three
observables
measured at
2.5 GeV2:
• Pt/Pl
• Ay*Pl
• ds
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 Y2g.
Three amplitudes (Re parts): R=mRe(GE)/Re(GM), Y2g, Re(GM) and Ay unknown
Plotted: Re(GM) (ds, Pt/Pl,R),
Y2g(Pt/Pl,R),
Ay(Ay*Pl,R)
Background corrections
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: 2g 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
Analyzing Power
Polarization Method: Spin Transport
Dispersive precession
  g (m 1)
Non-dispersive precession
  g (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
GEp/GMp Crisis: asymptotic behavior
Dirac and Pauli form factors:
GM  GE
F1 
1
F2 
GM  G E
 (1   )
Q 2 F2
 const.
F1
pQCD asym ptotic
Polarization Method: Systematics
Relate the evolution of the
velocity (trajectory) to the
evolution of the spin:

dS
e   g  || 
g  2   

S   B  1
g B 


dt mg
2
2

COSY
Geom. Approx.

dv
e  

v B
dt mg

B ||  0
g 
 1    f   
2 
  g 
s
 ( s)   sin  ( s) fd ( s)   f  (d   fp ) sin 
s
0

 ( s)   cos  ( s) fd ( s )  f     (d   fp )(1  cos  )

0
 Pn fp   S nn S nt S nl   Pn 
 fp  
 
P

S
S
S
 t   tn tt tl   Pt 
 fp  
 
 Pl   S ln S lt S ll   Pl 
Snt   sin  cos  sin   cos  sin  cos 
Snl  cos  sin 
Stt  cos  cos 
Stl  sin 
Geometrical Approx.
High Q2 Measurements