Two-photon exchange contribution in elastic

Two-photon exchange contribution in elastic
electron-proton scattering: measurements at VEPP-3
1
I. A. Rachek,
J. Arrington,
4
V. V. Gauzshtein,
V. V. Kaminsky,
1
V. V. Neufeld,
1
2
L. M. Barkov,
1,3
R. A. Golovin,
B. A. Lazarenko,
1
D. M. Nikolenko,
3
V. N. Stibunov,
1
1
1,3
V. F. Dmitriev,
1
A. V. Gramolin,
1
S. I. Mishnev,
N. Yu. Muchnoi,
1
D. K. Toporkov,
Yu. V. Shestakov,
4
H. de Vries,
and V. N. Zhilich
1,3
1,3
R. Sh. Sadykov,
1,3
2
R. J. Holt,
1
S. A. Zevakov,
1
1 Budker Institute of Nuclear Physics SB RAS, Novosibirsk, Russia
2 Argonne National Laboratory, Argonne, USA
3 Novosibirsk State University, Novosibirsk, Russia
4 Nuclear Physics Institute at Tomsk Polytechnical University, Tomsk, Russia
5 NIKHEF, Amsterdam, The Netherlands
Baryons-2013
I.A. Rachek
Baryons-2013
June 24, 2013
1
Proton electromagnetic form factors
The EM form factors are essential ingredients of our knowledge of the nucleon structure and this
justies the eorts devoted to their experimental determination
In one-photon (Born) approximation:
Nucleon Current Operator Γµ (q )
µν
Γµ (q ) = γ µ F1 (q 2 ) + i σ2Mqν F2 (q 2 )
Sachs Form Factors
Electric Form Factor
2
2
2
Q
GE (Q ) = F1 (Q ) −
4M F2 (Q )
( 2 ) non spin ip Dirac Form Factor
2
F2 (q ) spin ip Pauli Form Factor
F1 q
2
Magnetic Form Factor
2
2
2
GM (Q ) = F1 (Q ) + F2 (Q )
GE ≈ GM /µp ≈ GD ≡ (1 + Q 2 /0.71)−2
in non-relativistic limit GE and GM describe charge and magnetization distribution
in nucleon
I.A. Rachek
Baryons-2013
June 24, 2013
2
Measurements of Proton form factors
Study with elastic ep scattering
The Rosenbluth separation method at constant Q
2
Rosenbluth Formula
Rosenbluth, 1950
h i
dσ
τ
dσ
2
2
=
·
·
GE + GM
dΩ
d Ω Mott (1 + τ )
τ
−1
2
2
2
where τ = Q /4M and = 1 + 2(1 + τ ) tan (θ/2)
Polarized beams and targets and recoil polarimeters
Form factor ratio from polarization transfer
GE
GM
=
PT
PL
Akhiezer,Rekalo, 1968
×K
where PT and PL - transverse and longitudinal polarization components of proton,
K
p
= − τ (1 + )/2
I.A. Rachek
kinematic factor
Baryons-2013
June 24, 2013
3
Inconsistency ?
1.6
Unpolarized data:
Walker (1994),
global analysis
1.2
Qattan (2005)
µ GE ⁄ GM
1.4
1
0.8
0.6
Polarized data:
0.4
Jones (2000),
Punjabi (2005)
0.2
Gayou (2002),
Puckett (2011)
Puckett (2010)
0
0
1
2
3
4
5
6
7
8
9
Q2, GeV2
Clear discrepancy between unpolarized and polarized data is observed.
I.A. Rachek
Baryons-2013
June 24, 2013
4
Inconsistency ?
1.6
Unpolarized data:
Walker (1994),
global analysis
1.2
Qattan (2005)
µ GE ⁄ GM
1.4
1
0.8
0.6
Polarized data:
0.4
Jones (2000),
Punjabi (2005)
0.2
Gayou (2002),
Puckett (2011)
Puckett (2010)
0
0
1
2
3
4
5
6
7
8
9
Q2, GeV2
Clear discrepancy between unpolarized and polarized data is observed.
Radiative corrections, in particular, a short-range Two-Photon
Exchange (TPE) is a likely origin of the discrepancy
I.A. Rachek
Baryons-2013
June 24, 2013
4
Radiative Corrections to elastic (ep) scattering
Elastic scattering (e
MBorn
±
p
→ e ± p):
M2γ
Bremsstrahlung (e
±
p
Mvac
Mevert
Mpvert
Mpself
Meself
→ e ± p γ ):
Mebrem
Mp
brem
σ(e ± p ) = |MBorn |2 ± 2 Re M†Born M2γ +
+ 2 Re M†Born Mvac + 2 Re M†Born Mevert + 2 Re M†Born Mpvert + . . .
†
+ |Mebrem |2 + |Mpbrem |2 ± 2 Re Mebrem
Mpbrem + . . .
• Standard (soft photons) RC: dominant (infra-red) part can be factorized in the
observables.
I.A. Rachek
Baryons-2013
June 24, 2013
5
Radiative Corrections to elastic (ep) scattering
Elastic scattering (e
MBorn
±
p
→ e ± p):
M2γ
Bremsstrahlung (e
±
p
Mvac
Mevert
Mpvert
Mpself
Meself
→ e ± p γ ):
Mebrem
Mp
brem
σ(e ± p ) = |MBorn |2 ± 2 Re M†Born M2γ +
+ 2 Re M†Born Mvac + 2 Re M†Born Mevert + 2 Re M†Born Mpvert + . . .
†
+ |Mebrem |2 + |Mpbrem |2 ± 2 Re Mebrem
Mpbrem + . . .
• Standard (soft photons) RC: dominant (infra-red) part can be factorized in the
observables.
• Hard photons in box and ×-box: integral over o-shell proton intermediate state
contributions must be made.
I.A. Rachek
Baryons-2013
June 24, 2013
5
Example of calculation of the TPE contribution
P. G. Blunden, W. Melnitchouk and J. A. Tjon, Phys. Rev. C 72 (2005) 034612
without TPE contribution
with TPE contribution
⇒
If this model is correct, the contradiction in the measurements
p
p
of GE /GM is resolved
I.A. Rachek
Baryons-2013
June 24, 2013
6
(e + p )/(e − p )
Ratio
of elastic cross sections:
Direct method to measure a contribution of 2γ -process:
To measure a cross section ratio for elastic scattering of electrons and positrons on the proton
⇒
interference term can be extracted (after applying standard RC):
2
σ ∼ α(1γ) + α2 (2γ) + · · · = α2 (1γ) + α3 Re [(1γ)(2γ)] + · · ·
+
(2γ)
σ(e p )
≈ 1 + 2α ·
R ≡
σ(e − p )
(1γ)
Three experiments to measure R
= σ(e + p )/σ(e − p )
kinematical coverage
CLAS-2011 area
2.5
OL
YM
Q 2 (GeV/c)2
2
PU
S-
VE
PP
un
1.5
1
20
3,
R
I
(2011/12)
VEP
P3, R
1
un II
2
JLabCLAS: run is completed in
February-2011,
0.5
3
0
0
ε≡
NovosibirskVEPP-3: 2 runs
Ebeam = 1.6 GeV (2009) and 1.0 GeV
12
0.1
0.2
Q
1+2(1+
I.A. Rachek
0.3
0.4
ε
0.5
0.6
0.7
0.8
0.9
1
Ebeam = 0.5 ÷ 4 GeV
DORISOLYMPUS: run is completed in
December-2012,
Ebeam = 2 GeV
1
2
/4Mp2 ) tan2 θ/2
Baryons-2013
June 24, 2013
7
Milestones of the Novosibirsk experiment
• The proposal was published (Aug 2004): nucl-ex/0408020
• Data taking runs:
Run
Duration
Ebeam
Engineering run
MayJuly 2007
1.6
90
12
Run I
SepDec 2009
1.6
1100
320
Run II
Sep 2011 Mar 2012
1.0
2350
600
GeV
,
Number of
+
−
e +e
cycles
R
luminosity,
pb−1
• Some preliminary results were published (Dec 2011):
D. M. Nikolenko
proton,
et al., Two-photon exchange and elastic scattering of positrons/electrons on the
PoS ICHEP 2010, 164 (2010).
A. V. Gramolin
at VEPP-3,
et al., Measurement of the two-photon exchange contribution in elastic ep
scattering
Nucl. Phys. Proc. Suppl. 225-227, 216 (2012) [arXiv:1112.5369 [nucl-ex]].
• Final results of the data analysis are expected in 2013
I.A. Rachek
Baryons-2013
June 24, 2013
8
VEPP3 electron-positron storage ring
VEPP3 is a booster for the VEPP4M
electron-positron collider.
VEPP3 parameters for
Electron energy
Mean beam current
Energy spread
RF HV magnitude
revolution period
bunch length
E
I
e−
0
0
∆ E /E
U
T
72
σL
∗
vertical beam size
σz
∗
horizontal beam size σx
∗
vert. β -function
βz
∗
horiz. β -function
βx
E
İ
VEPP-3
beam:
2 GeV
150 mA
0.05%
0.8 MV
248.14 ns
15 cm
0.5 mm
2.0 mm
2 m
6 m
Internal Target Area
Injection beam energy inj
350 MeV
9
−1
Injection rate
1.5·10 s
inj
∗
parameters in the center of 2nd straight section
(in Internal Target Area)
Largest e
I.A. Rachek
+
current: 60 mA
Baryons-2013
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9
VEPP3 Internal Target section
target thickness
I.A. Rachek
= 1 − 2 × 1015 at /cm2
Baryons-2013
June 24, 2013
10
Novosibirsk experiment at the VEPP3 storage ring
A precise measurement of the ratio R
= σ(e + p )/σ(e − p )
at the energy of
electron/positron beams of 1.6 GeV (run I) and 1.0 GeV (run II).
Kinematic parameters of two runs
Parameter
Run I
LA
Ebeam , GeV
Ibeam dt , kC
R
Ldt , pb−1
R
θe ±
Run II
MA
SA
LA
MA
1.6
1.0
54
100
320
600
55◦ ÷75◦
15◦ ÷25◦
8◦ ÷15◦
65◦ ÷105◦
15◦ ÷25◦
Q 2 , GeV2
1.26÷1.68
0.16÷0.41
0.05÷0.16
0.71÷1.08
0.07÷0.17
ε
0.37÷0.58
0.90÷0.97
0.97÷0.99
0.18÷0.51
0.91÷0.97
1.1%
0.1%
0.3%
∆R /R ,
stat.
The smallest angle regions were used for luminosity monitoring only.
I.A. Rachek
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11
Detector Package for the Run I
wide aperture non-magnetic apparatus
ϑe acceptance:
ϕe acceptance:
I.A. Rachek
8◦
2
÷ 13◦
× 60◦
,15◦
÷ 25◦
and 55◦
÷ 75◦
Baryons-2013
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12
Detector Package for the Run II
e
NaI
CsI
*
*
Drift chambers
Proportional
chambers
CsI
NaI
e+/e- beam
E = 1 GeV
Storage cell
(hydrogen target)
Scintillators
* (polystyrene)
p
*
CsI
*
NaI
ϑe acceptance:
ϕe acceptance:
I.A. Rachek
0.5 m
15
2
◦
×
÷ 25◦
and 65
◦
÷ 105◦
◦
60
Baryons-2013
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13
Suppression of the systematics: alternation of
During data collection
e−
and
e+
beams were swapped regularly. This allows us to suppress
eects of slow drift in time of the target thickness, detection eciency
e
One cycle ( + and
e−
e − and e +
etc.
beams) per 1 hour approximately.
1100 cycles in Run I, 2350 cycles in Run II
Starting and ending values of beam currents and beam lifetime for
e−
and
e+
beams in each
cycle were kept as close as possible.
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14
Suppression of the systematics: beam position
Using the VEPP3 beam orbit stabilization system.
Continuous measurement of the beam position at the entrance and exit of the experimental
section by pick-up electrodes.
Periodical absolute beam position measurements using movable shutters.
Determination of beam position in the target from data analysis.
Two symmetrical sets of detector arms: the sum is insensitive to vertical shifts of
e
e
( + / − )-beams.
Measurement of beam position by the
I.A. Rachek
Baryons-2013
2P3
pick-up electrode:
June 24, 2013
15
Suppression of the systematics: beam energy
Reconstruction of beam energy (at
∼ 0 .1
MeV accuracy) from
an energy spectrum of laser photons backscattered on beam
particles.
Ebeam = 0.5 · ωmax ·
1
+
q
1
+ me2 /ω0 ωmax
This allows us to tune the VEPP3 operation regimes and to
monitor the beams energy during the experiment.
VEPP3 energy measurement
- positrons
1 MeV
- electrons
I.A. Rachek
Baryons-2013
photon spectrum
June 24, 2013
16
Suppression of the systematics: No Magnetic Field!
Non-magnetic Detectors
Magnetic_eldfree target area
⇒ Exactly identical acceptance for electrons and positrons
Entries
Run II
142644
3500
3000
e--p
e+p
2500
2000
1500
1000
500
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
epsilon
I.A. Rachek
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17
Suppression of the systematics: No Magnetic Field!
Non-magnetic Detectors
Magnetic_eldfree target area
⇒ Exactly identical acceptance for electrons and positrons
Entries
Run II
142644
3500
3000
e--p
e+p
2500
2000
1500
1000
500
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
epsilon
Total systematic error is < 0.3%
I.A. Rachek
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June 24, 2013
17
Selection of the elastic scattering events
correlations characteristic for two-body nal state:
φp ) → coplanarity
θp ) → collinearity in CM
angle and proton energy (θe ± vs. Ep )
angle and electron energy (θe ± vs. Ee ± )
e
Correlation between azimuthal angles (φ ± vs.
e
Correlation between polar angles (θ ± vs.
Correlation between lepton scattering
Correlation between lepton scattering
particle ID:
Time-Of-Flight analysis for low-energy protons
∆E E
analysis for middle-energy protons
Energy deposition in EM-calorimeter for electrons/positrons
angular correlations
φ-angles correlation
Entries
77505
4000
3500
GEANT4
3000
DATA
2500
2000
σ = 0.7o
1500
1000
500
0
176
178
180
182
Θ-angles correlation
184
ϕe - ϕp, deg
Entries
64809
2500
GEANT4
2000
DATA
1500
σ = 0.8o
1000
500
0
-4
-2
0
2
4
θp - θp(e), deg
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18
Standard radiative corrections: new event generator
Elastic Scatterring of Electrons and Positrons on Proton
ESEPP
A. Gramolin
more precise calculation of bremsstrahlung instead of soft photon approximation (Fadin,
Gerasimov, and Feldman)
evaluation of the bremsstrahlung with excitation of
∆-isobar
generator used for simulation of the detector with GEANT4
Comparison of the results of calculations
γµ
1.07
Soft photon approximation (SPA)
Γµ
Calculation by Fadin & Feldman (FF)
1.06
elastic electron
scattering
electron vertex
correction
electron self-energy
diagrams
Calculation by Fadin & Gerasimov (FG)
vacuum
polarization
proton vertex
correction
proton self-energy
diagrams
box and crossedbox diagrams
Ratio RMC
1.05
1.04
1.03
1.02
1.01
inelastic amplitudes
1
0
from Maximon&Tjon PRC 62(2000)054320
2
4
6
8
Cut on angular correlation (∆θ = ∆φ), degree
10
http://www.inp.nsk.su/~gramolin/esepp/
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19
Radiative Corrections for
e± Ratio
1.08
R
as a function of kinematic cuts
e± Ratio
No Rad Corr
1.08
e± Ratio
Mo&Tsai
dipole FF
1.08
1.07
1.07
1.06
1.06
1.05
1.05
1.04
1.04
1.04
1.03
1.03
1.03
1.02
1.02
1.02
1.01
1.01
1.01
1
0.26
1.07
∆=1.5
o
∆=3.0
o
∆=6.0
o
1.06
1.05
1
0.36
epsilon
0.46
0.26
Maximon&Tjon
Puckett FF
1
0.36
epsilon
0.46
0.26
0.36
0.46
epsilon
RUN II: single point with various event selecting angular correlation cuts
Left panel before any RC applied big dierence!
Middle panel conventional Mo&Tsai approach for RC, proton FF in dipole form
Right panel approach of Maximon&Tjon, proton FF parametrization by Puckett
I.A. Rachek
Baryons-2013
et al.
June 24, 2013
20
MC simulation of background processes
GEANT4
detector model
MAID2007 and 2-PION-MAID based event generator for single- and double-pion
electro-production
ESEPP
event generator for elastic
(ep)
scattering with bremsstrahlung
Missing mass spectrum, reconstructed from energy and direction of particle detected in LA arm,
assuming this is
elastic scattered e −
soft cut on
e
(for E ±
=1
GeV)
(∆φ, ∆θ)
DATA and ESEPP+MAID2007+GEANT4
∆φ,∆θ < 6.0
o
8000
e p → e' p (γ )
7000
5000
e p → e' n π+
e p → e' p π0
+
γ* p → n π
-γ * p → p π π+
4000
MC Total
6000
DATA
3000
2000
1000
0
700
800
I.A. Rachek
900
1000 1100 1200 1300 1400 1500 1600 1700
Missing Mass, MeV
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MC simulation of background processes
GEANT4
detector model
MAID2007 and 2-PION-MAID based event generator for single- and double-pion
electro-production
ESEPP
event generator for elastic
(ep)
scattering with bremsstrahlung
Missing mass spectrum, reconstructed from energy and direction of particle detected in LA arm,
assuming this is
elastic scattered e −
standard cut on
e
(for E ±
=1
GeV)
(∆φ, ∆θ)
DATA and ESEPP+MAID2007+GEANT4
∆φ,∆θ < 3.0
o
e p → e' p (γ )
7000
5000
e p → e' n π+
e p → e' p π0
+
γ* p → n π
-γ * p → p π π+
4000
MC Total
3000
DATA
6000
2000
when all cuts applied:
1000
0
700
Nbackground /Nelastic < 1.5%
800
I.A. Rachek
900
1000 1100 1200 1300 1400 1500 1600 1700
Missing Mass, MeV
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21
Comparison of Three TPE Experiments
VEPP-3
OLYMPUS
EG5 CLAS
Novosibirsk
DESY
JLab
Beam energy
2 xed
1 xed
wide spectrum
equality of e± beam energy
measured
assumed
reconstructed
precisely
(measured?)
half-hour
8 hours
e + /e −
e + /e −
swapping frequency
lumi monitor
elastic low-Q2
elastic low-Q2 ,
simultaneously
from simulation
Möller/Bhabha
energy of scattered e±
proton PID
e + /e −
detector acceptance
luminosity
systematic error
EM-calorimeter
∆E /E ,
TOF
mag. analysis
mag. analysis
mag. analysis, TOF
mag. analysis, TOF
identical
big dierence
big dierence
1.0
2.0
2.5
× 1032
< 0.3%
× 1033
1%
× 1032
1%
Novosibirsk experiment is inferior to the other two in experimental luminosity and in quality
of particle ID;
however, the detector performance is sucient for reliable identication of elastic scattering
events;
non-magnetic detector, measurement of beams energy, frequent swapping of
e + /e −
beams
allow lowest systematic error;
Novosibirsk is the rst to provide results on precise measurement of
I.A. Rachek
Baryons-2013
R (e ± p ) ratio.
June 24, 2013
22
Preliminary results of the Novosibirsk TPE experiment
Run I (2009):
Run II (20112012):
GeV
Anderson (1966)
Bartel (1967)
Anderson (1968)
VEPP-3 (Run 1), preliminary
0.95
Ratio R
Theory (Blunden et al.), E = 1 GeV
Theory (Tomasi-Gustafsson et al.), E = 1 GeV
Theory (Borisyuk&Kobushkin), E = 1 GeV
Coulomb corrections (Arrington et al.), E = 1 GeV
0.9
0
0.2
2
Theory:
0.4
ε
0.6
1.5
Q2, GeV2
0.8
1
1.05
P. G. Blunden, et al.,
D. Borisyuk and A. Kobushkin,
E. Tomasi-Gustason, et al.,
J. Arrington and I. Sick,
M
1
AR
Y
0.9
0
IN
Browman (1965), E = 0.85 GeV
Anderson (1966), E = 1.2 GeV
Anderson (1968), E = 1.2 GeV
Bouquet (1968), E = 0.981 GeV
VEPP-3 (Run 2), preliminary
Theory (Blunden et al.), E = 1 GeV
Theory (Tomasi-Gustafsson et al.), E = 1 GeV
Theory (Borisyuk&Kobushkin), E = 1 GeV
Coulomb corrections (Arrington et al.), E = 1 GeV
0.95
1
0.5
normalization point
(standard RC applied)
Ratio R
IM
IN
AR
Y
1
PR
EL
I
GeV
1.1
(standard RC applied)
PR
EL
1.1
1.05
=1
Ebeam
normalization point
= 1.6
Ebeam
0
0.2
1.2
0.4
1
ε
0.6
0.8
0.6
Q2, GeV2
0.8
0.4
1
0.2
0
Phys. Rev. C72 (2005) 034612 :hadronic TPE calculation
Phys. Rev. C78 (2008) 025208 :dispersion relations
arXiv:0909.4736
:analytical model
Phys. Rev. C70 (2004) 028203 :Coulomb corrections
error bars are statistical errors, hashed areas show -range and systematic uncertainties;
the standard radiative corrections are taken into account.
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23
Run II data versus theoretical calculations
Run-II data at large scattering angle in a single point:
Run II
Entries 234891
3500
Blunden et al
1.06
3000
Borisyuk&Kobushkin
Ratio R
(standard RC applied)
1.05
Arrington&Sick
counts
2500
Tomasi-Gustafsson et al
2000
1500
1000
500
Run II, preliminary
1.04
0
0
syst errors & ∈-range
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
epsilon
1
1.03
1.02
points on theoretical
1.01
curves are weighted
means, obtained with
experimental
1
0.99
epsilon-distribution.
0
I.A. Rachek
0.1
0.2
0.3
0.4
ε
0.5
0.6
Baryons-2013
0.7
June 24, 2013
24
Conclusion
A precision measurement of the ratio R
= σ(e + p )/σ(e − p )
has been
performed. Data taking has been completed, analysis is in nal stage.
Systematic errors in VEPP-3 experiment is expected to be lower than
those at OLYMPUS and CLAS TPE experiments.
It is very important to carefully consider the standard radiative
corrections. Procedure of account for RC has been developed (ESEPP
event generator
+
Geant4 detector simulation).
Preliminary (nearly nal) results are presented. They are overestimated
by the theoretical predictions of Blunden et al and Borisyuk&
Kobushkin, but are underestimated by Tomasi-Gustafsson et al.
Final results of the experiment are expected by the end of 2013.
Support
This work was supported by Ministry of Education and Science of the Russian Federation; RFBR grants:
08-02-00624-a, 08-02-01155-a; Russian Federal Agency for Education, State Contract P522; Russian Federal
Agency for Science and Innovation, Contract 02.740.11.0245.1;
US DOE grant: DE-AC02-06CH11357; US NSF grant: PHY-03-54871
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