1. Proposal for high precision measuremens of
the e-p differential cross section at small t-values
with the recoiled proton detector
Rp = fm or Rp =0.841 fm ???
A.Vorobyev Petersburg Nuclear Physics Institute
Mainz April 6, 2016
Meeting at Mainz April 6, 2016

2. Proposal for high precision measuremens of
the e-p differential cross section at small t-values
with the recoiled proton detector
Rp = fm or Rp =0.841 fm ???
To buy or not to buy ?
A.Vorobyev Petersburg Nuclear Physics Institute
Mainz April 6, 2016
Meeting at Mainz April 6, 2016

3. The main goal of the proposed experiment
To measure absolute dσ/dt
in the t-range – Gev2
with
≤ 0.2% point -to-point precision
≤ 0.2 % absolute precision
This could distingwish the two options
(0.887 fm and fm) on the 7σ confidence level
~1/t2
0.001
0.04
-t,GeV2
0.02
-t = 2MTR

4. The proposed experiment is based on
the recoiled proton detection method
which was used in WA9 and NA8 experiments
at CERN to measure small angle pp- and πp- scattering.
RecoiIed proton detector ICAR at CERN

5. Detector ICAR in WA9/NA8 experiments at CERN
Time-projection hydrogen ionization chamber
Active target
+10 kV
0kV
-15 kV
H2 10 bar
Drift velocity:
(1±0.003) mm / 200 ns
σ(z) : ± 300 µm
Gas target thickness: ± 0.4%
-t = (Pπ θS )2 E π θS π
106 /sec p
TR- proton energy
σ(TR) = 70 keV
σ(θR) = 2 mrad (≥4MeV)
-t = 2MpTR
100,0±0.1 mm

6. Advantages and problems of the recoil method
-t = (Pπ θS )2 π π
No wall effects
Well defined gas target thickness
100% angular acceptence
Absolute measurement of dσ/dt
-t = 2MpTR
High resolution in TR (>100 resolved points in to 0.04 GeV2)
t - value does not depend on the scattering particle’s energy
TR – θS correlation (BG rejection)
θR –measurement (additional constraint)
However, TR scale needs to be precisely calibrated !!!

7. 0.4% TR-scale calibration 1% absolute precision in dσ/dt
An example from cross sections of πp- and pp- scattering measured with ICAR
Nuclear Physics B217 (1983)
ρ= ReA(0)/ImA(0)
b = dσ/dt(t=0)
0.4% TR-scale calibration
1% absolute precision in dσ/dt

8. Measurements of ReA(0)/ImA(0) in π-p scattering confirmed the validity of the forward dispertion relations and allowed to predict the rise of the πp total cross sections at least up to energy of 2000 GeV.
Nuclear Physics B217 (1983)
ρ= ReA(0)/ImA(0) in π-p scattering
π±p total cross sections

9. Measurements of dσ/dt(t=0) in πp- and pp-scattering discovered Universal shrinkage of the hadronic diffraction cone at high energies with α’P=0.14 GeV-2
Nuclear Physics B217 (1983)

10. Study of elastic scattering of exotic nulei on proton
Nuclear Physics A766 (2006)1-24
11Li
11Li p
4He, 6He, 8He
6Li, 8Li, 9Li, 11Li
7Be, 9Be, 10Be,11Be, 12Be, 14Be 8B
13C,14C,15C,17C.
ICAR in GSI 10

11. Extraction of proton radius from differential e-p cross section
0.002
0.04
-t,GeV2
0.02
-t = 2MTR

12. Difference between cross sections corresponding to Rp=0.84 fm and Rp=0.88 fm
RpE =RpM=0
Electrons 500 MeV
RpE =RpM=0.84 fm
RpE =RpM=0.88 fm
Main t-range:1MeV ≤ TR ≤ 10MeV
Measurements up to TR =20 MeV
help to see non-liniarity effects
∆ Rp = 1.2% at TR =10 MeV
0.2% precision in dσ/dt is needed
to distingwish reliably the two options

13. Problems of large scattering angles
Pe = 500 MeV/c eS e θS
-t=2MTR θR p
Sin(θR) = (εe+М)ТR /(РeРR)

14. Combined recoiled proton @ scattering electron detector
H2 20 bar
Film separating volumes
Ar+CH4 20 bar
e-detection coordinates
σX = σY = 30µm
0.5 mm Be window
σ(θS) ≤ 5 ·10-4
-15 kV
-90kV
-15kV
Scattering point coordinates
σX = σY = 30µm ( determined by beam telescope)
σZ = 150 µm (determined by TPC)

15. Why 20 bar ? To stop 10 MeV protons inside the sensitive volume.
Also, to increase counting rate.
P=20 bar
10 MeV TR
MeV R mm 1
4,7 2 16 3 33 4
55.5 5
83.5 6
116 7
154 8
196 9
244 10
296
20MeV
1MeV
5 MeV
Diam 700 mm

16. Lower pressure can be used for measurements at the lowest t-values with better TR resolution
4 MeV
P=4 bar TR
MeV R mm 1
23.5 2 80 3
165 4
277
3 MeV
2 MeV
1 MeV
Diam 700 mm

17. H2 20 bar
Ar+CH4 20 bar
Mylar foil
TPC
Electron detector
CSC

18. CSC
TPC

19. Gas pressure up to 20 bar
Pressure control 10-4
Temperature control 0.1 deg
H2 purity
Diameter 1 meter
Length meters

20. Comparison of the TPC parameters in the WA9/NA8 experiments with those in the proposed experiment
H2 pressure
10 bar
20 bar, 4 bar
Drift distance, mm
100,0 ± 0.1
300,0 ± 0.1
Drift velocity,mm/200ns
1,000 ± 0,003
1,000 ± 0,001
σ(z-coordinate)
±300µm
±150µm
σ (target thickness)
0.4%
0.1%
σ (TR)
60 KeV
40 KeV
TR-scale calibration
0.5%

21. TR –scale calibration - t = 2MTR
To determine t with 0.1 % precision from the scattering angle
one should provide better than 0.05% absolute precision
both in θs and in Ee . !!!
Request to the accellerator
Absolute value of Ee better than 5·10-4

22. Measurement of absolute value of beam momentum
NIM 177(1980)
Gas filling
He(90%) + H2 (10%)
(P*θ)2 = 2MTR
234 U Eα
4 774,6 кэВ (71,38 %
Absolute precision
σP= 0.05%

23. Possible TPC calibration in hadronic beams
For example, in a proton beam at Gatchina synchrocyclotron.
ep- scattering MeV
Advantages: \
Flat dσ/dt.
Higher rates
Higher precision.
Goal :
Calibration of TR –scale
to 0.1% precision
pp-scattering 250 GeV
-t=2MTR

24. Statistics and beam time
Target thickness = 5.2·1022 p/cm2
P =20bar L =50cm
Beam intensity 2·106 sec-1
Running time 18 days (1.5 ·106 sec)
N events
norm
t-scale
σ(Rp)
1.5 ·107
fixed to 1
fixed
± fm
free
± fm
Goal: σ(Rp) ≤ ± fm

25. Radiative corrections

26. Radiative corrections
Two advantages
Wide kinematic range, experimental cuts can be varied offline
• Control of radiative corrections at the smalles t –values by absolute measurement of dσ/dt.

27. Conclusions
The proposed experiment could provide measurements of the ep- elastic cross sections in the t-range from to 0.04 GeV2 with 0.2% point-to-point and 0.2% asolute precisions.
This would allow to extract the proton radius with 0.5% precision
This experimental method could be applied also to study the small
angle scattering on deuterium and 4He.
Also, there is a possibility to extend the t-range up to 0.08 GeV2
by filling the TPC with CH4.

28. Back up slides

29. Vacuum polarization correction
Q2 GeV2
e-loop
µ-loop
0.002
1.13%
0.02
1.49%
0.048%
0.04
1.59%
e,µ,τ

30. Electron vertex correction
Q2 Gev2
δvertex
0.0001
-2.12%
0.002
-6.26%
0.02
-10.85%
0.04
-12.46%

31. Real photon emission by electronsln
Sp(0)=0
Sp(1)= π2/6

32. Partial mutual cancellation of δV and δR
δV +δR = δV +δR(1 )+δR(2) =
= α/π {3/2 ln(Q2/m2) -2} + α/π {ln(∆E2/EE`) ln(Q2/m2) }
Q2 Gev2
δV +δR(1 )
δR(2)
∆E/E=0.1
0.0001
1.6%
-6.3%
0.002
2.65%
-9.58%
0.02
3.43%
-12%
0.04
3.69%
Note that δR(2) depends on the experimental conditions (cuts).
Hope in our experiment it will be much less and controlable
( the cuts mostly off-line )

33. Two Photon Exchange correction
example:
Pe =500 Mev, Q2 = 0.02, θ = 16 deg, ε = 0.98,
a and b were free parameters in the fits and were
obtained to be a ≈ 0.1 and b ≈ 0.4 GeV-2
Therefore δTPE ≈ 10-5 at Q2 =0.02 GeV2

34. Corrections with proton contributions
Relatively small corrections
But to be understood

35. ∆Es cuts in A1
855 MeV

37. e-p - Scattering Layout Block Diagram
RPD
ESD
HV1
RPD_FE
ESD_FE
RPD_LOG BD
BD_FE BK X Y
ESD_LOG
BK_LOG
CRB
Ethernet
Beam
RST TR
ESD (RQ; DT; CL)
RPD (RQ; DT; CL)
BD_FE - Beam Detector Front-End RPD_LOG – RPD Logic
RPD_FE – Recoiled Proton Detector Front-End ESD_LOG = TSD Logic
ESD_FE – Electron Scattering Detector Front-End BK_LOG – Beam Killer Logic
CRB – Control Readout Box
TR – Trigger, RQ – Request, DT – Data, CL – Clock, RST - Reset
e-p - Scattering Layout Block Diagram

38. Fig.2 e-p - Scattering Trigger, Control & Readout Timing Diagram
DATA ENCODING &
READOUT REQUEST
100 ns
ESD: RQ
~ 70 mks
RPD: CL
~ 10 mks
TRIGGER
TR = BD·BK
ESD: DT
RPD: RQ
RPD: DT
ESD: CL
RST
READOUT
TR Reset if no ESD_DT
Fig.2 e-p - Scattering Trigger, Control & Readout Timing Diagram