1. Update: Proton charge radius Experiment (PRAD)
Zhihong Ye
Duke University
CLAS Collaboration Meeting
03/06/2014
Hello everything, My name is Zhihong Ye from Duke Univ. I was asked to give this talk on Tuesday so it is a post-deadline talk. I hope I won’t keep you too long so I will try to make it short. My talk is about the status update of the Proton charge radius experiment, or Prad.

2. Physics Motivation About “Proton”:
It is one of the primary building blocks of all visible matter
It has finite size – a bag of quarks and gluons
It has a fuzzy boundary
We want to know the charge radius of the proton:
A precise test of QED
Understanding QCD in the non-perturbative region
So why we care about proton and its charge radius. Well, because it is one of the primary blocks of all visible matter in the universe. It is not a point-like particle, but consisted of quarks and gluons, and has a fuzzy boundary.
We want to know what is the charge radius of the proton, so we can test the QED calculation and compared with other more precious measurement, like lamb shift. And we also can understand the QCD in the non-perturbative region.
In nowadays, there are three major experimental techniques to measure the proton charge radius, ….
Three major experimental methods:
Electron-Proton elastic scattering  Electric Form Factor
Hydrogen spectroscopy (Lamb Shift)  CODATA
Muonic Hydrogen spectroscopy (Lamb Shift)

3. Charge Radius from Form Factor:
Assuming static charge distribution
In Breit frame, the Fourier transform of the charge distribution gives form factor:
With
Why the form factor can give us the charge radius?
Assuming the proton has a static charge distribution p(r), we can perform a Fourier transform in the Breit Frame, to correlate the charge radius and the form factor. If the charge distribution only depends on the radius, the formula can be simplified as these polymonius terms. Ignoring all high order term, the r.m.s. charge radius can be given by this fomular, where I use the Sachs charge Form Factor.
The proton r.m.s. charge radius can be obtained from:
Sachs Form Factor
, where

4. How to measure the Form Factor:
Unpolarized e-p elastic scattering:
Polarized e-p scattering:
Rosenbluth Separation
GMp can be ignored
where
There are two major way to obtain the form factors through the electron scattering experiment. For the unpolarized e-p elastic scattering, we can use the Rosenbluth Separation to extract both GE and GM. At low Q2, the GM term can be ignored.
In the polarized e-p scattering measurement, we use the polarized electron beam to hit on the proton target, and measure the polarization of the scattered proton, then we can use the super ratio to obtain the Gep and Gmp.
where are the transverse and longitudinal polarization of the proton.

5. Recent e-p Scattering Experiments
(slide from Haiyan)
Mainz
The most recent ep scattering experiment using Rosenbluth method was carried at at Mainz. It obtained large amount of overlapping data set with very small statistic errors, and cover a wide range of Q2.
– Large amount of overlapping data sets
– Statistical error ≤ 0.2%
– Luminosity monitoring with spectrometer
Q2 = – 1.0 (GeV/c)2
result: rp =0.879(5)stat(4)sys(2)mod(4)group
J. Bernauer, PRL 105,242001, 2010

6. JLab Recoil Proton Polarization Experimental
(slide from Haiyan)
Δp/p0: ± 4.5% ,
out-of-plane: ± 60 mrad
in-plane: ± 30 mrad
ΔΩ: 6.7msr
QQDQ
Dipole bending angle 45o
VDC+FPP
Pp : 0.55 ~ 0.93 GeV/c
LHRS
Focal-plane polarimeter
Ee: 1.192GeV
Pb: ~83%
BigBite
The polarized e-p scattering measurements were performed at BLAST and recently used in the hall-A experiment. We used the LHRS to detect proton, where the polarization was measured by the focal-plane polarimeter. The BigBite spectrometer was used to detect the scattered electrons.
Non-focusing Dipole
Big acceptance.
Δp: MeV
ΔΩ: 96msr
PS + Scint. + SH
X. Zhan et al. Phys. Lett. B 705 (2011) 59-64
C. Crawford et al. PRL98, (2007)

7. Charge Radius from Hydrogen Lamb Shift:
The absolute frequency of Hydrogen energy levels has been measured with very high accuracy.
Since Hydrogen is a very simple system, its energy levels can be precisely calculated in QED with correction for the finite size of the proton.
If the proton is point-like, Corrected for the finite size,
The energy level is related to the proton charge radius:
In atomic physics, people measure the Hydrogen Lamb Shift to obtain the proton charge radius. The basic idea is that, for a very simple atom like hygrogen, the absolute frequency of Hydrogen energy level can be measured with very high accuracy.
And the QED can precisely calculate the energy level with the correction for the finite size of the proton. For example, if the proton is point-like, the potential can be given by this well known formula, with the finiate size correction, the proton charge radius goes in. The energy difference between two states is directly connected to the proton charge radius. In this formula, the ml can be either the mass of the electron or the mass of the muon. Since the muon mass is 200 times larger than the electron, the muonic hydrogen lamb shift should give us a much more precise measurement of the proton charge radius.
where mlme for electrons, or mlmu for Muons.
Since mu=200me, Muonic Hydrogen Lamb Shift gives much more precise measurements
Comparing the measurements and the QED calculations can determine the proton r.ms. Charge radius with high resolution.

8. Muonic Hydrogen Lamb Shift Experiment at PSI
This kind of measurement has been carried out at PSI and the result was published in the Nature magazine. They used the muon beam to hit on the Hydrogen target and the muon replaced the electrons and formed the mounoic hydrogen. They used the laser to pump the muon state to a higher energy level, 2p and measure the spectrum when the muon decayed to the ground state.

9. Charge Radius Results:
The proton radius puzzle!
The results from Muonic Lamb Shift measurements are 7-σ away from the e-p elastic measurements and electronic Hydrogen Lamb Shift.
The value of the charge radius obtain from the muonic lamb shift measurement were compared with the traditional measurement, like the e-p elastic scattering and the electronic hydrogen lamb shift. As you can see, the charge radius is 7 sigma less than all other measurements. We refer it as the proton radius puzzle. The most recent muonic lamb shift measurement also give a similar result.
To solve this puzzle, there are seveal experiments have been proposed and in Hall-B at Jefferson, we proposed a new electron elastic scattering experiment to measure the proton charge radius with high resolution.

10. PRad Experiment
High resolution, large acceptance, hybrid HyCal calorimeter (PbWO4 and Pb-glass)
Q2 range of 2x10-4 – 2.0x10-2 GeV2 (lower than all previous electron scattering experiments.)
Simultaneous detection of elastic and Møller electrons
Windowless H2 gas flow target
XY – veto counters
Vacuum box, one thin window at HyCal only
Here are the experimental setup.
Spokesperson: A. Gasparian,
Co-spokesperson: D. Dutta, H. Gao,
M. Khandaker

11. High Resolution Calorimeter (HyCal):
A PbWO4 and Pb-glass calorimeter
2.05 x 2.05 cm2 x18 cm (20 rad. Length)
1152 modules arranged in 34x34 matrix at the central region
5 m from the target, and 0.5 sr acceptance
The major detector we are going to use is the High Resolution Calorimeter

12. Windowless Gas Flow Target:
Target thickness1.0 x 1018 atoms/cm2 at 25K
Target supported by NSF - MRI grant
One of the most important applications in this experiment is the windowless gas flow target. For high precision experiment, the target windows are always the majored source of background, in practically when we use the gas target, like the hydrogen gas.
To avoid this background, we are developing a windowless gas target, with the help from the Jlab target group. This cartoon shows the design of the target cell, the hydrogen gas goes into the tube from the top, and there are two holes on each end of the tube with the diameter of 4mm to allow the beam goes through. The target density with this design will be 1 x 10^18 at 25K.
Target windows are the major sources of background for typical magnetic spectrometer experiments
PRad will avoid this background by developing a new windowless target cell
Working closely with JLab target group to design and build this target.

13. Simulation Windowless Gas Flow Target: (Simulations by Y. Zhang/Duke)
windowless target
5608 sccm
2nd stage,
1500 Lt/s Trubo Pump
1st stage, 3000 Lt/s
Turbo Pump
2nd stage
1500 Lt/s Trubo Pump
From this plot, you can see the preliminary design of the target system – the target chamber at the center is connected with two secondary chambers on each end. Three chambers are connected to powerful vacuum pumps.
Our graduate student Yang Zhang performed a simulation of this target. The simulations show that we are able to achieve the desired target density at 3.43 x 10^18. We are working closely with Josh Piers from the target group to construct this target.
Simulation
Target density was studied by COMSOL Multiphysics
Simulations show that the desired densities can be achieved.
Thickness at the center: 3.42 x 1018 H/cm2
Target construction well underway.

14. Position Detector:
PRad aims to measure GEp at very low Q2. The high precision of angular measurements at very forward direction is crucial.
Angles are determined by the position of the scattered electron.
HyCal provides 2.5 mm position resolution which gives 7% uncertainty of Q2 measurement at 10-4 GeV2.
We are working on designing a new position detector which must has the features:
Thin  Not too much space
Minimum radiation materials  Control the background events at a small level.
Allow a hole at the center to allow the electron beam goes through
If you were in this week’s Hall-B meeting, you may still remember this project I presented. …
Possible candidates: GEM, Drift Chambers, and Scintillator Fiber Tracker (SFT).

15. BNC->LEMO (Ribbon?)
Position Detector: Scintillator Fiber Tracker
Use 1mm scintillator fibers which gives 0.3 mm position resolution
Use Silicon Photomultipliers (SiPMs) as read-outs.
Replace Veto-Counter; Provide timing and position at the same time.
Thin, light weight, relatively easy to build.
A prototype is developing to study the design of the full SFT.
Y-Plane
1300 mm
SFT Prototype (Not to Scale)
50 mm
100 x Pre-Amplifiers
100 x FastBus
ADC
50 x SiPMs
X-Plane
100x long
BNC->LEMO (Ribbon?)
1300 mm
50 mm
Analog Signals
Receiving great helps from all four halls. Special thank to Stepan and other Hall-B staffs.
See my talk in this week’s Hall-B meeting minutes.
100 x NIM Discriminators
100 x FastBus
TDC
Power
Supplies
50 x SiPMs
100x short
BNC-LEMO
100x long
Ribbon Cables
Analog Signals

16. Extracting the e-p elastic cross sections:
Will detect e-p and Møller electrons simultaneously
Extract e-p->e-p event yields
Same for e-e->e-e
Normalizing the ep cross section to the Møller:
Main sources of systematic uncertainties Nbeam and Ntgt
other sources can be canceled out in the normalization.
In this experiment we will measure the ep elastic cross section and extract the Gep values at low Q2. To obtain the cross sections, we will detect both the e-p scattering electrons and the Molle scattering electrons at the same time.
Since the Moller scattering cross sections are well known, we will use the yield ratio method to normalize the ep cross section to the Moller cross section. With this method, the main source of the systematic uncertainties will be from the beam and the target.

17. Simulation Extracting the e-p elastic cross sections:
Will detect e-p and Møller electrons simultaneously ep
Extract e-p->e-p event yields
Same for e-e->e-e
0.8 degree line
Normalizing the ep cross section to the Möller:
Møller
These simulation plot basically tell you how the ep events and the moller event distribute. Ep events have a narrower energy distroubtion compared with the moller event. We will perform the angle-binning above 0.8 degree to extract the yields of the two processes.
Simulation
Main sources of systematic uncertainties Nbeam and Ntgt
other sources can be canceled out in the normalization.

18. preliminary Beam Halo: Signal to noise ratio of 107.
Can be improved with fine tuning of the accelerator
Add a collimator in front of the target?
preliminary
Halo e-
Target cell
This experiment will run with a very low rate since we use 15uA beam and a gas target, so the beam halo becomes a significant source of background. The beam halo refer to as the beam having a large spread in diameter and hitting on the target cell and other objects. We can improve the suppression of beam halo by asking the accelerator site to perform a fine tune of the beam. We are also considering to add a collimator in front of the target.
Beam e-

19. Simulation Simulation GEANT4 Simulation: (by Chao Peng/Duke)
A detailed study of backgrounds and radius extraction.
Subtraction has been performed using this simulation
Study shows that we need 20% beam time for empty target runs
Empty target
Full target
Simulation
We have developed a Geant4 simulation package to simulate this experiment setup, to understand the background with different setup, and study the procedure of radius extraction. The study shows that we need 20% of the beam time to run empty target if we want to properly subtract the background.
Simulation

20. Simulation Simulation GEANT4 Simulation: Input radius, rp = 0.8768 fm
(by Chao Peng/Duke)
Better precision anticipated by extending the Q2 range using Pb-glass part of calorimeter, and adding position detector
Input radius, rp = fm
Including lead glass part up to 10 deg
rp = (50) fm
Including 3.3 GeV beam up to 4 deg
rp = (52) fm
During the simulation study we also learn that to improve the precision of the radius extraction, we can extend the Q2 by using the Pb-glass part of the HyCal which provide wider angles. As I mentioned earlier, we are also considering to add a position detector to improve the angular measurement.
Simulation
Simulation

21. Simulation Radiation Correction: (by M. Meziane/Duke)
ep elastic radiative corrections were simulated using ELRADGEN1
Møller radiative corrections were simulated using MERADGEN2
Both are modified to include the electron mass
1 I. Akushevich, O. Filoti, A. Ilyichev, and N. Shumeiko,
arXiv:hep-ph/ v1, (2011).
2 A. Afanasev, E. Chudakov, V. A. Zukunov and A. N. Ilyichev,
Comp. Phy. Comm, 176, 218 (2007) ep ep
Simulation
The radiation correction will be another important task to extract the ep elastic cross sections and also the Moller cross section. We used two packages to perform the radiation correction of these two processes.
Møller
Møller

22. Møller cross section ~2-3%
Radiation Correction:
(by M. Meziane/Duke)
ep elastic radiative corrections were simulated using ELRADGEN1
Møller radiative corrections were simulated using MERADGEN2
Both are modified to include the electron mass
1 I. Akushevich, O. Filoti, A. Ilyichev, and N. Shumeiko,
arXiv:hep-ph/ v1, (2011).
2 A. Afanasev, E. Chudakov, V. A. Zukunov and A. N. Ilyichev,
Comp. Phy. Comm, 176, 218 (2007)
Correction to the
Møller cross section ~2-3%
The package shows that at the 1GeV and 2GEV electron beam, the correction for ep can be up to 13%, while for the moller part, the correction would be 2 to 3%
Corrections to the
ep cross section: ~8 -13%

23. Status & plan
Windowless target design is nearly done. Target vacuum pump, motion system, chiller and cryo-cooler are in hand.
The target & secondary chambers are under production in Germany.
The HyCal will be refurbished soon.
A prototype of a new Scintillator Fiber Tracker (SFT) is being developed. The SFT will improve the Q2 resolution by a factor of 3.
Geant4 simulation is undergoing smoothly to study the background, systematic uncertainty and so on.
Experimental techniques to suppress beam halo are under discussion, e.g. adding a collimator
Radiation Correction can be well handled.
Still many things are needed to finished but we are working very hard to make the experiment ready!

24. Thank you!
This project is supported by DOE under the contract# DE-FG02-03ER41231 and NSF MRI award PHY

25. Estimated Uncertainty (%) Acceptance (including Radiative corrections
Expected Uncertainties
Contributions
Estimated Uncertainty (%)
Statistical
0.2
Acceptance (including
Q2 determination)
0.4
Detection efficiency
0.1
Radiative corrections
0.3
Background and PID
Fitting
Total
0.6