PRad-II: A New Upgraded High Precision Measurement of the Proton Charge Radius
A. Gasparian, H. Gao, D. Dutta, N. Liyanage, E. Pasyuk, D. W. Higinbotham, C. Peng, K. Gnanvo, W. Xiong, X. Bai, PRad collaboration
PPRad-II: A New Upgraded High Precision Measurement of the Proton Charge Radius
A. Gasparian ∗ , † , H. Gao † ,
2, 3
D. Dutta † , N. Liyanage † , E. Pasyuk † , D. W. Higinbotham † , C. Peng † , K. Gnanvo † , I. Akushevich, A. Ahmidouch, C. Ayerbe, X. Bai, H. Bhatt, D. Bhetuwal, J. Brock, V. Burkert, D. Byer, C. Carlin, T. Chetry, E. Christy, A. Deur, B. Devkota, J. Dunne, L. El-Fassi, L. Gan, D. Gaskell, Y. Gotra, T. Hague, M. Jones, A. Karki, B.Karki, C. Keith, V. Khachatryan, M. Khandaker, V. Kubarovsky, I. Larin, D. Lawrence, X. Li, G. Matousek, J. Maxwell, D. Meekins, R. Miskimen, S. Mtingwa, V. Nelyubin, R. Pedroni, A. Shahinyan, A.P. Smith, S. Srednyak, S. Stepanyan, S. Taylor, E. van Nieuwenhuizen, B. Wojtsekhowski, W. Xiong, B. Yu, Z. W. Zhao, J. Zhou, B. Zihlmann, and the PRad collaboration. North Carolina A & T State University, Greensboro, NC 27424 , USA Duke University, Durham, NC 27708, USA Triangle Universities Nuclear Laboratory, Durham, NC 27708, USA Mississippi State University, Mississippi State, MS 39762, USA University of Virginia, Charlottesville, VA 22904, USA Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA Argonne National Lab, Lemont, IL 60439, USA Hampton University, Hampton, VA 23669, USA University of North Carolina, Wilmington, NC 28402, USA Energy Systems, Davis, CA 95616 University of Massachusetts, Amherst, MA 01003 Yerevan Physics Institute, Yerevan Armenia Syracuse University, Syracuse, NY 13244
PACS numbers:
Abstract
The PRad experiment has credibly demonstrated the advantages of the calorimetric method in e − p scatteringexperiments to measure the proton root-mean-square (RMS) charge radius with high accuracy. The PRad result,within its experimental uncertainties, is in agreement with the small radius measured in muonic hydrogen spectroscopyexperiments and it was a critical input in the recent revision of the CODATA recommendation for the proton chargeradius. Consequently, the PRad result is in direct conflict with all modern electron scattering experiments. Mostimportantly, it is 5.8% smaller than the value from the most precise electron scattering experiment to date, and thisdifference is about three standard deviations given the precision of the PRad experiment. As the first experiment ofits kind, PRad did not reach the highest precision allowed by the calorimetric technique. Here we propose a new (and)upgraded experiment – PRad-II, which will reduce the overall experimental uncertainties by a factor of 3.8 comparedto PRad and address this as yet unsettled controversy in subatomic physics. In addition, PRad-II will be the firstlepton scattering experiment to reach the Q range of 10 − GeV allowing a more accurate and robust extractionof the proton charge radius. The muonic hydrogen result with its unprecedented precision ( 0.05%) determines theCODATA value of the proton charge radius, hence, it is critical to evaluate possible systematic uncertainties of thoseexperiments, such as the laser frequency calibration that was raised in recent review articles. The PRad-II experimentwith its projected total uncertainty of 0.43% could demonstrate whether there is any systematic difference between e − p scattering and muonic hydrogen results. PRad-II will establish a new precision frontier in electron scatteringand open doors for future physics opportunities. ∗ Contact person † Spokesperson a r X i v : . [ nu c l - e x ] S e p NTRODUCTION
The proton is the dominant ingredient of visible matter in the Universe. Consequently, determining the proton’sbasic properties such as its root-mean-square (RMS) charge radius, r p , has attracted tremendous interests in its ownright. Accurate knowledge of r p is essential not only for understanding how strong interactions work in the confinementregion, but is also required for precise calculations of the energy levels and transition energies of the hydrogen (H)atom, for example, the Lamb shift. The extended proton charge distribution changes the Lamb shift by as much as2% [1] in the case of µ H atoms, where the electron in the H atom is replaced by a ”heavier electron”, the muon. It alsohas a major impact on the precise determination of fundamental constants such as the Rydberg constant ( R ∞ ) [2].The first principles calculation of r p in the accepted theory of the strong interaction - Quantum Chromodynamics(QCD), is notoriously challenging analytically and are being carried out by computer simulations, known as the latticeQCD calculations. Currently, such calculations cannot reach the accuracy demanded by experiments, but are on thecusp of becoming precise enough to be tested experimentally [3].Prior to 2010 the two methods used to measure r p were: (i) ep → ep elastic scattering measurements, where theslope of the extracted electric form factor ( G pE ) down to zero 4-momentum transfer squared ( Q ), is proportional to r p ;and (ii) Lamb shift (spectroscopy) measurements of ”regular” H atoms, which, along with state-of-the-art calculations,were used to determine r p . Although, the e − p results can be somewhat less precise than the spectroscopy results,the values of r p obtained from these two methods [2, 4] mostly agreed with each other [5]. New results based onLamb shift measurements in µ H were reported for the first time in 2010. The Lamb shift in µ H is several milliontimes more sensitive to r p because the muon is about 200 times closer to the proton than the electron in a Hatom. To the surprise of both the nuclear and atomic physics communities, the two µ H results [1, 6] with theirunprecedented, < ”proton radius puzzle” [7], unleashing intensive experimental and theoreticalefforts aimed at resolving this ”puzzle”.The PRad experiment completed in 2016, was the first high-precision e − p experiment since the emergence ofthe ”puzzle”. It was the first electron scattering experiment to utilize a magnetic-spectrometer-free method alongwith a windowless hydrogen gas target, which overcame several limitations of previous e − p experiments andreached unprecedentedly small scattering angles. The PRad result, r p = 0.831 ± stat . ± syst . femtometer,is consistent within uncertainties, with the µ H results and was one of the critical inputs in changing the recentCODATA recommendation for r p [8]. But, the PRad result is in direct conflict with the world average of all modern e − p results [19]. For example, it is 5.8% smaller than the most precise electron scattering experiment to date - the2010 experiment at Mainz [4]. In particular, the G pE has a systematic difference in the higher Q range of the PRadexperiment. A new e − p scattering experiment with reduced total uncertainties and exploring the lowest Q feasibleis required to address this as yet unsettled controversy in subatomic physics. As the first experiment of its kind,PRad did not reach the highest precision allowed by the novel magnetic spectrometer-free technique. Therefore, itis timely and incumbent on the collaboration to conduct an upgraded PRad experiment with significantly reduceduncertainties while reaching the lowest scattering angles probed in lepton scattering experiments.The µ H result with its unprecedented precision (0.05%) determines the current average value of r p [8]. Severalrecent review articles have raised the possibility of additional systematic uncertainties in the µ H results, such as thelaser frequency calibration. Therefore it is critical to evaluate all the systematic uncertainties of those experiments.Moreover, among the three most recent H spectroscopy measurements [9–11], two experiments found a small radius [9,11] consistent with the µ H results, but they disagree with another one which supports a larger value [10]. While thePRad result and those from [9, 11] are consistent with the µ H results within the experimental uncertainties, thecentral values from these electron based experiments are all smaller than those from the µ H experiments. Theseobservations have injected a new dimension to the ongoing controversy involving r p measurements. A fundamentaldifference between the e − p and µ − p interactions, could be the origin of the discrepancy. However, there are abundantexperimental constraints on any such ”new physics”, and yet models that resolve the puzzle with new force carriershave been proposed [7, 12]. On the other hand, more mundane solutions continue to be explored, for example, thedefinition of r p used in all three major experimental approaches has been rigorously shown to be consistent [13]. Theeffect of two-photon exchange on µ H spectroscopy [14, 15] and form factor nonlinearities in e − p scattering [16–18]have also been examined. None of these studies could adequately explain the observations and have reinforced theneed for additional high-precision measurements of r p , using new experimental techniques with different systematics.In summary, the PRad experiment was the first electron scattering experiment to utilize a new technique withcompletely different systematics compared to all previous magnetic-spectrometer based e − p experiments. ThePRad result is consistent with the µ H results and consequently it agrees with the recently announced shift in theRydberg constant [8], one of the best-known fundamental constants in physics. The PRad experiment has convincinglydemonstrated the validity and advantage of the new calorimetric technique, but further improvements are possible.ere we propose an enhanced version of the PRad experiment with an estimated uncertainty that is a factor of 3.8smaller than that of the PRad experiment. In addition, it will be the first lepton scattering experiment to reach the Q range of 10 − GeV allowing a more accurate and robust extraction of r p . The proposed experiment would makea crucial contribution towards the resolution of the discrepancy between PRad and other modern e − p scatteringexperiments. The projected total uncertainty of 0.43% will also be able to address possible systematic differencebetween e − p and the µ H experiments. It would then establish a new precision frontier in electron scattering allowingfor the exploration of future physics opportunities.
THE PRAD EXPERIMENTThe novel technique to measure the proton charge radius
The PRad collaboration at Jefferson Lab developed and performed a new e − p experiment as an independentmeasurement of r p to address the ”proton radius puzzle”. The PRad experiment, in contrast with previous e − p experiments, was designed to use a magnetic-spectrometer-free, calorimeter based method [20]. The innovative designof the PRad experiment enabled three major improvements over previous e − p experiments: (i) The large angularacceptance (0 . ◦ − . ◦ ) of the hybrid calorimeter (HyCal) allowed for a large Q coverage spanning two orders ofmagnitude (2 . × − − × − ) (GeV / c) , in the low Q range. The single fixed location of HyCal eliminated themultitude of normalization parameters that plague magnetic spectrometer based experiments, where the spectrometermust be physically moved to many different angles to cover the desired range in Q . In addition, the PRad experimentreached extreme forward scattering angles down to 0 . ◦ achieving the lowest Q (2 . × − (GeV / c) ) in e − p experiments, an order of magnitude lower than previously achieved. Reaching a lower Q range is critically importantsince r p is extracted as the slope of the measured G pE ( Q ) at Q = 0. (ii) The extracted e − p cross sections werenormalized to the well known quantum electrodynamics process - e − e − → e − e − Møller scattering from the atomicelectrons ( e − e ) - which was measured simultaneously with the e − p within the same detector acceptance. This leadsto a significant reduction in the systematic uncertainties of measuring the e − p cross sections. (iii) The backgroundgenerated from the target windows, one of the dominant sources of systematic uncertainty for all previous e − p experiments, is highly suppressed in the PRad experiment. FIG. 1: A schematic layout of the PRad experimental setup in Hall B at Jefferson Lab, with the electron beam incident fromthe left. The key beam line elements are shown along with the window-less hydrogen gas target, the two-segment vacuumchamber and the two detector systems.
The PRad experimental apparatus consisted of the following four main elements (Figure 1): (i) a 4 cm long,windowless, cryo-cooled hydrogen (H ) gas flow target with a density of 2 × atoms/cm . It eliminated the beambackground from the target windows and was the first such target used in e − p experiments; (ii) the high resolution,large acceptance HyCal electromagnetic calorimeter [21]. The complete azimuthal coverage of HyCal for the forwardscattering angles allowed simultaneous detection of the pair of electrons from e − e scattering, for the first timein these types of measurements; (iii) one plane made of two high resolution X − Y gas electron multiplier (GEM)coordinate detectors located in front of HyCal; and (iv) a two-section vacuum chamber spanning the 5.5 m distancefrom the target to the detectors.he PRad experiment was performed in Hall B at Jefferson Lab in May-June of 2016, using 1.1 GeV and 2.2 GeVelectron beams. The standard Hall B beam line, designed for low beam currents (0.1-50 nA), was used in this ex-periment. The incident electrons that scattered off the target protons and the Møller electron pairs, were detectedin the GEM and HyCal detectors. The energy and position of the detected electron(s) was measured by HyCal,and the transverse ( X − Y ) position was measured by the GEM detector, which was used to assign the Q for eachdetected event. The GEM detector, with a position resolution of 72 µ m, improved the accuracy of Q determina-tion. Furthermore, the GEM detector suppressed the contamination from photons generated in the target and otherbeam line materials; the HyCal is equally sensitive to electrons and photons while the GEM is mostly insensitive toneutral particles. The GEM detector also helped suppress the position dependent irregularities in the response of theelectromagnetic calorimeter. A plot of the reconstructed energy versus the reconstructed angle for e − p and e − e events is shown in Figure 2 for the 2.2 GeV beam energy. FIG. 2: The reconstructed energy vs angle for e − p and e − e events for the electron beam energy of 2.2 GeV. The red andblack lines indicate the event selection for e − p and e − e , respectively. The angles ≤ . ◦ are covered by the PbWO crystalsand the rest by the Pb-glass part of HyCal. The background was measured periodically with an empty target cell. To mimic the residual gas in the beam line,H gas at very low pressure was allowed in the target chamber during the empty target runs. The charge normalized e − p and Møller yields from the empty target cell were used to effectively subtract the background contributions.The beam current was measured with the Hall-B Faraday cup with an uncertainty of < e − p and e − e processes [24, 25]. Inelastic e − p scattering events were also included in the simulation using a fit [26] to the e − p inelastic world data. The simulationincluded signal digitization and photon propagation which were critical for the precise reconstruction of the positionand energy of each event in the HyCal.The e − p cross sections were obtained by comparing the simulated and measured e − p yield relative to thesimulated and measured e − e yield. The extracted reduced cross section is shown in Figure 3 (a). The e − p elasticcross section is related to G pE and the proton magnetic form factor ( G pM ) as per the Rosenbluth formula [20]. In thevery low Q region covered by the PRad experiment, the cross section is dominated by the contribution from G pE .Thus, the uncertainty introduced from G pM is negligible. In fact, when using a wide variety of parameterizations for G pM [4, 28–30], the extracted G pE varies by ∼ Q = 0 .
06 (GeV / c) , the largest Q accessed by the PRadexperiment, and < Q < .
01 (GeV / c) region. The largest variation in r p arising from the choice of G pM parametrization is 0 .
001 fm. The G pE ( Q ) extracted from our data is shown in Figure 3 (b), where the Kellyparametrization for G pM [28] was used. The results
The slope of G pE ( Q ) as Q → r p . A common practice is to fit G pE ( Q ) to a functional formand to obtain r p by extrapolating to Q = 0. However, each functional form truncates the higher-order moments of IG. 3: (a)
The reduced cross section ( σ reduced = (cid:0) dσd Ω (cid:1) e − p / (cid:20)(cid:0) dσd Ω (cid:1) point-like (cid:18) M p E (cid:48) (4 M p + Q ) E (cid:19)(cid:21) , where E is the electron beamenergy, E (cid:48) is the energy of the scattered electron and M p is the mass of the proton), for the PRad e − p data. Dividing out thekinematic factor inside the parentheses, the reduced cross section is a linear combination of the electromagnetic form factorssquared. The systematic uncertainties are shown as bands. (b) The G pE as a function of Q . The data points are normalizedwith the n and n parameters, for the 1.1 GeV and 2.2 GeV data separately. Statistical uncertainties are shown as error bars.Systematic uncertainties are shown as bands, for 1.1 GeV (red) and 2.2 GeV (blue). The solid black curve shows the G E ( Q )from the fit to the function given by Eq. 1. Also shown are the fit from a previous e − p experiment [4] for r p = 0.883(8) fm(green) and the calculation of Alarcon et al. [27] for r p = 0.844(7) fm (purple). G pE ( Q ) differently and introduces a model dependence which can bias the determination of r p . It is critical to choose arobust functional form that is most likely to yield an unbiased estimation of r p given the uncertainties in the data, andtest the chosen functional form over a broad range of parameterizations of G pE ( Q ) [31]. To simultaneously minimizethe possible bias in the radius extraction and the total uncertainty, various functional forms were examined for theirrobustness in reproducing an input r p used to generate a mock data set that had the same statistical uncertainty asthe PRad data. The robustness quantified as the root mean square error (RMSE) is defined as RMSE = (cid:112) ( δR ) + σ ,where δR is the bias or the difference between the input and extracted radius and σ is the statistical variation of thefit to the mock data [31]. These studies show [31] that consistent results with the least uncertainties can be achievedwhen using the multi-parameter Rational-function (referred to as Rational (1,1)): f ( Q ) = nG E ( Q ) = n p Q p Q , (1)where n is the floating normalization parameter, and the charge radius is given by r p = (cid:112) p − p ). The G pE ( Q )extracted from the 1.1 GeV and 2.2 GeV data were fitted simultaneously using the Rational (1,1) function. In-dependent normalization parameters n and n were assigned for 1.1 and 2.2 GeV data respectively, to allow fordifferences in normalization uncertainties, but the Q dependence was identical. The parameters obtained from fitsto the Rational (1,1) function are: n = 1 . ± . stat . ± . syst . , n = 0 . ± . stat . ± . syst . , and r p = 0 . ± . stat . ± . syst . fm. The Rational (1,1) function describes the data very well, with a reduced χ of1.3 when considering only the statistical uncertainty.To determine the systematic uncertainty in r p , a Monte Carlo technique was used to randomly smear the crosssection and G E ( Q ) data points for each known source of systematic uncertainty. The r p was extracted from thesmeared data and the process is repeated 100,000 times. The RMS of the resulting distribution of r p is recorded as thesystematic uncertainty. The dominant systematic uncertainties of r p are the Q dependent ones which primarily affectthe lowest- Q data: the Møller radiative corrections, the background subtraction for the 1.1 GeV data, and eventselection. The uncertainty of r p arising from the finite Q range and the extrapolation to Q = 0, was investigatedby varying the Q range of the mock data set as part of the robustness study of the Rational (1,1) function [31].This uncertainty was found to be much smaller than the relative statistical uncertainty of 0 . r p was found to be 1.4%.The r p obtained using the Rational (1,1) function is shown in Figure 4, with statistical and systematic uncertaintiessummed in quadrature. Our result obtained from Q down to an unprecedented 2 . × − (GeV/c) , is about 3-tandard deviations smaller than the previous high-precision electron scattering measurement [4], which was limited tohigher Q ( > .
004 (GeV/c) ). On the other hand, our result is consistent with the µ H Lamb shift measurements[1, 6],and also the recent 2S-4P transition frequency measurement using ordinary H atoms [9]. Given that the lowest Q reached in the PRad experiment is an order of magnitude lower than the previous e − p experiments, and thecareful control of systematic effects, our result indicates that the proton is indeed smaller than the previously acceptedvalue from e − p measurements. Our result does not support any fundamental difference between the e − p and µ − p interactions and is consistent with the shift in the Rydberg constant announced by CODATA [8]. [fm] p Proton charge radius r
CODATA-2014CODATA-2014 (ep scatt.)CODATA-2014 (H spect.)H spect.) m Antognini 2013 (H spect.) m Pohl 2010 (Beyer 2017 (H spect.) Fleurbaey 2018 (H spect.)Bernauer 2010 (ep scatt.)
PRad exp. (ep scatt.) s FIG. 4: The proton charge radius. The r p extracted from the PRad data, shown along with the other measurements of r p since2010 and the CODATA recommended values.The PRad result is 2.7- σ smaller than the CODATA recommended value for e − p experiments [19]. In summary, the PRad experiment is the first e − p experiment to cover a two orders of magnitude span of Q ,in one setting. The experiment also exploited the simultaneous detection of e − p and e − e scattering to achievesuperior control of systematic uncertainties, which were by design different from previous e − p experiments. Further,the extraction of r p by employing functional forms with validated robustness is another strength of this result. Ourresult introduces a large discrepancy with contemporary precision e − p experiments. On the other hand, the resultsalso imply that there is consistency between proton charge radii obtained from e − p scattering on regular hydrogenand spectroscopy of muonic hydrogen [1, 6] and that the value of r p is consistent with the recently updated CODATAvalue [8]. The PRad experiment demonstrates the clear advantages of the calorimeter based method for extracting r p from e − p experiments and points to further possible improvements in the accuracy of this method. It also validatesthe recently announced shift in the Rydberg constant [8], which has profound consequences, given that the Rydbergconstant is one of the most precisely known constants of physics. PRAD-II: GOING BEYOND-THE-STATE-OF-THE-ART
Based on the experience gained from the PRad experiment, there are a number of improvements one can make in anupgraded experiment. The low-hanging fruits amongst the possible improvements are additional beamtime to reducethe statistical uncertainty and a better beamline vacuum upstream of the target, to help reduce the small angleexperimental background. The rest of the improvements are related to reducing the key systematic uncertaintiesthat dominated the PRad experiment, namely i) the precision of the efficiency determination of the GEM basedcoordinate detector, ii) the need to cover a wider range of Q than PRad, by reaching the lowest Q accessed bylepton scattering experiments iii) the non-linear detector response of the Pb-Glass portion of the HyCal calorimeter andiv) the subtraction of background associated with the beam line. Lastly, improved radiative correction calculationswill further improve the precision of the proton radius determination from the PRad and the upgraded PRad-IIxperiment. The improved radiative corrections will be discussed later in the proposal in section . New tracking capabilities
The precision of the GEM detector efficiency contributed indirectly to the systematic uncertainty of the PRadexperiment. A precise measurement of the GEM detector efficiency (at the level of 0.1%) allows the integratedMøller method to be used over the entire angular acceptance of the experiment. The uncertainties associated withMøller counts used in this method are normalization type uncertainties and thus, do not contribute to the systematicuncertainty of extracting r p . However, this method relies on a correction for the inefficiency of the GEM detector.As can be seen in fig. 20-right, the presence of the spacer grids (which are used to keep the GEM foils apart fromeach other) in the PRad GEM detectors caused narrow regions of lower efficiency along the spacers. While theseefficiencies were measured relative to HyCal and corrected in data analysis, the relatively poor position resolutionof the HyCal led to larger uncertainties in the locations of these low efficiency areas of the GEM detectors. Thisresulted in systematic uncertainties as large as 0.5% in the forward scattering angular region. These larger systematicuncertainties precluded the integrated Møller method from being applied in the forward angle region. Instead, thePRad result relied on the bin-by-bin method for the forward angle region. While the bin-by-bin method is excellent incanceling the effect of the GEM detector inefficiency, it introduces Q -dependent systematic uncertainties due to theangular dependence of Møller scattering with contributions from Møller radiative correction, Møller event selection,beam energy and acceptance. Higher precision in the determination of the GEM efficiency would allow for the useof the integrated Møller method over the full experimental acceptance eliminating these Q -dependent systematicuncertainties.Using new GEM detectors with no spacer grids significantly reduces the efficiency fluctuations across the activearea. Furthermore, a high precision measurement of the GEM detector efficiency profile can be achieved by addinga second GEM detector plane. In this case, each GEM plane can be calibrated with respect to the other GEMplane instead of relying on the HyCal, minimizing the influence of the HyCal position resolution. It will also helpreduce various backgrounds such as, cosmic backgrounds and the high-energy photon background that have an impacton the determination of the GEM efficiency. In addition, the tracking capability afforded by the pair of separatedGEM planes will allow measurements of the interaction z − vertex. This can be used to eliminate various beam-linebackgrounds, such as those generated from the upstream beam halo blocker. The uncertainty due to the subtractionof the beamline background, at forward angles, is one of the dominant uncertainties of PRad. Therefore, the additionof the second GEM detector plane will reduce the systematic uncertainty contributed by two dominant sources ofuncertainties.The tracking capabilities of PRad-II will be enhanced significantly compared to PRad by replacing the originalGEM layer with a new GEM-type coordinator detector with no spacer grid and with the addition of a second GEMlayer, 40 cm upstream of the first GEM location next to HyCal. These two new tracking layers will be built by theUVa group. The outer dimensions and readout parameters of these new layers will be similar to the original PRadGEM layer; with an active area of 123 cm ×
110 cm composed of two side by side detectors, each with an activearea of 123 cm ×
55 cm, arranged so that there is a narrow overlap area in the middle. These two new trackinglayers will be based on the novel µ RWELL technology. The biggest advantage of using this new technology for thePRad-II tracking layers is that it would allow each detector module to be built without a spacer grid. The presenceof the spacer grid in the original GEM detector caused narrow regions of lower efficiency along the spacers. Havingtwo spacer-less layers will eliminate the regions of low efficiency. Furthermore, having two layers allows for highlyaccurate determination of efficiency profile for the entire GEM area; i.e much smaller inefficiency corrections to makeand the inefficiency corrections determined with much higher accuracy. µ RWELL is a single-stage amplification Micro Pattern Gaseous Detector (MPGD) that is a derivative of the GEMtechnology. It features a single kapton foil with GEM-like conical holes that are closed off at the bottom by gluing thekapton foil to a readout structure to form a microscopic well structure. A cross section of a µ RWELL detector is shownin Fig. 5-left. The technology shares similar performances with a GEM detector in term of rate capability and positionresolution but presents the advantages of flexibility, no need for spacers and lower production cost that makes it theideal candidate for large detectors. The UVa group built a 10 ×
10 cm µ RWELL prototype detector that was testedwith cosmic-rays at the UVa Detector Lab as well as in test beam at Fermilab (June-July 2018). Preliminary resultsfrom the test beam data, shown shown in Fig. 5-right, are very encouraging with spatial resolution performancessuperior to those of standard Triple-GEM detectors of similar dimensions. The UVa group plans to continue basicR&D studies of the MPGD technology and build large area flat µ RWELL structures for the PRad-II setup. reliminary µ Rwell results from Fermilab test beam
X-stripposi7on resolu7on Y-strip posi7on resolu7on
FIG. 5: µ RWELL prototype with 2D readout : ( left :) Cross section of the prototype; ( center :) Prototype installed intest beam area at Fermilab (June-July 2018); ( right ): Preliminary results of spatial resolution performances of the µ RWELLprototype with 2D X-Y strip readout layer.
Enhancing the Q coverage PRad-II will cover a significantly larger range in Q compared to the PRad experiment. It will reach anunprecedented low Q of ∼ − GeV while simultaneously covering up to Q = 6 × − GeV . The entire rangewill be covered in a single fixed experimental setup, just as in PRad, using 3 different beam energies of 0.7, 1.4 and2.1 GeV. In order to reach the lowest scattering angles of up to 0.5 deg a new rectangular cross shaped scintillatordetector will be placed 25 cm from the target center. The scintillator detector covers the angular range beyond thelargest angles reached by HyCal. This detector will be used to separate the elastic e − p events from Møller scatteringevents down to scattering angles as low as 0.5 degree thus reaching Q of ∼ − GeV . The distribution of theMøller electrons where the second scattered electrons is detected in the two inner-most layers of PbWO crystalsin the HyCal is shown in Fig. 6(a). For most of the Møller electrons incident at the two inner-most layers ofHyCal, the second Møller electron falls outside the HyCal acceptance. By detecting this second Møller electron ina scintillator detector placed at z = 25 cm from the center of the target, as shown in Fig. 6(b), the e − p electronscan be distinguished from the Møller electrons at the scattering angles between 0.5-0.8 degrees helping reach lower Q compared to the PRad experiment.The detector system will include 4-linear stages such that each scintillator tile can be moved individually in x/ydirection enabling them to intersect with the electrons detected in the HyCal. This feature will be used to calibratedthe detector and determine its efficiency at the level of 0.1%. An alpha source based monitoring system will beincluded on each scintillator tile to help monitor the efficiency continuously during the experiment. An all PbWO Calorimeter with flash-ADC based readout
The non-linear behaviors in the energy response of the Pb-glass shower detectors are usually few time larger thanPbWO detectors and also much more non-uniform. In addition, their energy resolution is about 2.5 times worsethan that of the PbWO detectors, which increases the inelastic e − p contribution to the elastic e − p yield. Eventhough the contributions of these factors to the r p systematic uncertainty are not as large as those from the Møller,their contributions to the cross section and G pE are much larger and primarily affect the high Q data. The only wayto reduce this uncertainty is to replace the Pb-glass detectors with PbWO detectors. This will suppress the inelastic e − p contribution to less than 0.1% for the entire Q range, compared to the maximum 2% in the case of PRad.And it will suppress the Q -dependent systematic uncertainties due to differences in the detector properties betweenthe PbWO and Pb-glass detectors. Further, converting the calorimeter readout electronics from a FASTBUS basedsystem to a flash analog to digital converter based setup would dramatically improve the uncertainty due to detectorgain and pedestal stability. The flash-ADC readout system not only allows one to measure the pedestal event-by-event, but also provides excellent timing information and digital trigger information, which allows the rejection ofvarious accidental events and improved trigger efficiency.PRad-II will use an upgraded HyCal calorimeter which will be an all PbWO Calorimeter rather than the Hybridversion used in PRad. The lead-glass modules of HyCal will be replaced with new PbWO crystals. This willsignificantly improve the uniformity of the electron detection over the entire experimental acceptance. Such uniformityof the detector package is critical for the precise and robust extraction of r p . Moreover, the readout electronics will IG. 6: a) The distribution of a Møller electron on the scintillator detector, when the other Møller electron is detected inthe two inner-most layers of the HyCal. The red lines show the outline of scintillator tiles. b) A schematic of the scintillatordetector to detect these Møller electrons which help can be used to separate them from the e − p electrons in the 0.5-0.8 degrange of scattering angles. be converted from a FASTBUS based system used during PRad to an all flash-ADC based system which is expectedto provide a seven fold improvement in the DAQ speed. A faster DAQ will allow us to collect an order of magnitudemore statistics within a reasonable amount of beamtime. Note that the projected uncertainties can still be achievedwith the current hybrid calorimeter. Beamline enhancements
The window on the Hall-B tagger is being replaced with an aluminum windows; this upgrade is expected to resultin a significant improvement in the beamline vacuum, particularly upstream of the target. This will help reduce oneof the key sources of background observed during the PRad experiment. Further, a new beam halo blocker will beplaced upstream of the Hall-B tagger magnet. This will further reduce the beam-line background critical for accessingthe lowest angular range and hence the lowest Q range in the experiment. Other desirable upgrades - Windowless target
The proposed reduction in the total uncertainties of PRad-II does not rely on the upgrade discussed below but itis nonetheless desirable for performing the best possible experiment.The factor of 3.8 improvement expected in the PRad-II experiment does not require any further improvements tothe windowless gas flow target used during PRad. The projected precision and all of the experimental goals can beachieved with the existing PRad target. However, because of recent technological advances, the experiment couldbenefit from a liquid-drop hydrogen target with a laser based gating. The PRad target is a window-less target whichproduces two gas plumes escaping from the two ends of the target cell. The effect of these plumes cannot be completelysubtracted using the ”empty” target runs, where the target chamber is filled with gas at the same flow rate as thegas filling the target cell during the ”full” target run. The effect of the plumes was estimated using the PRad targetprofile simulations. It was difficult to further reduce the systematic uncertainty contributed by the plumes, as the gasprofile simulation at low densities is highly non-trivial. A liquid-drop target with an adequate gating mechanism, onhe other hand, will be effectively a point-like target, and it should minimize systematic uncertainties associated withthe extended target effects, including these plumes. Such a target is being investigated by the JLab target group.However, all the estimates in this proposal are based on the existing PRad gas flow target.
THE NEW PROPOSED EXPERIMENTIntroduction
The proposed PRad-II experiment plans to reuse the PRad setup (shown in Fig. 1 but with improvements to therange of Q covered, an additional GEM detector plane, and an improved high efficiency PbWO crystal electromag-netic calorimeter together with a new fADC based readout system for the calorimeter. Just as in the PRad exerimentthe scattered electrons from ep elastic and Møller scatterings will be detected simultaneously with high precision. Asdemonstrated by the PRad experiment a windowless target cell has a definitive advantage over closed cell targets inminimizing one of the primary sources of background.A small scintillator detector placed 25 cm from the target cell will help distinguish between Møller electronsand and ep elastic electrons at the lowest angles covered in this experiment (0.5-0.7 deg), allowing access to anunprecedented low Q of 10 − GeV . FIG. 7: The placement of the new GEM- µ Rwell chamber in the proposed experimental setup for PRad-II.
Just as in the PRad experiment the scattered electrons will travel through the 5 m long vacuum chamber witha thin window to minimize multiple scattering and backgrounds. The vacuum chamber matches the geometricalacceptance of the calorimeter. The new second GEM detector layer will be placed about 40 cm upstream of the GEMdetector layer location in PRad, as shown in Fig. 7. Both GEM layers will be made of spacer-less detectors based onthe novel µ RWELL technology. The pair of GEM- µ RWELL detector planes will ensure a high precision measurementof the GEM detector efficiency needed for applying the integrated Møller method to the full angular range of theexperiment. The two GEMs- µ RWELL layers will also add a modest tracking capability to help further reduce thebeam-line background.The elements of the experimental apparatus along the beamline are as follows: • windowless hydrogen gas target • ×
11 cm scintillator detector with a 4 × hole placed 25 cm from the center of the target. • Two stage, large area vacuum chamber with a single thin Al. window at the calorimeter end • A pair of GEM- µ RWELL detector planes, separated by about 40 cm for coordinate measurement as well astracking. • high resolution all PbWO crystal calorimeter (the Pb-glass part of the HyCal will be replaced with PbWO crys-tals) with fADC based readout.Figure 8 shows a schematic layout of the PRad-II experimental setup. IG. 8: The proposed experimental setup for PRad-II.
Electron beam
We propose to use the CEBAF beam at three incident beam energies E = 0.7, 1.4 and 2.1 GeV for this experiment.The beam requirements are listed in Table I. All of these requirements were achieved during the PRad experiment.A typical beam profile during the PRad experiment is shown in Fig. 9 and the beam X, Y position stability was (cid:39) ± TABLE I: Beam parameters for the proposed experimentEnergy current polarization size position stability beam halo(GeV) (nA) (%) (mm) (mm)0.7 20 Non < ≤ ∼ − < ≤ ∼ − < ≤ ∼ − Windowless hydrogen target
A critical component of this proposed experiment is a windowless hydrogen gas target used during the PRadexperiment. PRad-II will reuse the windowless hydrogen gas flow target. This target had a thickness of ∼ . × hydrogen atoms/cm , hence, with an incident beam current of 20 nA the luminosity is L ≈ × cm − s − .Thehigh density was reached by flowing cryo-cooled hydrogen gas (at 19.5 ◦ K) through the target cell with a 40 mm longand 63 mm diameter cylindrical thin copper pipe. The upstream and downstream windows of this cell were coveredby thin (7.5 µ m) kapton films with 2 mm holes in the middle for the passage of the electron beam through the target.Four high capacity turbo-pumps were used to keep the pressure in the chamber (outside the cell) at the ∼ . ∼
470 mtorr.The target cell was specifically designed to create a large pressure difference between the gas inside the cell and thesurrounding beam line vacuum.Figure 11 (left) is a cut-thru drawing of the PRad target chamber and shows most of its major components.High-purity hydrogen gas ( > IG. 9: Typical beam profile during the PRad experiment, showing a beam size of σ x = 0.01 mm and σ y = 0.02 mm.FIG. 10: Beam X,Y position stability ( (cid:39) ± temperatures using a two-stage pulse tube cryocooler with a base temperature of 8 K and a cooling power of 20 Wat 14 K. The cryocoolers first stage serves two purposes. It cools a tubular, copper heat exchanger that lowers thehydrogen gas to a temperature of approximately 60 K, and it also cools a copper heat shield surrounding the lowertemperature components of the target, including the target cell itself. The second stage cools the gas to its finaloperating temperature and also cools the target cell via a 40 cm long, flexible copper strap. The temperature of thesecond stage was measured by a calibrated cernox thermometer and stabilized at approximately 20 K using a smallcartridge heater and automated temperature controller.The target cell, shown in Fig. 12, was machined from a single block of C101 copper. Its outer dimensions are 7.5 × × , with a 6.3 cm diameter hole along the axis of the beam line. The hole is covered at both ends by 7.5 µ mthick polyimide foils, held in place by aluminum end caps. Cold hydrogen gas flows into the cell at its midpoint and Cryomech model PT810 Lakeshore Cryotronics
IG. 11: (left)Annotated drawing of the PRad gas flow target indicating most of the targets main components. The locationand dimensions of various polyimide pumping orifices are shown, where Z is the distance from target center. The direction ofthe electron beam is indicated by a red arrow. (right) Downstream view of the PRad target in the beamline.FIG. 12: The PRad target cell. Hydrogen gas, cooled by the pulse tube cryocooler, enters the cell via the tube on the left. Thecell is cooled by a copper strap attached at the top, and is suspended by the carbon tube directly above the cell. The 2 mmorifice is visible at the center of the polyimide window, as are the wires for a thermometer inside the cell. Two 1 µ m solid foilsof aluminum and carbon attach to the cell bottom, but are not shown in the photograph. exits via 2 mm holes at the center of either kapton foil. The holes also allow the electron beam to pass through the H gas without interacting with the foils themselves, effectively making this a windowless gas target. Compared to a longthin tube, the design of a relatively large target cell with small orifices on both ends has two important advantages.First, it produce a more uniform density profile along the beam path, allowing a better estimate of the gas densitybased upon its temperature and pressure. Second, it eliminates the possibility of electrons associated with beam haloscattering from the 4 cm long cell walls. Instead, the halo scatters from the 7.5 µ m thick polyimide foils. A secondcalibrated cernox thermometer, suspended inside the cell, provides a direct measure of the gas temperature. The gaspressure was measured by a capacitance manometer located outside the vacuum chamber and connected to the celly a carbon fiber tube approximately one meter long and 2.5 cm in diameter. The same tube is used to suspend thetarget cell, in the center of the vacuum chamber, from a motorized 5-axis motion controller. The controller can beused to position the target in the path of the electron beam with a precision of about ± µ m. It was also used tolift the cell out of the beam for background measurements. Also, two 1 µ m thick foils, carbon and aluminum, wereattached to the bottom of the copper target cell for additional background and calibration measurements. High-speedturbomolecular pumps were used to evacuate the hydrogen gas as it left the target cell and maintain the surroundingvacuum chamber and beam line at very low pressure. Two pumps, each with a nominal pumping speed of 3000l/s, were attached directly under the chamber, while pumps with 1400 l/s speed were used on the upstream anddownstream portions of the beam line. A second capacitance manometer measured the hydrogen gas pressure insidethe target chamber, while cold cathode vacuum gauges were utilized in all other locations.Polyimide pumping orifices were installed in various locations to limit the extent of high pres- sure gas along thepath of the beam. With this design, the density of gas decreases significantly outside the target cell, with 99% ofscattering occurring within the 4 cm length of the cell. Target performance
During the PRad experimet 600 sccm cold H gas was flown through the target cell. Under these conditions, typicalpressure and temperature measurements inside the target cell were 0.48 torr and 19.5 K, respectively, resulting in agas density of 0.83 mg/cm [32]. Table II gives typical pressure measurements obtained in other regions of the electronbeam path. The hydrogen areal density is calculated as the product of the gas number density and the length of theregion. In all regions except the target cell, a room temperature of 293 K is assumed when calculating the gas density.The vast majority of the hydrogen gas was confined to the 4 cm long target cell, with the majority of the remaininggas being measured in the 5 m long, 1.8 m diameter vacuum chamber just upstream of the calorimeter. Here theachievable vacuum pressure was limited by the conductance between the chamber and its vacuum pump. Two types TABLE II: Hydrogen gas pressures and areal densities for the PRad beam line. Refer to Fig. 11 (left) for more details.Roomtemperature gas is assumed in calculating the areal density of all regions except Region 1 (target cell), where a temperature of19.5 K was used. Region Length Pressure Areal density Percentage of total(cm) (torr) (atoms/cm )Target cell 4 0.48 1.9 × × − × × − × × − × × − × × − × of background measurements were made. In the first, the H gas flow was maintained at the same 600 sccm, but thegas was directed into the vacuum chamber rather than the target cell. In this case, the chamber pressure increasedslightly to 2.9 mtorr, and the cell temperature warmed to 32 K. For the second type of background measurements,the gas flow was set to zero, in which case both the cell and chamber pressures dropped below 0.001 torr.The measured temperature values, together with the inlet gas flow rate, pumping speeds of the pumps, and thedetailed geometry of the target system were used to simulate the hydrogen density profile in the target using theCOMSOL Multiphysics R (cid:13) simulation package. The average pressure obtained from the simulation agreed with themeasured values within 2 mTorr for both the target cell and the target chamber, under the PRad production runningconditions. Fig. 13 shows the simulated density profile along the beam path for both the full target cell configurationand the full chamber background configuration. During the PRad experiment the target pressure and temperatureremained stable throughout. The variation of target pressure and temperature with time is shown in Fig. 14. Large volume vacuum chamber
For the PRad experiment a new large ∼ . IG. 13: Density profile of hydrogen atoms along the electron beam line. Here, the target cell is centered at 0 cm, and theelectron beam transverses the target from negative to positive values. The red line indicates a measurement with 600 sccm ofhydrogen flowing into the target cell. The green line indicates a background measurement with the same flow of gas directlyinto the target vacuum chamber. t a r ge t p r e ss u r e ( m T o rr) t a r ge t ga s t e m pe r a t u r e ( K ) FIG. 14: The variation of PRad target pressure and temeperature vs. run number. Each run was about 1 hr long. any additional material other than the hydrogen gas in the target cell, all the way down to the Hall-B beam dump.The vacuum box also helped minimize multiple scattering of the scattered electrons en route to the detectors. Aphotograph of the vacuum chamber is shown in Fig. 15. This vacuum chamber will be reused for PRad-II.
High resolution forward calorimeter
The scattered electrons from e − p elastic and Møller scatterings in this precision experiment will be detectedwith a high resolution and high efficiency electromagnetic calorimeter. In the past decade, lead tungstate (PbWO )has became a popular inorganic scintillator material for precision compact electromagnetic calorimetry in high andmedium energy physics experiments (CMS, ALICE at the LHC) because of its fast decay time, high density and highradiation hardness. The performance characteristics of the PbWO crystals are well known mostly for high energies( >
10 GeV) [34] and at energies below one GeV [35]. The PrimEx Collaboration at Jefferson Lab constructed a novelstate-of-the-art multi-channel electromagnetic hybrid (PbWO -lead glass) calorimeter (HYCAL) [33] to perform ahigh precision (1.5%) measurement of the neutral pion lifetime via the Primakoff effect. The advantages of using theHyCal calorimeer was also demonstrated in the PRad experiment.For PRad-II we are proposing to replace the outer Pb-glass layer with PbWO modules turning the calorimeter intoa fully PbWO calorimeter. A single PbWO module is 2 . × .
05 cm in cross sectional area and 18.0 cm in length IG. 15: A photograph of the ∼ (20 X ). The calorimeter consists of 1152 modules arranged in a 34 ×
34 square matrix (70 ×
70 cm in size) withfour crystal detectors removed from the central part (4 . × . in size) for passage of the incident electron beam.An additional ∼ ∼
800 Pb-glass modules. As the light yield of the crystalis highly temperature dependent ( ∼ ◦ C at room temperature), a special frame was developed and constructedto maintain constant temperature inside of the calorimeter with a high temperature stability ( ± . ◦ C) during theexperiments. Figure 16 shows the assembled PrimEx HYCAL calorimeter that was used in the PRad experiment.For the PRad-II experiment the calorimeter will be placed at a distance of about 5.5 m from the target which willprovide a geometrical acceptance of about 25 msr.
FIG. 16: The PrimEx HYCAL calorimeter with all modules of the high performance PbWO crystals in place. During PRad the energy calibration of HyCal was performed by continuously irradiating the calorimeter with theHall B tagged photon beam at low intensity ( <
100 pA). An excellent energy resolution of σ E /E = 2 . / √ E hasbeen achieved by using a Gaussian fit of the line-shape obtained from the 6 × σ =3.0mm), the overall position resolution reached was σ x,y = 2 . / √ E for the crystal part of the calorimeter. Thealorimeter performed as designed during the experiment, as shown in Fig. 17, which shows the resolution achievedduring the PRad experiment and the energy dependence of the trigger efficiency. E (MeV)
400 600 800 ( E ) / E s s (GeV) g E t r i gge r e ff i c i en cy PbWOtransitionPbGlass
FIG. 17: Energy resolution of the PbWO crystal part of the HyCal calorimeter (left) and the energy dependence of the triggerefficiency (right). These data are from the PRad experiment. The upgraded calorimeter will provide enhanced uniformity across the entire calorimeter and reduce the uncertaintydue to e − p inelastic contribution to the elastic e − p yield (event selection). The impact of the upgraded HyCalon the uncertainty in event selection and detector response was studied using the PRad comprehensive Monte Carlosimulation. Fig. 18 shows the projected improvement in the one standard deviation systematic uncertainty band inthe extracted G pE . The trigger for the PRad-II experiment will be total energy deposited in the calorimeter ≥
20% of
FIG. 18: The one standard deviation systematic uncertainty band in the extracted G pE for the current HyCal and the upgradedcalorimeter. E . This will allow for the detection of the Møller events in both single-arm and double-arm modes. IG. 19: The PRad GEM chambers (left) and the GEM chambers mounted on the HyCal during the experiment (right).
GEM µ RWELL based coordinate detectors
The PRad experiment used Gas Electron Multiplier (GEM) based coordinate detectors with ∼ µ m positionresolution. The active area of the GEM PRAd layer was 123 cm ×
110 cm to match the area of the calorimeter. TheGEM layer was made of two large area GEM detectors, each with an active area of 123 cm ×
55 cm, arranged so thatthere is a narrow overlap area in the middle. An especially designed through hole with a 4 cm radius built into GEMdetectors at the center of the active area allowed for the passage of the beamline. The GEM detectors were tripleGEM foil structures followed by a 2D x-y strip readout layers. The chambers were mounted to the front face of theHyCal calorimeter using a custom mounting frame. A pre-mixed gas of 70% Argon and 30% CO was continuouslysupplied to the chambers. Figure 19 shows the PRad GEM detector and a view of it mounted to the front of theHyCal calorimeter during the PRad experiment.The chambers were designed and constructed by the University of Virginia group and are currently the largestsuch chambers to be used in a nuclear physics experiment. These GEM chambers provided more than a factor of20 improvement in coordinate resolution and a similar improvement in the Q resolution. They allowed unbiasedcoordinate reconstruction of hits on the calorimeter, including the transition region of the HyCal calorimeter. TheGEM detectors also allowed us to use the lower resolution Pb-glass part of the calorimeter, extending the total Q range covered at a single beam energy setting.The PRad GEM detectors were readout using the APV25 chip based Scalable Readout System (SRS) developed atCERN. An upgraded firmware configuration developed for the PRad setup allowed the experiment to collect data at ∼ ∼
400 MB/sec and ∼
90% live time. This was the highest DAQ rate achieved by a APVbased system at the time.The PRad GEM detectors consistently performed well throughout the experiment. The efficiency of the chamberwas mostly uniform over the entire chamber, except for over the spacer locations, as shown in Fig. 20, and it achievedthe design resolution of < µ m. The performance of the detector remained stable throughout the experiment. Inthe PRad GEM chambers the 2 × µ m) margins. The GEM efficiency loss due to thepresence of spacers and sector margins was measured relative to HyCal using data and was modeled in the simulation.The new µ RWELL based tracking layers will have an identical size and outer design to the PRad GEM detectors.However, new advances in µ RWELL detector technology such as spacer-free construction with a smaller materialsbudget will be incorporated into the new detectors. The impact of using two advanced technology coordinate detectorlayers on the determination of inefficiency profile and the associated uncertainty, as well as the improvement in thevertex reconstruction capabilities was studied using a simulation of the GEM detectors. The improvement in thedetermination of the efficiency and its uncertainty is shown in Fig. 22. In addition the improvement in the resolutionof the reconstructed reaction vertex is shown in Fig. 23.The readout of the two GEM µ RWELL layers requires approximately 20 k electronic channels. This readout forthe proposed experiment will be done by using the high-bandwidth optical link based MPD readout system recently
00 400 200 0 200 400 600 mm mm remove spacerwith spacer (degree) q e ff i c i en cy FIG. 20: A plot of the GEM efficiency over the X-Y coordinates of the detector (left), and the GEM efficiency over the regionoverlapping with the PbWO crystals of the HyCal calorimeter vs. polar angle (right). The drops in efficiency seen in the 2Dplot in the left is due to spacers inside the GEM modules. A software cut to remove the spacers yields an efficiency profileuniform to within +/- 1% level as seen by red circles. The cut to remove spacers reduce the available statistics by only about4.7%.FIG. 21: (Left) The position resolution (approximately 56 µ m) for GEM detectors achieved during PRad experiment; thisrepresents a factor of 20-40 improvement over the resolution available without the GEM tracker in the setup. (Right) Thescattered Møller ee pair rings detected by PRad GEM tracker illustrating the high position resolution and accuracy providedby the GEMs. Furthermore, this plot shows the very low background level in the reconstructed GEM hit locations. developed for the SBS program in Hall A. This system is currently under rigorous resting. This new system uses theAPV-25 chip used in the PRad GEM readout. However, the readout of the digitized data is performed over a high-bandwidth optical link to a Sub-System Processor (SSP) unit in a CODA DAQ setup. Given its 40 MHz samplingrate and the number of multiplexing channels, the limiting trigger rate for the APV chip is 280 kHz in theory. Inpractice we expect it to be lower and assume a 100 kHz limit. Currently tests are underway by the JLab electronicsgroup in collaboration with the UVa group to test the SBS GEM readout system to operate at this high trigger ratelimit. Given the aggressive R&D program currently in place to reach this goal, we do not anticipate any difficulty ofreaching the 25 kHz trigger rate assumed for the PRad-II experiment. IG. 22: (left) Simulated GEM efficiency uncertainty as a function of scattering angle, when using a single GEM detectorplane along with the HyCal compared to when using two spacer-less GEM- µ RWELL detector planes. (right) The uncertaintyin determining the efficiency for single GEM − µ RWELL vs two GEM- µ RWELL detector planes.FIG. 23: Reconstructed reaction z-vertex when using one GEM plane along with the HyCal vs using two GEM- µ RWELLdetector planes.
The option for an even faster GEM readout system is now available with the currently ongoing work as part of thepre R&D program for Jefferson Lab Hall A SoLID project. This fast GEM readout system is based on the new VMMchip was developed at BNL for the ATLAS large Micromegas Muon Chamber Upgrade. VMM chip is an excellentcandidate for large area Micro Pattern Gaseous Detectors such as GEM and µ RWELL detectors. The VMM is arad-hard chip with 64 channels with an embedded ADC for each channel. This chip is especially suited for highrate applications and is much more advanced than the 20 year old APV chip. The VMM chip has an adjustableshaping time which can be set to be as low as 25 ns. In the standard (slower) readout mode, the ADC provides10-bit resolution, while in the faster, direct readout mode the ADC resolution is limited to 6-bits. The fast directreadout mode has a very short circuit-reset time of less than 200 ns following processing of a signal. The VMM chiphas already been adapted by the CERN RD-51 collaboration for Micro-Pattern Gas Detectors to replace the APV-25chip. The electronics working group of the RD-51 collaboration has already created a new version of its ScalableReadout System (SRS) based on the VMM chip. The UVa group, which has extensive expertise operating the APVbased SRS readout, recently acquired a 500 channel VMM-SRS system and is testing it in collaboration with the JlabDAQ group. Furthermore, the as part of the SoLID pre R&D program the Jlab electronics group is now developinga GEM readout system capable of running at 300 kHz based on the VMM chip.The 170 k channel APV based GEM readout for the HallA SBS project has been already acquired and built, whileas part of the HallA SoLID project, a 200+ k channel VMM based readout system will be assembled. Given thesevery large volume fast readout systems, we do not see any problem acquiring the 20 k channel GEM readout system
IG. 24: The VMM chip based CERN RD-51 SRS readout card. The previous generations of this readout card (for examplethe card used for PRad) were based on the APV-25 chip. needed for PRad-II
Electronics, data acquisition, and trigger
The high resolution calorimeter in this proposed experiment will have around 2500 channels of charge and timinginformation. These will be readout using the JLab designed and built flash-ADC modules (FADC250), each with16 channels. The DAQ system for the calorimeter is thus composed of 160 FADC250 modules that can be heldin ten 16-slots VXS crates. The major advantages of the flash-ADC based readout are the simultaneous pedestalmeasurement (or full waveform in the data stream), sub-nanosecond timing resolution, fast readout speed, and thepipeline mode that allows more sophisticated triggering algorithms such as cluster finding.Additionally, some VME scalers will read out and periodically inserted into the data stream.The DAQ system for the proposed experiment is the standard JLab CODA based system utilizing the JLab designedTrigger Supervisor. A big advantage of the CODA/Trigger Supervisor system is the ability to run in fully bufferedmode. In this mode, events are buffered in the digitization modules themselves allowing the modules to be “ live ” whilebeing readout. This significantly decreases the deadtime of the experiment. With the upgraded flash-ADC moduleswe expect to reach a data-taking rate of about 20 kHz events, which is about 4 times higher than the data-taking ratein PRad experiment. Such a capability of the DAQ system has already been demonstrated by CLAS12 experiments.A large fraction of the electronics needed for the PRad-II DAQ and trigger, including the high voltage crates andall necessary cabling for the detectors, are available in Hall B from the PRad experiment.Our approach in organizing the first level hardware trigger in this proposed experiment is to make it as simple aspossible to reach the highest efficiency for the event selection process and in the mean time, to meet the DAQ raterequirements. The primary trigger will be formed from the PbWO calorimeter by only using the analog sum of alldynode outputs from each of the crystal cells.The scattered electrons from the ep → ep reaction carry almost the same energy as the incident beam. Therefore, forthis process alone, one can organize a very efficient trigger by requiring the total energy in the calorimeter to be 0 . × E including the resolutions. We are planning to detect simultaneously the electrons from the e − e − → e − e − process inthis experiment in two single-arm and coincidence modes. For the coincidence mode, we are required to lower thetotal energy threshold level to about one-fifth of the beam energy − . × E including the resolutions. This will bestill reasonable for this low luminosity ( L ≈ × cm − s − ) and low background experiment. mproved Radiative corrections at forward angles In order to reach a high precision in proton radius experiments such as PRad [36, 37], in addition to a tight control ofsystematic uncertainties and a precise knowledge of backgrounds associated with the experiment, a careful calculationof radiative corrections (RC) is necessary. It should be noted that the RC calculations carried out for small scatteringangles give radiative corrections that are smaller than the corrections obtained from larger angles. Consequently,small angle scattering experiments like PRad/PRad-II, in this respect have a significant advantage as compared toother scattering experiments performed at larger angles.Since in the PRad experiment both elastic e − p and Møller e − e scattering events are taken simultaneously duringthe experiment, the integrated luminosity is canceled out in the ratio between the two differential cross sections since itis the same for both reaction channels. However, one also needs to take into account that an experimental differentialcross section cannot be used directly for a form factor extraction, as it contains radiative effects. To obtain the Bornlevel differential cross section at a particular angle, one needs to apply precisely calculated RC to the cross sectionand also include a systematic uncertainty associated with the calculation.There are already such calculations for the elastic e − p [38, 39], however, carried out within the ultrarelativisticapproximation where the electron mass squared has been neglected ( m ee (cid:28) Q ). The code called MASCARAD [38]was developed for RC calculations, and another one called ELRADGEN [39] was developed to generate radiativeevents for a full Monte Carlo simulation of the PRad-type experiment. The Møller RC (events) have been calculated(generated) using the codes called MERA [40] and MERADGEN [41]. In this case the ultrarelativistic approximationwas also utilized. The explicit expressions without this approximation for one-loop (i.e. vertex, self-energies and twophoton exchange) contributions to Møller scatterings are presented in [42], nevertheless, the contribution from hardphoton emission was not considered. This contribution was taken into account in [43] where they have extended theresults of [42] with exact single hard-photon bremsstrahlung calculations .For the radiative effects of the elastic e − p and Møller e − e scatterings that happened in the actual PRad experiment,separate event generators [24, 44] were built, which included the NLO contributions to the Born cross sections of thesescattering processes. Ref. [24] has a complete set of analytical expressions for calculated RC diagrams to e − p andMøller scatterings , obtained within a covariant formalism and beyond the ultrarelativistic approximation, beforethose were calculated in [43]. Another independent elastic e − p event generator [25] was used as a cross-check. Thecorrections to the proton line, which were often neglected, were included in this generator. However, these correctionsare highly suppressed due to proton’s heavy mass, and are negligible in the PRad kinematic range. The two e − p event generators were found to be in excellent agreement with each other. They also included the contribution fromthe two-photon exchange processes [45–47], which were estimated to be less than 0.2% for the e − p elastic scatteringcross section in the PRad kinematic range. All the generators are able to generate hard radiated photons, beyondthe peaking approximation, by which the radiated photon will be co-linear with the electron. This is crucial forcalorimeter simulations, as the HyCal will integrate some of the radiated photons into an electron cluster, if they areclose enough to each other when they hit the HyCal. Details and results on the NLO RC for the elastic e-p and Møllerscatterings for the PRad experiment can be found in [24].We would like to discuss our estimation of higher order RC systematic uncertainties based upon elastic e − p and e − e scatterings for PRad. If we consider both elastic e − p and Møller e − e scatterings, then in these processesthe systematic uncertainties due to radiative corrections arise mainly from their higher order contributions to thecross sections. As we discussed, the NLO RC diagrams are meticulously worked out beyond the ultrarelativisticapproximation in Ref. [24, 44]. And these corrections also include multi-photon emission and multi-loop processes,which are approximated at the Q → e − p and Møller are correlated and Q -dependent. These uncertaintieson the cross sections are shown in Fig. 25 for the 1.1 GeV and 2.2 GeV data sets. The Q -dependence is larger for theMøller RC and it affects the cross section results through the use of the bin-by-bin method [37]. This can be seen fromthe uncertainties below 1.6 ◦ for the 2.2 GeV data set and below 3.0 ◦ for the 1.1 GeV data set, where the bin-by-binmethod is applied. On the other hand, the Q -dependence for the e − p RC is estimated to be much smaller relatively. The calculations in [43], containing no ultrarelativistic approximation, permit a complete analysis of the next-to-leading-order (NLO)RC for both Møller and Bhabha scattering in the low energy kinematics of the OLYMPUS experiment. The calculations of [24] do not include two-photon exchange, radiation off proton and up-down interference, and hadronic vacuumpolarization. f we transform these cross section uncertainties into the uncertainties on the proton radius, then for e − p we have FIG. 25: Relative systematic uncertainties for the cross sections due to radiative corrections for the e − p and e − e scatterings.The blue squares are for the 2.2 GeV energy setting, the red dots are for the 1.1 GeV energy setting. The figure is from Ref. [37]. ∼ e − e we have ∼ r p = 0.0069 fm.The Q -dependent systematic uncertainties from the Møller scattering can be suppressed by using the integratedMøller method for all angular bins, which will turn all systematic uncertainties from the Møller into normalizationuncertainties for the cross sections. However, this procedure requires high precision GEM efficiency measurementsparticularly for the forward angular region, which cannot be achieved with the PRad setup, but can be achieved withan additional GEM plane for the PRad-II setup.Given that the Q -dependent systematic uncertainty is much larger for the Møller scattering and the potentialimpact on r p can be more significant, another independent estimate is performed by the Duke group. This estimationfollows the method developed for the MOLLER experiment at JLab [49], where the authors have calculated two-loopelectroweak corrections to the parity-violating polarization asymmetry in the Møller scattering in MOLLER kinematicrange. Based on their mathematical framework, we were able to estimate the contribution from the next-to-next-leading order (NNLO) diagrams on the Born cross section in the PRad kinematic range. The estimated Q -dependentsystematic uncertainties are smaller than those estimated in the first approach, for any reasonable photon energy cutfor the PRad experiment (from 20 MeV to 70 MeV) . Thus, we still use the uncertainty (∆ r p = 0.0069 fm) from thefirst approach as a conservative estimate on r p .Next we discuss the RC systematic uncertainty in Møller scattering for PRad-II setup based on the integratedMøller method. The common systematic uncertainty of the PRad r p result from [36] is dominated by the Q -dependent uncertainties. In particular, it is dominated by those uncertainties that primarily affect the low Q datapoints, such as those stemming from the Møller scattering. These uncertainties include the Møller RC, Møller eventselection, beam energy, detector positions, etc. They are introduced into the cross section measurements by the useof the bin-by-bin method, in which one obtains the e − p to e − e ratio by taking the e − p and e − e counts from thesame angular bin. In other words, the e − p count in each angular bin gets a different normalization factor from theMøller e − e count.On the other hand, the r p result is insensitive to the normalization uncertainties, which may shift all data points In our estimation one caveat is that we estimated the NNLO RC based on a restricted set of diagrams considered in [49]. p or down at the same time. The Q -dependent systematic uncertainties on r p can be eliminated by introducing afloating parameter in the radius extracting fitter. The studies in [31] have already shown that the effect on r p is nearlyzero, even with a normalization uncertainty that is as larger as 5% (ten times larger than the typical normalizationuncertainties for PRad). Thus, in order to reduce the systematic uncertainties on r p , one can rely more on theintegrated Møller method rather than on the bin-by-bin method. In this case, one would integrate the Møller countsin a fixed angular range, and use it as a common normalization factor to the e − p counts from all angular bins. Thiswill turn all systematic uncertainties from the Møller into normalization uncertainties on the cross section, and thuscompletely eliminate any possible effect on r p . An example is illustrated in Fig. 26, where the e − p to e − e ratios fromsimulations with different beam energies are plotted relative to those obtained with the nominal beam energy. Forthe upper plot, the results with scattering angles less than 1.6 ◦ are obtained with the bin-by-bin method, while theresults with larger scattering angles are obtained with the integrated Møller method. There is a clear Q -dependentsystematic uncertainty caused by the bin-by-bin method in the forward angular region. On the other hand, for thebottom plot the integrated Møller method is applied for all angular ranges. In this case, the beam energy affectsmostly just the normalization of the data points. The effect on the extracted r p will be significantly smaller.While the integrated Møller method is excellent in eliminating systematic effects on r p due to the Møller, one wouldneed to correct for the GEM efficiency as well, which can be cancelled by using the bin-by-bin method. This is thereason why the integrated Møller method has not been applied for the full angular range in the PRad case, since theGEM efficiency was very difficult to measure precisely in the forward angular region. This is mostly due to the HyCalfinite resolution effect. In the case of PRad there was only effectively a single GEM plane. When measuring the GEMefficiency, the incident angle of the electron was measured by HyCal, the position resolution of which (on the order of1 mm or worse) was not good enough to resolve various dead areas on the GEM detectors (such as those caused bythe GEM spacers). In PRad-II, there will be a second GEM plane), so one can apply the integrated Møller methodfor the entire kinematic region.Thereby, the procedure described above will be applicable to PRad-II experiment that will give us almost zerosystematic uncertainty on r p , in particular for the Møller RC, however, it would be very relevant to obtain it alsofrom the theory side. One of our priority goals is to calculate exactly the NLO and NNLO RC in unpolarized elastic e − p and Møller e − e scatterings beyond ultrarelativistic limit, when the electron mass will be taken into accountat PRad/PRad-II beam energies. In this case we will have the e − p and Møller radiatively corrected cross sectionswith both NLO and NNLO RC included. Based upon such new calculations we will also modify the event generatorof [44], which has been used in the analysis of the PRad data. Its new version will be used in the analysis of thePRad-II data.It will be an outstanding problem to calculate the corresponding one-loop and two-loop Feynman diagrams system-atically. In general, it is highly desirable to develop methods for numerical semi-analytic evaluation of such diagramfunctions, like Feynman integrals. The problem of studying these integrals is a classic one, on which many papers havebeen written. However, some very basic questions still remain unanswered. For example, even in the one-loop case theprecise representation of fundamental group of the base by a multi-valued function defined by a Feynman integral isunknown [50]. There has been tremendous number of research works accomplished on supersymmetric amplitudes onmass shell, with one of the landmark papers being Ref. [51]. However, it is known that not all amplitudes evaluate topolylogarithms, therefore the subject of elliptic polylogarithms is being intensely studied [52]. On the mathematicalside, the structures of flat bundles defined by the Gauss-Manin connection are actively studied [53]. For generic valuesof parameters, it is known that the Gamma-series are a known tool to construct convergent expansions [54].However, despite this great progress, these techniques have not been applied to the problem at hand, namelyon-shell amplitudes relevant to e − p or e − e scatterings. One of the difficulties stems from the fact that theseamplitudes need to be evaluated on the mass shell, and thus they are infrared divergent. Also, one needs to have asystematic mapping of the space of kinematic invariants and convergent expansions in a covering of this space by opencylinder domains. Besides, there is a need for a new method to expand dimensionally regulated integrals away fromsingularties, as well as obtain the asymptotic expansion near the singular locus. Our method is based on identificationof small parameters in the corresponding domain, and expanding the integrand into series that are convergent on thechain of integration. The calculated results, namely amplitudes or cross sections, can be represented as power series,for the coefficients of which recursive relations in mathematical literature are available. Infrared regulators will berepresented by off-shellness of lines and show up as overall factors.There is a plan to calculate the NLO and NNLO RC in e − p and Møller scattering processes beyond ultrarelativisticlimit. These calculations will be based upon a new method (that will address the aforementioned issues), which is econstructed scattering angle [deg] s i m / ( e p / ee ) x s i m ( e p / ee ) Reconstructed scattering angle [deg] s i m / ( e p / ee ) x s i m ( e p / ee ) FIG. 26: The e − p to e − e ratios from simulations with different beam energies (labeled as sim x ) are plotted relative to thoseobtained with the nominal beam energy (labeled as sim), for the 2.2 GeV setting. In the upper plot the integrated Møllermethod is applied for all angular bins above 1.6 ◦ . In the lower plot the integrated Møller method is applied for all angular bins. nder development [55] . New results on e − e and e − p NLO RC, which will be coming from such a new andindependent method, shall be compared with the corresponding results from [24], in order to make sure in robustnessof the method before proceeding to calculations of NNLO RC contributions to the cross sections of both processes.In [24] such calculations have been performed for a very small scattering angle range of PRad, in 0 . ◦ ≤ θ ≤ . ◦ ,which corresponds to the Q range of 2 · − GeV ≤ Q ≤ · − GeV . For PRad-II the planned calculationswill be carried out with the lowest Q at ∼ − GeV (corresponding to a scattering angle at ∼ . ◦ ) up to Q at6 · − GeV . A Comprehensive Simulation
A comprehensive Monte Carlo simulation of the PRad setup was developed using the Geant4 toolkit [23]. Thissimulation takes into account realistic geometry of the experimental setup, and detector resolutions. The simulationconsists of two separate event generators built for the e − p and e − e processes [24, 25]. Inelastic e − p scattering eventswere also included in the simulation using a fit [26] to the e − p inelastic world data. The simulation included signaldigitization and photon propagation which were critical for the precise reconstruction of the position and energy ofeach event in the HyCal. For the PRad analysis, the comprehensive Monte Carlo simulation played a critical role in FIG. 27: Comparison between reconstructed energy spectrum from the 2.2 GeV data (black) and simulation (red) for: (a) the PbWO modules which cover scattering angles from 3.0 ◦ to 3.3 ◦ , corresponding to Q around 0.014 (GeV/c) ; (b) thePb-glass modules which cover scattering angles from 6.0 ◦ to 7.0 ◦ , corresponding to Q around 0.059 (GeV/c) (largest Q forPRad). Blue histograms show the inelastic e − p contribution from the simulation. The green dash lines indicate the minimumelastic cut for selecting e − p event for the two different detector modules. Due to the large difference in amplitudes, the elastic e − p peak (amplitude 2800 counts/MeV) is not shown in (a) , to display the ∆-resonance peak. the extraction of the next-to-leading order e − p elastic cross section from the experimental yield. The simulationconsists of two separate event generators built for the e − p and e − e processes, and they include next-to-leadingorder contributions to the cross section (radiative corrections), such as Bremsstrahlung, vacuum polarization, self-energy and vertex corrections. The calculations of the e − p elastic and Møller radiative corrections are performedwithin a covariant formalism, without the usual ultra relativistic approximation [24], where the mass of the electronis neglected. The two generators also include contributions from two-photon exchange processes [45–47]. A secondindependent e − p elastic event generator [25] was used as a cross check. The radiative corrections to the proton,which are typically neglected, were included in this generator. The two e − p generators were found to be in excellentagreement.Inelastic e − p scattering events were included in the simulation using an empirical fit [26] to the e − p inelasticscattering world data. Inelastic e − p scattering contributes a background to the e − p elastic spectrum which,when included in the simulation was able to reproduce the measured elastic e − p spectrum as shown in Fig. 27. The current status of the method will be reported in CFNS Ad-Hoc workshop “Radiative Corrections”, July 9-10 (2020) at Stony BrookUniversity, NY. n the PbWO segment of the calorimeter, there was a clear separation between the elastic and inelastic e − p events, and it was established that the position and amplitude of the ∆-resonance peak in the simulation agreedwith the data to better than 0.5% and 10%, respectively. The ∆-resonance contribution was found to be negligible( (cid:28) . segment of the HyCal, and no more than 0.2% and 2% for the Pb-glass segment, at1.1 GeV and 2.2 GeV, respectively. The generated scattering events were propagated within the Geant4 simulationpackage, which included the detector geometry and materials of the PRad setup. This enabled a proper accountingof the external Bremsstrahlung of particles passing through various materials along its path. The simulation includedphoton propagation and digitization of the simulated events. These steps were critical for the precise reconstructionof the position and energy of each event in the HyCal.To simuate the proposed PRad-II experiment, the comprehensive simulation of the PRad experiment was updatedto include the second plane of GEM detectors and the scintillator detector. The comprehensive simulation was usedto generate mock data for the PRad-II experiment. The mock data was then used with the PRad analysis package toextract the cross section and form factor G pE ( Q ). The robust r p extraction method developed for PRad (describedin sec. ) was use to obtain r p from the mock data (shown in Fig. 32). The simulations was also used for estimatingthe expected rates, the systematic uncertainties and the projected results of the PRad-II experiment (see sec. ). The FIG. 28: The anglular resolution (left) over the angular range covered in the experiment and Q resolution (right) as a functionof Q , at 0.7 GeV (red), 1.4 GeV (green) and 2.1 GeV (blue) electron beam energy. simulation as also used to show that two layers of coordinate detectors will provide an angular resolution of 0.001 -0.004 mrad for the smallest angle at the 0.7 - 2.1 GeV beam energy and 0.004 - 0.04 mrad for the largest angle coveredat these beam energies. The energy and angular resolutions were used to obtain the Q resolution shown in Fig. 28.The angular resolution is used to determine the size of the Q bins used to extract the cross section and electric formfactor from the simulated yield. Rates and beamtime request
The expected rates are calculated assuming the hydrogen gas-flow target used in the PRad experiment, whichachieved an areal density of 2 × H atoms/cm . We propose to run the PRad-II experiment with three differentbeam energy settings, 0.7 GeV, 1.4 GeV and 2.1 GeV. The projected scattering angle coverage is from 0.50 ◦ to 7.00 ◦ for all energy settings. All scattering angles below 5.2 ◦ are expected to have a full azimuthal angular coverage so thatthe geometric acceptance factor (cid:15) geom is nearly 1. Larger scattering angles are covered by the corners of HyCal andthus, only part of the azimuthal angles are covered. In the worst case (6.0 ◦ to 7.0 ◦ ), the geometric acceptance factorcan drop down to about 0.15. For estimating the overall rate, the acceptance is still close to 1 as the e − p crosssection falls roughly as 1 / sin( θ/ . The detector efficiency (cid:15) det will be dominated by the GEM efficiencies, which isabout 93% for the PRad GEMs. For PRad-II, one shall require two coincident hits on the two GEM planes for eachscattered electron. This lead to about 86% for e − p events and about 75% for e − e events.The event rate can be estimated using: N = N e · N tgt · ∆ σ · (cid:15) geom · (cid:15) det (2)where N e is the number of incident electron per second, N tgt is the target areal density, ∆ σ is the integrated elasticcross section, for which we will use the Born level cross section for simplicity. This leads to ∆ σ of 6.940 × − cm ,.730 × − cm and 0.766 × − cm for the 0.7, 1.4 and 2.1 GeV beam energy setting, respectively, for thescattering angular ranges mentioned above. The choice of beam current is based on the expected maximum datarate allowed by the new GEM detector DAQ (25 kHz), the expected trigger rate for the calorimeter and maximumpower allowed on the Hall-B Faraday cup (160 W). The Faraday cup is essential for the background subtractionusing the empty target data. We plan to use a current of 20 nA (1.248 × e − /s) at 0.7 GeV beam energy and70 nA (4.370 × e − /s) current at both 1.4 and 2.1 GeV beam energies. The 70 nA current limit is imposed by themaximum power allowed on the Hall-B Faraday cup.For the e − e scattering, if we require double-arm Møller detection, the scattering angular coverage will be 0.5 ◦ to9.5 ◦ for the 0.7 GeV (the electron at scattering angles larger than HyCal acceptance will be detected by the proposedscintillating detector) and 0.5 ◦ to 4.8 ◦ for the 1.4 GeV and 0.5 ◦ to 3.2 ◦ for the 2.1 GeV. In this case, the detectorefficiency will be 0.75 as we requires two hits on the two separated GEM planes for both scattered electrons. Theevent rates for e − p scattering and e − e scattering are shown in Table. ?? .We are requesting 4 days of beam time for 0.7 GeV, 5 days for 1.4 GeV and 15 days for 2.1 GeV production runs.For all energy settings, these will ensure that the statistical uncertainty of the largest angular bin (6.0 ◦ to 7.0 ◦ ) to beabout 0.3%, which is about 3 times smaller than that for the PRad experiment. We are also requesting an additional33% of beam time (8 days) for various empty target measurements, for the purpose of the empty target subtractionand beam background studies. The total requested beam time for various stage of the proposed experiment is listedin Table. III item e − p event rate e − e event rate TimeM e − /day M e − /day daysSetup checkout, tests and calibration 7.0Production at 0.7 GeV 129 230 4.0Production at 1.4 GeV 112 205 5.0Production at 2.1 GeV 50 90 15.0Empty target runs 8.0Energy change 1.0Total 40.0TABLE III: The PRad-II event rate and beam time request Robust extraction of the proton charge radius
Method and main results for PRad
There are various well-developed proton electric form factor, G E , models, such as [28, 56–62]. Most of them havebeen fitted with experimental data in high Q ranges. Meanwhile, these models have different kinds of extrapolationin lower Q ranges, for example, in the PRad Q range, which is from 2 · − to 2 · − (GeV / c) . Such studieshave been accomplished in Ref. [31], which in particular gives a general framework with input form factor functionsand various fitting functions (fitters) for determining functional forms that allow for a robust extraction of the inputcharge radius of the proton, R p , for the PRad experiment.The robustness of any suitable fitter when extracting the root-mean-square (RMS) charge radius of the protonin a lower Q range can be tested by fitting pseudo-data generated in that range by different G E models [31].In the fitting procedure, depending on a fitting function, different bias and variance are obtained. The bias iscalculated by taking the difference between the fitted radius mean value and the input radius value from a model:bias ≡ ∆ R p [bias] = R p [mean fit] − R p [input]. The variance is the fitting uncertainty ( σ ) represented by the RMSvalue of a fitting result. To control the total uncertainty, the number of free parameters in a fitting function shouldnot be too large. Otherwise, the variance from the fitting will be very large. If the variance coming out from a givenfit is small and the bias is within this variance, then the corresponding fitter is considered to be robust (the figuresin this note show it quantitatively). To compare the goodness between different robust fitters, the quantity calledroot-mean-square-error (RMSE) is used: RMSE = (cid:112) bias + σ . (3)The smaller the RMSE value is, the better the corresponding fitter is. In this section, we concisely show the methodand main results from [31] on R p ’s robust extraction for PRad. In Sec. we present our new results for PRad-II butsing the same method of PRad’s R p extraction. Generators:
Various G E generators (models) have been used in Ref. [31] for generating pseudo-data in the PRad Q range: namely, Kelly-2004 [28],
Arrington-2004 [56],
Arrington-2007 [57],
Ye-2018 [58],
Alarcon-2017 [59–61],
Bernauer-2014 [62], as well as
Dipole , Monopole , and
Gaussian [63].
Fluctuation adder and pseudo-data generation procedure:
In the PRad experiment, there are thirty three bins from0.7 ◦ to 6.5 ◦ at 1.1 GeV beam energy, and thirty eight bins from 0.7 ◦ to 6.5 ◦ at 2.2 GeV. To mimic the bin-by-binstatistical fluctuations of the data, the G E pseudo-data statistical uncertainty is smeared by adding G E (in each Q bin) with a random number following the Gaussian distribution, N ( µ, σ g ), given by N ( µ, σ g ) = 1 (cid:113) πσ g e − ( GE − µ )22 σ g , (4)where µ = 0 and σ g = δG E , and δG E comes from the statistical uncertainty of the PRad data. In the case ofthe PRad-II experiment, δG E in each bin will be the half of δG E in the PRad data, by assuming that the PRad-IIstatistics will have four times of that of PRad (discussed in the next section). Let us also give some more details onthe pseudo-data generation and fitting procedure:(i) To add the statistical fluctuations to the final results, the seventy one (thirty three + thirty eight) generatedpseudo-data points are added by seventy one different random numbers according to Eq. (4).(ii) The set of pseudo-data are fitted by a specific fitter f E ( Q ). In this procedure, the pseudo-data points at 1.1GeV and 2.2 GeV are combined and fitted by the fitter with two different floating parameters correspondingto two different energy setups. The other fitting parameters in the fitter are required to be the same for bothenergy setups.(iii) The fitted radius is calculated from the fitted function in (ii), with R p [fit] = (cid:32) − f E ( Q )d Q (cid:12)(cid:12)(cid:12)(cid:12) Q =0 (cid:33) / . (5)(iv) The above steps are repeated for 10,000 times for obtaining 10,000 sets of G E pseudo-data diluted by Eq. (4),and 10,000 R p [fit] values are also calculated.(v) R p [mean fit] is the mean value of the 10,000 R p [fit] results, and the variance is the RMS value of this R p [fit]distribution, which is also determined. Fitters:
One of the best fitters determined in Ref. [31], which robustly extracted R p for PRad, is the Rational(1,1), based on the multi-parameter rational-function, Rational (N,M) of Q , given by f rational ( Q ) = p G E ( Q ) = p (cid:80) Ni =1 p ( a ) i Q i (cid:80) Mj =1 p ( b ) j Q j , (6)where p is a floating normalization parameter, and p ( a ) i and p ( b ) j are free fitting parameters. For the Rational (1,1),the orders N and M are equal to one, and the input radius is calculated by R p = (cid:114) (cid:16) p ( b )1 − p ( a )1 (cid:17) . Tho morerobust fitters were found to be the 2 nd -order continuous fraction (CF) and 2 nd -order polynomial expansion of z .The other fitter functions, used to fit the generated pseudo-data in [31], are the Dipole, Monopole, Gaussian, andmulti-parameter polynomial expansion of Q . Although the 2 nd -order CF exactly has the same functional form as theRational (1,1), in Fig. 29 we show the results from the three best fitters plus also the 2 nd -order polynomial expansionof Q . One can see that the bias remain well within variance in the first, second and fourth plots for all the ninemodels, as shown in Fig. 29. In particular, the Rational (1,1) controls both the variance and RMSE at best. As aresult, PRad used the Rational (1,1) to obtain the proton radius [36]. Projections for PRad-II
Given the method and procedure for robustly extracting the proton radius, we can now look into PRad-II, for whichthe statistical uncertainty for measuring R p is planned to be ∼ IG. 29: The variance from the fitted PRad pseudo-data generated by nine G E models using the Rational (1,1), 2 nd -order CF,2 nd order polynomial expansion of Q , and 2 nd -order polynomial expansion of z , for which the bias is smaller than the variance.This figure is from [31].FIG. 30: Four variance-bias plots from fits with pseudo-data generated by the considered nine proton G E models, madeanalogously to Fig. 29, but for the PRad-II statistics. In these plots, the error bars are too small to be seen. Rational (1,1) is still suitable for this case, the statistical uncertainty of G E is taken to be the half of δG E in Eq. (4).By using the nine different proton electric form factor models for generating 10,000 sets of G E pseudo-data, and thenfitting them with the different fitters, we obtain the results shown in Fig. 30. The other fitters mentioned in Sec. arealso tested, but they are not as good as the ones shown here.We notice that the fitters of the Rational (1,1) and 2 nd -order polynomial expansion of z are still robust with thestatistics of PRad-II. However, the latter gives a larger variance compared to that obtained from the Rational (1,1).By comparing the RMSE from Eq. (3) in Fig. (31), one can see that overall the Rational (1,1) has the smallest RMSEvalues for all nine models. IG. 31: The RMSE for PRad-II obtained from all the fitters based upon the nine different proton G E models under consid-eration. Summary
As shown in Fig. 30, the
Ye-2018 model gives a much larger bias compared to the other models. The bias fromfitting the Rational (1,1) with the pseudo-data generated by the
Ye-2018 model is 0.476%. We can consider thisnumber as an upper bound, which corresponds to a 3 σ uncertainty. Then 1 σ of the bias will be 0.159% (0.0013 fm ofthe PRad-II projected uncertainty in the proton radius). If we add 0.0013 fm quadratically to the total uncertainty,then its absolute increment by considering this number will be 0.0001 fm, which is a very small number. Estimated uncertainties and projected results
The major improvement for the PRad-II r p result comes from the proposed use of a second GEM detector plane,which allows for more precise determination of the detector efficiency (see Fig. 22 in Sec. ). This in turn will enablethe use of integrated Møller method over the full angular range. This alone can already reduce the total systematicuncertainty by about a factor of 2, if the GEM efficiency is determined to better than 0.1% precision. As discussedearlier in this proposal, the integrated Møller method converts the Q dependent systematic uncertainties due toMøller scattering events into normalization type uncertainties which do not contribute to the systematic uncertaintiesof r p . Such systematic uncertainties include the Møller event selection, Møller radiative correction, acceptance andbeam energy related uncertainties. The contribution from uncertainty in detector acceptance was determined byshifting the GEM detectors by ± ∼ r p when using the integrated Møller method. Similarly, the beam energy related uncertainty was determined by shiftingthe 0.7 GeV electron beam energy by ± r p .The reduction in the uncertainties due to event selection is a result of both the second GEM detector and theHyCal upgrade, while the uncertainty due to HyCal detector response is reduced because of the upgrade of HyCalto an all PbWO calorimeter as shown in Fig. 18 in Sec. . The uncertainty from the beam-line background rejectionis reduced because of the anticipated better beam-line vacuum, the additional beam halo blocker and the improvedvertex reconstruction and tracking with the second GEM detector, as shown in Fig. 23 in Sec. . The proposal alsoincludes reduced uncertainty due to radiative corrections because of the new calculations that include the next-to-next-leading order Feynman diagrams in the radiative correction (see Sec. ). The projected result also assumes afactor of ∼
19 increase of the total statistics compared to PRad. This leads to > tem PRad δr p [fm] PRad-II δr p [fm] ReasonStat. uncertainty 0.0075 0.0017 more beam timeGEM efficiency 0.0042 0.0008 2nd GEM detectorAcceptance 0.0026 0.0002 2nd GEM detectorBeam energy related 0.0022 0.0002 2nd GEM detectorEvent selection 0.0070 0.0027 2nd GEM + HyCal upgradeHyCal response 0.0029 negligible HyCal upgradebetter vacuumBeam background 0.0039 0.0016 2nd halo blockervertex res. (2nd GEM)Radiative correction 0.0069 0.0004 improved calc.Inelastic ep pM parameterization 0.0006 0.0005 HyCal upgradeTotal syst. uncertainty 0.0115 0.0032Total uncertainty 0.0137 0.0036TABLE IV: The uncertainty table for r p from the PRad experiment, and the projected uncertainties for PRad-II. Uncertaintiesare estimated using the Rational (1,1) function. uncertainty of r p . The additional statistics will also slightly improve the systematic uncertainties that are statisticsdependent, such as the statistical uncertainties in the detector efficiencies and calibrations. The total systematicuncertainty is about a factor of 3.6 times smaller than that from the PRad and the total uncertainty is about 3.8times smaller. The projected uncertainties for PRad-II are shown in Table. IV. FIG. 32: (left) The G pE ( Q ) obtained from the mock data generated by the comprehensive simulation at 0.7 (blue), 1.4 (red)and 2.1 GeV (green) beam energies, which is then fit to a rational (1,1) functional form (dashed line) to extract the r p . (right)The same information shown in log scale on the x-axis. The comprehensive simulation of the PRad-II experiment was used to generate 10,000 mock data sets at the 3proposed beam energies. The G pE ( Q ) obtained from the mock data are shown in Fig. 32. The G pE ( Q ) was fit to arational (1,1) functional form to extract the r p as shown in Fig. 32. The r p extracted from the fits along with thestatistical uncertainty is r p = 0.8314 ± r p from the PRad-II experiment along with other measurements and the CODATA values are shownin Fig. 33. SUMMARY
We propose an enhanced proton rms charge radius experiment, PRad-II, which will achieve a factor of 3.8 loweruncertainty in the extracted radius compared to PRad. This improvement in uncertainty will be achieved by; i)collecting over an order of magnitude more statistics, reducing the statistical uncertainty by a factor of 4. This
IG. 33: The projected r p result from PRad-II, showing along with the PRad result and other measurements. is especially important for the highest Q region covered in the experiment and for reducing the total systematicuncertainties. ii) Adding a new GEM coordinate detector to incorporate tracking capability in the experiment.This will enable using the reconstructed interaction vertex to significantly reduce the beam-line background in theexperiment. This is especially important for the smallest scattering angles which is critical for reaching the lowestQ range of 10 − GeV for the first time in lepton scattering experiments. iii) Upgrade of HyCal to an all PbWO calorimeter. This will significantly enhance the uniformity of the detector package, a critical requirement for theprecise and robust extraction of the proton rms rcharge radius. iv) Upgrade of the FASTBUS-based HyCal readoutelectronics to a flash-ADC-based system speeding up the DAQ system by a factor of 7 and reducing the total beamtime to achieve the required statistics. v) Improvements to the beamline vacuum, and a second beam halo blockerupstream of the tagger, to further suppress the beamline background. This is critical for a clean separation of the ep and ee scattering events at the small scattering angles covered in the experiment. vi) Improved radiative correctionsfor both ep and ee scattering which will significantly reduces the uncertainty due to radiative corrections.In addition to the factor of 3.8 reduction in the total uncertainties compared to PRad, we also propose to enhance therange of Q covered in PRad-II. The proposed experiment will reach the lowest Q range of 10 − GeV accessed byany lepton scattering experiment and at the same time cover up to Q of 6 × − GeV in a single fixed experimentalsetup. The lowest Q range and hence the lowest scattering angles (0.5 - 0.7 deg.) will be covered with the helpof a new cross-shaped scintillator detector with a square hole in the center, placed 25 cm downstream of the target.The projected ∼ coverage of PRad-II will enable us to access the lowestQ range reached in lepton scattering experiments, thereby enhancing the robustness of the extracted charge radiusand help establish a new precision frontier in electron scattering. It will also help address the difference betweenthe results from PRad and all modern electron scattering experiments, in particular Mainz 2010 − the most preciseelectron scattering measurement to date. Finally, as the most precise lepton scattering experiment, PRad-II willexamine possible systematic differences between the e − p and µ H results.
ACKNOWLEDGEMENTS
This work was funded in part by the U. S. National Science Foundation (NSF MRI PHY-1229153) and by theU.S. Department of Energy (Contract No. DE-FG02-03ER41231), including contract No. DE-AC05-06OR23177under which Jefferson Science Associates, LLC operates Thomas Jefferson National Accelerator Facility. We are alsograteful to all granting agencies for providing funding support to the authors throughout this project.
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