Measurement of deuteron carbon vector analyzing powers in the kinetic energy range 170-380 MeV
JEDI Collaboration, F. Müller, M. Zurek, Z. Bagdasarian, L. Barion, M. Berz, I. Ciepal, G. Ciullo, S. Dymov, D. Eversmann, M. Gaisser, R. Gebel, K. Grigoryev, D. Grzonka, V. Hejny, N. Hempelmann, J. Hetzel, F. Hinder, A. Kacharava, V. Kamerdzhiev, I. Keshelashvili, I. Koop, A. Kulikov, A. Lehrach, P. Lenisa, N. Lomidze, B. Lorentz, P. Maanen, G. Macharashvili, A. Magiera, D. Mchedlishvili, A. Nass, N.N. Nikolaev, A. Pesce, D. Prasuhn, J. Pretz, F. Rathmann, V. Rolando, M. Rosenthal, A. Saleev, V. Schmidt, Y. Senichev, D. Shergelashvili, V. Shmakova, A. Silenko, J. Slim, H. Soltner, A. Stahl, R. Stassen, E. Stephenson, H. Ströher, M. Tabidze, G. Tagliente, R. Talman, F. Trinkel, Yu. Uzikov, Yu. Valdau, E. Valetov, C. Weidemann, A. Wronska, P. Wüstner
MMeasurement of deuteron carbon vector analyzingpowers in the kinetic energy range 170 - 380 MeV
F. M¨uller , M. ˙Zurek , Z. Bagdasarian , L. Barion , M. Berz ,I. Ciepal , G. Ciullo , S. Dymov , D. Eversmann , M. Gaisser ,R. Gebel , K. Grigoryev , D. Grzonka , V. Hejny , N. Hempelmann ,J. Hetzel , F. Hinder , A. Kacharava , V. Kamerdzhiev ,I. Keshelashvili , I. Koop , A. Kulikov , A. Lehrach , P. Lenisa ,N. Lomidze , B. Lorentz , P. Maanen , G. Macharashvili , A. Magiera ,D. Mchedlishvili , A. Nass , N.N. Nikolaev , A. Pesce , D. Prasuhn ,J. Pretz , F. Rathmann , V. Rolando , M. Rosenthal , A. Saleev ,V. Schmidt , Y. Senichev , D. Shergelashvili , V. Shmakova ,A. Silenko , J. Slim , H. Soltner , A. Stahl , R. Stassen ,E. Stephenson , H. Str¨oher , M. Tabidze , G. Tagliente ,R. Talman , F. Trinkel , Yu. Uzikov , Yu. Valdau , E. Valetov ,C. Weidemann , A. Wro´nska , and P. W¨ustner Institut f¨ur Kernphysik, Forschungszentrum J¨ulich, 52425 J¨ulich,Germany III. Physikalisches Institut B, RWTH Aachen University, 52056Aachen, Germany University of Ferrara and INFN, 44100 Ferrara, Italy Department of Physics and Astronomy, Michigan State University,East Lansing, Michigan 48824, USA Institute of Nuclear, Physics Polish Academy of Sciences, 31342Crakow, Poland Laboratory of Nuclear Problems, Joint Institute for Nuclear Research,141980 Dubna, Russia Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia JARA–FAME (Forces and Matter Experiments), ForschungszentrumJ¨ulich and RWTH Aachen University, Germany High Energy Physics Institute, Tbilisi State University, 0186 Tbilisi,Georgia a r X i v : . [ nu c l - e x ] S e p Institute of Physics, Jagiellonian University, 30348 Cracow, Poland L.D. Landau Institute for Theoretical Physics, 142432 Chernogolovka,Russia Moscow Institute for Physics and Technology, 141700 Dolgoprudny,Russia Research Institute for Nuclear Problems, Belarusian State University,220030 Minsk, Belarus Bogoliubov Laboratory of Theoretical Physics, Joint Institute forNuclear Research, 141980 Dubna, Russia Institut f¨ur Hochfrequenztechnik, RWTH Aachen University, 52056Aachen, Germany Zentralinstitut f¨ur Engineering, Elektronik und Analytik (ZEA-1),Forschungszentrum J¨ulich, 52425 J¨ulich, Germany Indiana University Center for Spacetime Symmetries, Bloomington,Indiana 47405, USA INFN, 70125 Bari, Italy Cornell University, Ithaca, New York 14850, USA Dubna State University, 141980 Dubna, Russia Department of Physics, M.V. Lomonosov Moscow State University,119991 Moscow, Russia Zentralinstitut f¨ur Engineering, Elektronik und Analytik (ZEA-2),Forschungszentrum J¨ulich, 52425 J¨ulich, Germany * corresponding author [email protected] September 3, 2020 (JEDI collaboration)
Abstract
A measurement of vector analyzing powers in elastic deuteron-carbon scat-tering has been performed at the Cooler Synchrotron COSY of Forschungszen-trum J¨ulich, Germany. Seven kinetic beam energies between 170 and 380 MeVhave been used. A vector-polarized beam from a polarized deuteron source wasinjected, accelerated to the final desired energy and stored in COSY. A thinneedle-shaped diamond strip was used as a carbon target, onto which the beamwas slowly steered. Elastically scattered deuterons were identified in the forwarddirection using various layers of scintillators and straw tubes. here data exist in the literature (at 200 and 270 MeV), excellent agreementof the angular shape was found. The beam polarization of the presented data wasdeduced by fitting the absolute scale of the analyzing power to these references.Our results extend the world data set and are necessary for polarimetry of futureelectric dipole moment searches at storage rings. They will as well serve as aninput for theoretical description of polarized hadron-hadron scattering. The main motivation for the measurements arise from plans to search for electric dipolemoments (EDMs) of charged hadrons in storage rings [1]. The existence of electric dipolemoments is connected to CP-violation and is therefore closely related to fundamentalquestions of the dominance of matter over anti-matter in the universe [2]. A storagering EDM measurement is based on the observation of a vertical polarization build-up of an initially horizontal polarization. This build-up is proportional to the EDMitself and to the analyzing power of the scattering process used to determine the beampolarization. The statistical error of the EDM measurement is inversely proportionalthe absolute value of the analyzing power. It is thus important to know the analyzingpower in a wide energy range.The paper is organized as follows. Section 2 outlines the theoretical backgroundand gives an overview of existing data. Section 3 explains the experimental setup. Theanalysis and results are presented in section 4.
The elastic cross section for purely vector polarized deuterons scattering from a spin 0target like carbon is given by [3]: (cid:32) d σ dCpol. (Θ , Φ)dΩ (cid:33) = (cid:32) d σ (Θ)dΩ (cid:33) · (cid:18) A y (Θ) P y cos(Φ) (cid:19) , (1)where the polar and azimuthal angles of the detected particles in the laboratory systemare denoted by Θ and Φ, respectively, see Figure 1. The vector analyzing power A y (Θ)is a property of the elastic scattering C(d , d) C between the carbon target and thepolarized deuteron beam. The projection of the polarization vector along the verticalaxis is denoted by P y .Due to azimuthal symmetry, the unpolarized deuteron carbon cross section (cid:16) dσ (Θ) d Ω (cid:17) depends only on the polar angle Θ. The number of detected scattered particles is givenby: d N (Θ , Φ)dΩ =
L · α (Θ , Φ) · (cid:32) d σ (Θ)dΩ (cid:33) · (cid:18) A y (Θ) P y cos(Φ) (cid:19) , (2)where L denotes the integrated luminosity and α (Θ , Φ) the detector acceptance. Equa-tion 2 is the basis for the extraction of the vector analyzing power as described inSection 4. 3 eam x zy
Θ Φ
Figure 1: Definition of the laboratory coordinate system with the z − axis along thebeam direction. The blue arrow indicates the direction of the scatterd deuteron.From previous measurements at T = 200 [4] and 270 MeV [5] it is known thatthe unpolarized differential cross section of elastic deuteron carbon scattering at a fewhundred MeV has a pronounced diffractive structure with some minima and maximain the forward hemisphere. Furthermore, the vector analyzing power of this reaction, A y , has a maximum value close to unity. As a result, this reaction is ideally suited forprecision polarization measurements. Therefore, high quality experimental data on the A y for d C elastic scattering in a broad range of kinetic energy and scattering angleof the deuteron are of importance.Available data on unpolarized differential cross sections of d C elastic scatteringcan be found at T =94 MeV, 125 MeV, 156 MeV [6], at 110 MeV and 120 MeV [7], at170 MeV [8], 425 MeV [9], and 650 MeV [10]. Theoretical interpretation of this dataat high energy of 650 MeV was done within the Glauber multiple scattering theory fornucleus-nucleus scattering using the harmonic oscillator shell model wave functions forthe C nucleus and using the nucleon-nucleon data [11], or nucleon-nucleus scatteringamplitudes [12], and deuteron proton scattering data [13] as input. At lower energies T =94 MeV, 125 MeV, 156 MeV the Glauber theory was applied to the d C elasticscattering in [14].Experimental data on polarized d C elastic scattering in the considered region ofenergy are poorer. In reference [5] the vector A y and tensor A yy analyzing powers andthe unpolarized differential cross section were measured in elastic and inelastic d Cscattering at T = 270 MeV. Data at T = 200 MeV are discussed in reference [4].The aim of this paper is the measurement of the vector analyzing power A y of d Celastic scattering at several kinetic energies in the region T = 170 −
380 MeV in theforward hemisphere. In addition to the use of this data for polarimetry in storage EDMexperiments, it can be used for a better understanding of the dynamics of the d Celastic scattering and its connection to the properties of the C nucleus and NN-, dN-,4nd CN-scattering amplitudes, where N denotes the proton or neutron.
The measurements were performed at the COSY accelerator facility at the
Forschungszen-trum J¨ulich in Germany [15]. A pure vector polarized deuteron beam was produced [16],accelerated and stored in the COSY ring. Seven different beam energies (180 MeV,200 MeV, 235 MeV, 270 MeV, 300 MeV, 340 MeV, and 380 MeV) were used. For theextraction of the vector analyzing power, the beam polarization was set to cycle throughthree polarization states: Unpolarized ( P ), upwards polarized in the laboratory framealong the vertical axis ( P y = P ↑ ), and downwards polarized along the vertical axis( P y = − P ↓ ). The absolute polarization value in the vertical state had to be deter-mined later, see Section 4. For data taking, the beam was slowly steered onto a thin,needle-shaped diamond target to undergo a scattering reaction with the carbon nuclei.The detector rate was kept constant at a level of 60-80k events/s by sending it into afeedback loop controlling the strength of the steerers. The beam intensity was about10 particles per cycle of 5 minutes duration. The angular distribution and energyof the scattered deuterons were recorded with the forward part of the former WASAdetector ( W ide A ngle S hower A pparatus ) shown in Figure 2, which is installed in theCOSY storage ring [17]. The WASA forward detector consists of five thick hodoscopelayers composed of pizza shaped plastic scintillators for energy measurement. Eachscintillator segment was read out by an individual photomultiplier tube. A four-layerstraw tube array was used to extract the angular information of each deuteron trackwith a resolution of 0 . ◦ in Θ and 0 . ◦ (at Θ = 2 ◦ ) and 2 . ◦ (at Θ = 17 ◦ ) in Φ. [17]. Anadditional set of three layers of thin plastic scintillators as well as the first forward rangehodoscope was used to generate the trigger signal. The signals from these four layerswere discretized by discriminators for each segment and then fed into an FPGA basedsystem that provided the trigger signal for the ADC modules. The trigger requirementwas an uninterrupted track from the very first scintillator layer all the way throughthe first forward range hodoscope layer. The detector covers a polar (Θ) angular rangefrom 2 ◦ to 17 ◦ and the full azimuthal (Φ) range.This detector setup allows one to record events in bins of Θ, Φ and energy of thescattered particle. The next section explains how to extract the analyzing power A y from the event rates. In order to select elastically scattered deuterons, a Monte-Carlo simulation was usedto perform an energy calibration of each detector layer. The multi-layer design ofthe detector allowed generating ∆ E n − vs. ∆ E n plots for the stopping layer n (lastreachable layer for a given energy) and the layer before (n-1) that could be used for5 ange Hodoscope:3 x 24 Elements (10 cm)2 x 24 Elements (15 cm)Pizza ShapedTrigger Hodoscope:1 x 48 Elements (5 mm)Pizza ShapedStraw Tubes:4 x 4 Layers0°, 90°, 45°, -45°Window Counter:2 x 24 ElementsPizza Shaped Carbon Target
Angular Coverage: θ : 2° - 17° Φ : 0° - 360° Beam z-direction
Figure 2: Schematic cross section of the forward part of the WASA detector. It iscomposed of two layers of thin plastic scintillators called FWC1 and FWC2 ( F orward W indow C ounter ) whose main purpose together with the FTH ( F orward T rigger H odoscope ) is to generate the trigger signal for the data acquisition system. Thefour successively rotated layers of straw tubes provide the angular information for eachtrack. The five layers of thick plastic scintillators called FRH1 to FRH5 ( F orward R ange H odoscope ) are used to obtain the energy information for each track.6igure 3: Energy loss in the second (FRH2) versus the third (FRH3) layer of theforward range hodoscope, ∆ E vs. ∆ E for various bins in Θ for a beam energy of270 MeV. The centers of the one degree wide bins are indicated in the plots. Thedata were fitted to a two dimensional normal distribution. Events within the 1 σ ellipseindicated in the figure entered the analysis. The diagonal areas at the bottom left ofthe plots originates from protons produced in a stripping reaction. All histograms werenormalised to the their respective maximum number of events in one bin.7article identification. The elastically scattered deuterons were selected using graphicalcuts on these plots (see Figure 3). The elastically scattered deuterons were binned in∆Θ = 1 ◦ wide bins for the identification of the elastic events but the final analysis wasperformed in 0 . ◦ -bins. The energy resolution of the forward detector is approximately5%. This allows to exclude events originating from break-up reactions. Note, that thecontribution of the excited state 2+ (4.4 MeV) of the carbon nucleus cannot be resolvedwith our detector. According to [5] its contribution to the cross section at a beam energyof 270 MeV amounts to 1 – 23% in the angular range 2–17 degrees with an analyzingpower of similar size compared to the elastic scattering. In order to extract the vector analyzing power A y from this data, it is useful to definean asymmetry parameter (cid:15) as follows: (cid:15) (Θ) = 32 A y (Θ) P y . (3)The classical way to extract (cid:15) would be to look at a left-right asymmetry (leftcorresponds to Φ = 0) for two data sets with opposite vertically polarized beams [3].This requires assumptions about acceptance and integration limits in Φ not to dilutethe sample with events where cos(Φ) ≈ i by cos(Φ i ) , the statistical error is given by: σ ( (cid:15) ) ≈ (cid:113) (cid:104) cos ∆Φ (cid:105) N , (4)whereas in the cross ratio method [3] one reaches σ ( (cid:15) ) ≈ (cid:113) (cid:104) cos ∆Φ (cid:105) N . (5)The gain in statistical error is thus (cid:118)(cid:117)(cid:117)(cid:116) (cid:104) cos ∆Φ (cid:105)(cid:104) cos ∆Φ (cid:105) ≥ , where (cid:104) . . . (cid:105) denotes the acceptance weighted average over Φ. Due to the weighting pro-cedure the full polar range ∆Φ from 0 to 2 π can be used for the asymmetry calculationwithout an increase of the statistical error for larger ∆Φ. Since the events at Φ ≈ ± ◦ are assigned with a very small weight, they cannot dilute the sample anymore. Further,8his method does not require the detector acceptance α to be flat in Φ but it can evenbe determined. In addition this method reaches the Cramer-Rao bound [19] of minimalvariance on (cid:15) .The analysis was performed in the following way: Cycles with polarization state upand down were analyzed together with an unpolarized cycles, and asymmetries (cid:15) ↑ and (cid:15) ↓ were extracted for every Θ bin independently. Dividing these asymmetries by thecorresponding polarization values P y = P ↑ and P y = − P ↓ yields the analyzing power A y .The asymmetry determination involves a χ minimization, (see [18], eq. 14), hereusing as input 9 measurements: For each of the three polarization states (up, down,unpolarized) three sums (cid:80) N events i =1 cos(Φ i ) n with n = 0 , , (cid:15) ↑ and (cid:15) ↓ .Having 9 equations and only 8 parameters allows one to perform a χ test with onedegree of freedom. Figure 4 shows the corresponding χ probability distribution whichlooks reasonable flat as expected. Since the asymmetries were calculated independentlyfor every Θ bin (=28), and every energy data set (in total 8), the total number of entriesis 8 ×
28 = 224. -value p N u m be r o f E n t r i e s Figure 4: p -value distribution ( p = (cid:82) ∞ χ f ( χ , n )d χ ) for all extracted asymmetries. P ↑ and P ↓ The polarized ion source [20] used to create the polarized deuteron beam was set to pro-duce the maximum achievable magnitude of 2 / P ↑ [%] P ↓ [%]200 MeV 62 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . (cid:15) ↑ and (cid:15) ↓ to publishedanalyzing powers A y . The errors in the first three lines result from the fit in fig-ure 5. The last line is the the average ¯ P of the three measurements. The errorwas taken from the unbiased estimate of the standard deviation of the three values (cid:113)(cid:80) i =1 ( ¯ P − P i ) / ( N − A y for 200 MeV [4] and for 270 MeV [5] are available and were usedto evaluate the polarization value in our experiment.In order to obtain polarization values P ↑ and P ↓ , the asymmetry parameters (cid:15) ↑ and (cid:15) ↓ , calculated as described in section 4.2 for 200 MeV and 270 MeV, were fitted tothe published vector analyzing powers at the corresponding energies. This allowed oneto verify that the line-shape of our result was in agreement with the published data.From the scaling parameter of the fit, the polarization magnitude could be calculatedaccording to Equation (3). Figure 5 shows the result of these fits. Both polarizationstates were fitted independently, resulting in polarization value for each state. Thecalculated polarization magnitude is given in Table 1. The two data sets at 270 MeVwere also processed separately. The line-shapes for both energies and polarization statesare in a good agreement with the published data. The fit result for the comparison ofour 270 MeV data with [5] (see Figure 5 upper two plots) resulted in polarization valueswhich differ in the order of ∼
10 % between the two data sets. In the result for the vectoranalyzing power given in [5], the theoretical limit of A maxy = 1 . ∼ . ≈
25 degree, indicating an overestimation of A y . When this result isused to calculate the polarization of our beam, according to Equation (3) this leads toan underestimation of the fitted P y . The fit result of the comparison of our 200 MeVdata with [4] (see lower plot in Figure 5) yields a polarization magnitude that is veryclose to the limit of pure vector polarization P maxy = 2 /
3. In general, it is not possibleto decide which value of polarization from the three fits should be taken and, therefore,taking the average of all three results seemed to be appropriate. The average of allthree data sets was found to be P ↑ = 55 . ± . P ↓ = 37 . ± . (cid:113)(cid:80) i =1 ( ¯ P − P i ) / ( N − .4 Determination of analyzing power A y These average polarization values were now used for all beam energies to determine theanalyzing power A y . The result is shown in Figure 6 and Table 2. The statistical erroris indicated by the vertical error bars on the data points and is in most cases smallerthan the symbol size. The systematic error, mainly due to the error in the polarizationmeasurement, is indicated by the red error band. Contributions from other sources werefound to be negligible. For example, fits to the data allowing for a tensor polarizationcontribution showed that A y changes by less than 1% compared to fitting the dataallowing only for vector polarization. Other systematic uncertainties, e.g. smearing inΘ and Φ, have also a negligible contribution. The measurements show a maximum of A y in the interval of the scattering angle Θ =0 ◦ − ◦ and give some indication for the presence of a second maximum at largerscattering angles. One should note that two maxima are found in [5] at 270 MeV at Θ =13 ◦ and 25 ◦ , respectively, which were fitted by the optical model [5]. With increasingenergy the maximum observed moves to lower scattering angles. The maximum locatedat Θ ≈ ◦ for 200 MeV is shifted to Θ ≈ ◦ for 380 MeV. This property is qualitativelyreproduced by the three-body model of [21] formulated on the basis of the Glaubertheory with nucleon- C scattering amplitudes used as input. The maxima appear atthe same momentum transfer q for all seven energies. This feature is also reproducedby the three-body model [21] and reflects the key properties of the Glauber theorywhich is formulated in terms of the elastic form factors of colliding nuclei. The measurements performed at the COSY accelerator facility allowed for the extrac-tion of the vector analyzing power in elastic deuteron carbon scattering reaction usinga polarized deuteron beam with seven beam energies ranging from 170 to 380 MeV.These results represent a novelty with the exception of the measurements at 200 MeV[4] and 270 MeV [5] used as a reference. These results are mandatory inputs for figureof merit estimations for future polarimetry in the context of deuteron electric dipolemoment experiments planned at storage rings.11 [deg] Q y V e c t o r A na l yz i ng P o w e r A Satou et al. › ˛ Fitted fl ˛ Fitted dC Vector Analyzing Power for 270 MeV Part I [deg] Q y V e c t o r A na l yz i ng P o w e r A Satou et al. › ˛ Fitted fl ˛ Fitted dC Vector Analyzing Power for 270 MeV Part II [deg] Q y V e c t o r A na l yz i ng P o w e r A Kawabata et al. › ˛ Fitted fl ˛ Fitted dC Vector Analyzing Power for 200 MeV
Figure 5: Measured asymmetry for the upwards (cid:15) ↑ (blue) and downwards (cid:15) ↓ (black)polarized beam as a function of the polar angle in the laboratory. The asymmetrieswere fitted to the reference data (red) by Satou et al. [5] and
Kawabata et al. [4] toobtain the beam polarization. The 270 MeV data was measured in two sets that werefitted individually. 12 [deg] Q - - - - - a + y A na l yz i ng P o w e r A = 0.0 a
380 MeV = -0.4 a
340 MeV = -0.8 a
300 MeV = -1.2 a
270 MeV = -1.6 a
235 MeV = -2.0 a
200 MeV = -2.4 a
170 MeV
Vector Analyzing Power for Elastic dC Scattering
Figure 6: Reconstructed vector analyzing power for deuteron beam energies of (from topto bottom) 380 MeV, 340 MeV, 300 MeV, 270 MeV, 235 MeV, 200 MeV and 170 MeV.The curves are subsequently offset by 0.4 for better readability. The statistical errorsare indicated by the vertical error bars on the data points. In most cases they aresmaller than the symbol size. The red regions show the systematic errors, comingmainly from the uncertainty in the polarization measurement.13 cknowledgments
The authors would like to thank the staff of COSY for providing good working condi-tions and Colin Wilkin for comments on the manuscript. This work has been financiallysupported by an ERC Advanced-Grant srEDM ”Electric Dipole Momentsusing storage rings” of the European Union, and by the Shota Rustaveli National Sci-ence Foundation of the Republic of Georgia (SRNSFG grant No. DI-18-298: ”Highprecision polarimetry for charged-particle EDM searches in storage rings” .14 n g l e [ ◦ ] E n e r g y [ M e V ] . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
002 2 . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
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009 11 . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
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013 14 . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
014 14 . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
015 15 . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
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