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BATES 12C PARITY VIOLATION EXPERIMENT
S. Kowalski
To cite this version:
S. Kowalski. BATES 12C PARITY VIOLATION EXPERIMENT. Journal de Physique Colloques,
1990, 51 (C6), pp.C6-175-C6-183. �10.1051/jphyscol:1990614�. �jpa-00230877�
COLLOQUE DE PHYSIQUE
C o l l o q u e C6, s u p p l g m e n t au n 0 2 2 , Tome 51, 15 novembre 1 9 9 0
BATES
12c
PARITY VIOLATION EXPERIMENTS. KOWALSKI
Bates Linear Accelerator Center, Laboratory f o r Nuclear Science and Department o f Physics, Massachusetts I n s t i t u t e o f Technology, Cambridge, MA 0 2 1 3 9 , U.S.A.
Abstract
-
An experiment measuring the parity violating asymmetry in the elastic scattering of lon- gitudinally polarized electrons from 12C has been successfully completed. The asymmetry, which is due to the isoscalar vector hadronic piece of the weak neutral current, is dependent only on the weak mixing angle and predicted t o be 0.70 f 0.006 ppm by the Standard Model for our experimental kinematics. Our measured value is 0.60 rt 0.14 f 0.02 ppm where the first error is purely statistical and the second is systematic, dominated by uncertainties in our normalization. From this asymmetry we extract a value for the coupling constant = 0.136 & 0.032 f 0.009, which is consistent with the prediction of the Standard Model.Resum6 -
Nous avons rGalis6 une experience de mesure de l'asymetrie, qui v i o l e l a p a r i t 6 , dans l a d i f f u s i o n 6lastique d'blectrons longitudinalement polarises par l e ' * C . L'asymetrie due B l a p a r t i e hadronique v e c t o r i e l l e i s o s c a l a i r e du courant neutre depend seulement de l ' a n g l e de mblange e t
.
pour n o t r e cinbmatique, l e mod6le standard prevoit une valeur de 0 . 7 M . 0 0 6 ppm. Nous avons mesure une valeur de 0.6M.14M.02 ppm oa l a premiere e r r e u r e s t purement s t a t i s t i q u e e t l a seconde systematique, due pour l ' e s s e n t i e l A l ' i n c e r t i t u d e de n o t r e normalfsation. De c e t t e asymetrie, nous extrayons l a valeur =O. 136M.032W.009 de l a constante de couplage; e l l e e s t compatible avec l a prediction du Modele Standard.1 - INTRODUCTION
Experiments designed to probe the structure of the neutral currents continue to be of great interest to atomic, nuclear and particle physicists. All of the experiments in the field are in impressive agreement with the Standard Model (SM)/l/ of Glashow, Weinberg and Salam. At present the best value for the weak mixing angle, a free parameter in the theory, is sin28w = 0.233 z t 0.002./2/
The neutral currents are known t o be parity violating and this aspect of the structure may be studied by means of polarized electron scattering. Parity violating asymmetries were first observed in the scattering of high energy polarized electrons from deuterons at SLAC/3/ and in the spectra of heavy atoms/4/ at low energies. These results provided some of the early confirmations for the predictions of the SM. They also motivated later efforts at MAINZ/5/ and Bates to extend these measurements to other nuclei with improved accuracy and to probe further the structure of the neutral currents.
In the electron-quark sector the parity violating part of the neutral weak current can be described by the parity violating Lagrangian
The e; are a complete set of vector and axial vector parameters to be determined by experiment. We have ignored in this description possible couplings to strange quarks. Experiments depend on linear combinations of these couplings - models provide predictions for them. For purposes of nuclear physics it is convenient to redefine the couplings in terms of isoscalar and isovector combinations at the hadronic vertex. This is illustrated schematically in Figure 1.
The standard model predictions for the coupling constants/6/ are given by:
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990614
COLLOQUE DE PHYSIQUE
S
=-,E
-€gA
= 0 = 0.00 (5)The SLAC and atomic physics (CS) experiments are mainly sensitive to the hadronic vector current. These results depend in an almost orthogonal manner on linear combinations of & and -j. and provide our best model-independent values for these coupling constants.
The goal of the Bates 12C parity violation experiment was to measure ;j. precisely using a technique which involves very little theoretical ambiguity in the interpretation of its result. The experiment measured the spin dependence in the elastic scattering of longitudinally polarized electrons from carbon nuclei. The parity-violating asymmetry is defined as
where aR(oL) is the differential cross section for the scattering of electrons with right (left) helicity.
I2C is a spinless and isoscalar nucleus and the electromagnetic amplitude for elastic scattering is described by a single form factor. At low energies where a phenomenological four-fermion interaction is a good approximation, the asymmetry, A, may be written a t the tree- leve1/7,8/ as
where G F is the Fermi coupling constant, a is the fine structure constant, Q is the momentum transfer, and -j. is the parity-violating constant for an axial vector coupling to the electron and an isoscalar coupling to the hadronic matter. The expression for the asymmetry is completely independent of the form factors.
It is a direct consequence of our assumption that the weak and electromagnetic currents couple to exactly the same operators. The cancellation is Q2 independent and a precision test could be sensitive to possible extensions of the SM.
The measurements described in this workshop report were carried out a t the MIT-Bates Linear Accelerator Center. A description of the experiment and our results are described in a paper by P. Souder e t a1./9/
Fig. 1 - Isoscalar and isovector parity violating electroweak amplitudes.
2
-
EXPERIMENTThe choice of optimal kinematics for elastic scattering from 12C was influenced by several important con- siderations. To first order it was important to maximize A20 where A is the asymmetry to be measured and o is the differential cross-section. Signal-to-noise considerations, contamination due to Mott asymmetry and contributions due to the inelastic levels in I2C also influenced our choice.
We designed the experiment t o use a beam energy of 250 MeV, a scattering angle of about 35" and a momentum transfer Q = 150 MeV/c. With a beam polarization P, = 37%, the Standard Model predicts an experimental asymmetry A,,, = AP, = 0.70 X 10-6. Such a small asymmetry places severe demands on the apparatus, in terms of both acquiring sufficient statistical precision as well as maintaining adequate control of systematic errors.
The apparatus for this measurement consisted of a polarized electron source, a pair of single-quadrupole spectrometers, a M ~ l l e r spectrometer, precision beam monitors, and a high-capacity data acquisition sys- tem. A schematic layout of the experimental apparatus is shown in Figure 2. We briefly summarize below
0 Twoid (Intensity Monitor)
&am Position Monitor
Steering
4
Dipole W d ChicaneFig. 2
-
Schematic layout of the experiment showing the polarized source, accelerator, Meller apparatus and detector system.the essential features of these systems. A more detailed description of the hardware and a discussion of the techniques used can be found in the four theses/lO/ which resulted from this work.
a. Polarized Source
The source/ll/, which provides an intense beam of longitudinally polarized electrons was built especially for this experiment. It is based on photoemission from a GaAs crystal/l2/ using circularly polarized light.
The helicity of the electron beam is proportional to the helicity of the incident light and can be controlled electro-optically by the voltage applied to a Pockels cell in the laser beam.
The source design consists of three vacuum chambers isolated by valves, with magnetically coupled ma- nipulation devices used for crystal transfer between chambers. The hardware is enclosed in a Faraday cage that is maintained at -330 kV. The gun chamber, which houses the extraction electrodes and a GaAs crystal during operation, is connected to a high voltage accelerator column. Both the gun and preparation chambers must be maintained at vacuums better than 1 X 10-l' Torr. At poorer vacuums, trace con- tamination of the GaAs crystal results in a substantially reduced lifetime. An extraction chamber, which is connected to the preparation chamber, acts as an air-lock allowing crystals to be introduced from the outside into the ultra-high vacuum environment.
The main components of the optical system are a 2W cw krypton-ion laser and a series of optical shutters and circular polarizers. An electro-optical shutter, consisting of two crossed polarizers, half-wave plate and a Pockels cell, modulated the laser beam to match the 1% duty factor of the accelerator.
A "flipper" system consisting of a half-wave plate, crossed polarizer and a Pockels cell produced the circularly polarized light and controlled helicity reversal. The half-wave plate served as a "slow" helicity reversal device. The two different orientations of the plate produced a change in correspondence between the polarity of the potential difference applied to the Pockels cell and the handedness of the emerging laser light. The effect was to change the overall sign of all downstream helicity- correlated differellces including the electro-weak parity- violating asymmetry.
Following the optics table, the laser beam travelled approximately 20m through an optical transport system that included four mirrors and a vacuum window before reaching the Ga.As photocathode. A converging
C6-178 COLLOQUE DE PHYSIQUE
lens was installed at a point approximately half way along this path, between the second and third mirrors, to provide ~oint-to-point focussing between the Pockels cell and the GaAs crystal. The idea was to make the position of the laser beam on the crystal insensitive t o angular fluctua.tions which may be induced in the beam by misalignments or instability in the operation of the Pockels cell. The entire laser beamline was enclosed and stabilized to reduce position jitter due to air currents and temperature gradients.
b. Beamline I n s t r u m e n t a t i o n
The beam delivery system was designed and carefully instrumented to ensure that the expected small asymmetries could be accurately measured. A set of beamline monitors measured the unwanted effects of helicity reversal. They included seven toroid current monitors to measure the intensity, four microwave cavity position monitors (BPM's) in front of the target to determine the position and angle of the beam and a position monitor to measure the beam energy at a location in the chicane where the beam was dispersed in momentum.
A coil-pulsing system was designed and implemented which allowed the steering correctors along the beam transport line t o be synchronously adjusted during data acquisition. The coil current changes were triggered a t a 47Hz rate. This rate was fast enough so that the system calibration was unaffected by drifts and slow enough to add negligibly t o the statistical fluctuations in the measurement of the cross-section.
Approximately one-third of our data was acquired with the coil-pulsing system operational.
The combination of precision monitors and the coil pulsing scheme allowed us to measure and correct for systematic errors. We were also able to calibrate the BPM's and measure the sensitivity of the detector system t o known displacements of beam energy, position and angle at the target. This allowed us to locate and maintain the beam position and direction such as to minimize the sensitivity of the experiment to beam parameters.
c. Detector S y s t e m
The detector system (Figure 3) consisted of a pair of single-quadrupole spectrometers, UVT-lucite Ckrenkov counters, analog and control electronics and a high capacity data acquisition system.
h. Extended Target
Target Chamber
Fig. 3 - Detector system including pair of quadrupole spectrometers, extended 12C target and CCrenliov counters.
The two spectrometers were fixed on either side of the beam line a t a nominal scattering angle of 35".
Each had an acceptance of -1Omsr and a mon~entum resolution of -12MeV. Lead collimators at the front, rear and in the midplane of the quadrupoles defined the acceptance and momentum discrimination of the
system. The focussing was in the vertical plane. A bank of 12 C6renkov detectors directly coupled to phototubes formed the detector array. The integrated signals from adjacent phototubes were summed in pairs. Six signals (3 up13 down) were acquired and stored to tape from each spectrometer arm.
The electron beam impinged on a 5 g/cm2 segmented carbon target. About 10' electrons were detected during each 17ps burst and the integrated responses over the beam burst were recorded by 16-bit ADC's.
Beam polarization was measured frequently during the course of the experiment. The polarimeter that was used determined the polarization by measuring the asymmetry observed in relativistic electron-electron (Moller) scattering. This asymmetry can be shown to be given by
where PT and PB are the target and beam polarizations respectively. The asymmetry is a maximum for a center-of-mass scattering angle of 90°, which corresponds to a laboratory scattering angle of 3.66" at the incident beam energy of Elab = 250 MeV.
The polarimeter design is similar to that used at SLAC/12/. It consists of a lmil Supermendur foil target centered in a pair of Helmholtz coils and oriented at approximately 45' to the beam direction. The target polarization was measured to be 8.3 f: 0.3%.
The momentum of the scattered electrons, whose energy is half the beam energy, was analyzed in a magnetic spectrometer. A tungsten collimator selected those electrons which had scattered through 3.66". Excellent signal-to-noise was achieved with the system.
3 - RESULTS
In this short report we can only summarize briefly the careful planning and development, over many years, that was required to successfully complete this experiment. A large part of this effort was directed towards identifying and developing techniques for controlling and/or eliminating the many sources and contributions of systematic effects which make the measurement of small asymmetries extremely difficult.
a. Data Taking
A major consideration in implementing a data taking scheme was the issue of noise. It was important to use a technique where the noise contributions would be less than the statistical error per pulse. To achieve this we operated the accelerator at a pulse rate of 600Hz locked to the 60Hz line frequency. The noise associated with the 60Hz frequency was minimized by dividing the data into ten separate Lctimeslots"
corresponding to the 60Hz harmonics and then analyzing the data for each timeslot independently.
The beam helicity was set quasi-randomly for each pulse according to the following pattern. Ten random helicities were chosen, one for each timeslot. The pattern was complemented for the next ten beam pulses, and ten asymmetries were computed, each based on a complementary pulse-pair. This process was repeated every ten pulse pairs, i.e. at a 30Hz rate.
During typical operation, we ran with a relatively high average current of 30 - 60pA at the target. Our accumulated data amounted t o 307 half-hour runs, each of which filled a large magnetic tape. With each timeslot treated independently, we accumulated 3070 individual "mini-runs". The statistical error for each mini-run was computed using the variance of the asymmetries. Approximately 1% of the data was rejected by loose cuts which were associated with accelerator malfunctions.
A histogram of the measured asymmetry for each mini-run normalized to its statistical error is presented in Figure 4. The shape, as demonstrated by the solid curve, is Gaussian with the expected width over more than two decades. We are confident that our statistical errors are precisely understood.
b. S y s t e m a t i c Errors
The main objective in this experiment was to measure a cross-section which, apart from the electro-weak physics, is independent of the sign of the helicity. Our goal was to achieve this for a level of systematic errors below the statistical precision.
There were many sources of systematic errors which had to be evaluated and carefully understood in the course of this experiment. They 'include: bea.m parameters (intensity, energy, position, direction, emittance,transverse polarization); hardware (drifts and noise, crosstalk/pickup, linearity); nuclear physics
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LINEAR PLOT
LOG PLOT
0
Fig. 4
-
Histogram of the measured asymmetry, Ai, normalized to its statistical error, for each of the 3070 mini-runs. The solid curve is a Gaussian of unit variance with area equal to the number of mini-runs.(isospin admixtures, inelastic contributions, target purity, strangeness). In this report we will elaborate on some of the most important ones and on our techniques for dealing with them.
Correlations of beam parameters with helicity, such as energy, position and intensity, are the most impor- tant class of systematic errors. We controlled these errors by minimizing helicity-correlations during data acquisition and made corrections to the raw asymmetries using the position monitor data during analysis.
There were two major sources of such helicity-dependent correlations. First, the intensity of the laser light reaching the photocathode may depend slightly on helicity. The resulting helicity-correlated current changes are coupled by accelerator beam loading to energy changes:
The dependence of the electromagnetic cross-section on eneSgy is approximately given by (150MeVlc ''C - elastic)
To maintain spurious asymmetries a t a level AA < 1 0 - ~ requires that the helicity-dependent current fluctuation A I I I
<
7 X 1OW7.The principle source of the laser intensity correlation is the PITA/13/ (polarization induced transport asymmetry) effect, where the optical system transmission efficiency from the Pockels cell to the photo- cathode depends upon helicity. We start with light which is assumed to be linearly polarized with its polarization vector making an angle of ~ / 4 radians with respect to a fixed axis. On passing through a quarter-wave (X/4) retardation plate which has imperfections, the emerging light is not in general com- pletely circularly polarized, but has a small degree of ellipticity. In our case, the quarter-wave retardation was produced by a Pockels cell. Small deviations in the voltage applied to the Pockels cell resulted in light that was slightly elliptically polarized.
Leaving the Pockels ceIl we assume the light, now elliptically polarized, enters an asymmetric transport system in which the transport efficiency depends on the direction of the principal axes of the ellipse. These directions are slightly different for right- and left-handed beams, resulting in a helicity-dependent light intensity on the GaAs crystal.
In practice the PITA effect was easily controlled. We found that we could adjust electro-optically the appropriate phase through control of the voltage applied to the Pockels cell and in turn minimize the intensity asymmetry. This adjustment was implemented in practise by means of a slow feedback loop. The intensity asymmetry was calculated on- line every three minutes and the result used to adjust the voltage.
As a result, the helicity-correlated intensity asymmetry averaged over the entire run was reduced to about 1 PPm.
Another cause of intensity correlations is the helicity correlated trajectory of the electron beam which is due to the helicity dependent position of the laser beam striking the crystal. This shows up as beam position and angle correlations at the target, resulting in spurious asymmetries. One source for this effect is a deflection of the laser beam by the Pockels cell. We minimized the effect by very careful alignment of the cell and by using point-to-point focussing between the Pockels cell and the GaAs crystal.
In analyzing the data, we found it necessary to make small corrections for systematic asymmetries as measured by the beam monitors. The experimental asymmetries were derived from the raw asymmetries using the algorithm
5
Aezp = Araw
- C
ai 6Mi,i = l
(11) where A,,, is the measured uncorrected asymmetry, 6Mt are the helicity-correlated differences measured by the beam monitors, and ai are correction coefficients, which are a measure of the sensitivity of the asymmetry to fluctuations in the beam parameters. Ramping beamline steering coils, during data taking, allowed us to determine the correction coefficients using monitor measurements of beam position and angle at the target. Under normal accelerator operations, there are typically large, real fluctuations in the beam current and hence the energy. Correlation analysis of the energy measurement in the beamline chicane was used to extract the energy sensitive coefficient. An energy vernier (fast phase shifter) at the rf input to one of the accelerator klystron amplifiers provided a controlled and independent measure of the sensitivity. It was important to measure the sensitivities, a i , during data taking to ensure their validity for our specific running conditions. Typical values for the ai were about 10 ppmlpm, and the average helicity-correlated position differences were on the order of a fraction of l p m .
In this experiment it was important to exploit all approaches to detect and eliminate systematic errors. An important technique involved the reversal of the beam- helicity by a completely independent method. We changed the direction of the linear polarization of the laser light incident on the Pockels cell by means of a half-wave plate. This changed the sign of the parity-violating asymmetry without altering the contribution of most of the undesirable effects.
c. Experimental Results
In Table 1 we list all of the corrections (ppm) to our experimental asymmetry together with their estimated uncertainties. The root mean square value of the corrections due to the position and energy monitor differences for individual runs was 0.3 ppm. The average correction for the entire data sample is only 0.04 ppm.
Table 1. Systematic Corrections a n d Uncertainties
Correction Value
Energy and Position Monitors 0.04
Electronic Cross-Talk -
Transverse Polarization -
Nonlinearities -
Phase Space -
Magnetized Iron Bacliground - Total
Error f 0.006 f 0.001 f 0.005 f 0.007 f 0.006 f 0.010
&0.016
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A lot of attention was paid to minimize all identified sources of systematic errors. The elimination of ground loops was particularly important in reducing to a negligible level the electronic cross-talk from high voltage pulsing of the Pockels cell. The limits for possible contributions of transverse polarization to the asymmetry were determined by comparison of the difference in the asymmetries measured with each of the spectrometers (left and right) used in the experiment as shown in Figure 2. We have estimated that the following systematic errors are small; electronics nonlinearities, helicity-dependent beam phase-space differences, and helicity-dependent backgrounds resulting from beam electrons scattering from polarized electrons in magnetized iron.
An important check on our systematics is a measurement of an asymmetry that should vanish. If we neglect the reversal of the half-wave plate, in the data analysis, the measured asymmetry is 0.04f 0.14 ppm.
Similarly the difference in the measured asymmetry between the two spectrometers is 0.14 f 0.14 ppm.
This latter result gives us confidence that contributions due t o transverse polarizations are not significant in this experiment.
Table 2. Normalization Factors
Beam Polarization, P, 0.37 f 0.02 Nuclear Structure 1.00 f 0.01 Background 0.98 f 0.02
Our result for the measured raw and the corrected parity violating asymmetry is given by A,,, = 0.56 f 0.14ppm,
A,,, = 0 . 6 0 k 0 . 1 4 f 0.02ppm, (12)
where the first error is statistical and the second is systematic. To extract a value for -"y, we needed to account for various normalization factors. These included the average effective Q2, the beam polarization, and the backgrounds due to inelastic nuclear levels and scattered neutrons. These factors are summarized in Table 2. The beam polarization was measured 24 times during the experiment by using Mfiller scattering.
We obtain
-"y = 0.136 f 0.032 f 0.009, (13) which is consistent with the prediction of the Standard Model where,
We have used the best current value of 0.233 k 0.002 for the weak mixing angle to calculate -"ysM.
IV. Summary
We have demonstrated with this measurement that parity violation experiments in the electron-quark sector are possible a t sensitivity levels as low as 0.02 ppm. The Bates 12C experiment, in its data taking phase, represented a facility investment of a.pproximately 7000pA - hr of beam. At a realistic average current of 50pA, this is only 140 hr of beam on target. On the scale of most other major experiments this is a relatively modest commitment.
Based on these very promising results, it is clear that significant improvements in a future 12C measurement are entirely feasible. It is reasonable to imagine large acceptance spectrometers with factors of 10-30 increased acceptance which together with a substantially longer running time would result in a statistical error of a few percent. At this level of precision theoretical uncertainties may become important. We will need to understand that the effects of hadronic contributions to the radiative corrections,/l4/ parity admixtures,/l5 and isospin mixing/l6/ are tractable at this level before committing to such a major effort. A signi
d
cantly larger contribution, about which there is currently much speculation and a lot of interest, could come from a large charge radius of strange quarks in the nucleon./l7,18/Another parity violation experiment of great current interest is elastic scattering from hydrogen./l9/ The phenomenology is rich and varying the kinematics allows for sensitivity to different physics./20/ A low Q2 backward angle scattering measurement has recently been approved a t Bates.1211 The goal of this experiment is to measure the contribution of strange quarks to the static anomalous magnetic moment of the proton. A more speculative measurement would exploit parity violation at forward angles on hydrogen
as a probe of the neutron charge form factor.1221 Backward angle, low Q2 measurements are also sensitive to the poorly known axial vector hadronic coupling constant
p.
A parity violation experiment has been proposed at CEBAF/23/ which would exploit the expected excellent beam qualities of this new 4 GeV accelerator. The goal is to use scattering from hydrogen at far forward angles to measure sin26, at the level of 1%. This would be a very challenging experiment.The recent results from Mainz and MIT-Bates have stimulated an interest in even more precise future parity violation studies. Such measurements will require significant hardware investment as well as theoretical support if we are to advance our detailed understanding of the electro-weak interaction and the structure of the neutral currents.
Acknowledgements
The results reported here represent efforts spanning a decade, of a large dedicated group of physicists, graduate students, engineers and technicians. Without such a long- term commitment it would have been impossible to undertake an endeavor of this scale. This work is supported in part by the United Sates Department of Energy under contract No. DE- AC02-76ER03069.
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