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Parity Violation in Proton-Proton Scattering at 221 MeV

The parity-violating longitudinal analyzing power, Az, has been measured in pp elastic scattering at an incident proton energy of 221 MeV. The result obtained is Az =(0.84 +/- 0.29 (stat.) +/- 0.17 (syst.)) x 10^{-7}. This experiment is unique in that it selects a single parity violating transition amplitude, 3P2-1D2, and consequently directly constrains the weak meson-nucleon coupling constant h^pp_rho When this result is taken together with the existing pp parity violation data, the weak meson-nucleon coupling constants h^pp_rho and h^pp_omega can, for the first time, both be determined.

At the fundamental level, the weak interaction between nucleons is due to heavy boson (W ± and Z 0 ) exchanges between quarks. However, at low and intermediate energies a single meson exchange model with one strong, parity conserving, and one weak, parity nonconserving vertex is often used to describe parity violating effects. The parameters of the strong vertex are already quite well measured, while the weak interaction is parameterized by a set of six weak meson-nucleon coupling constants h 1 π , h 0,1,2 ρ , and h 0,1 ω , where the superscripts indicate the isospin change and the subscripts denote the exchanged meson. These couplings were calculated by Desplanques, Donoghue, and Holstein (DDH) [1] from the Weinberg-Salam model and quark bag wave functions. Subsequent calculations of the weak mesonnucleon coupling constants have been carried out by a number of authors [2,3,4,5,6], but it is apparent that the constants still carry considerable ranges of uncertainty (see reviews [7,8]).
The value of the weak meson-nucleon couplings has implications outside nuclear parity violation. For example, Holstein [9] has concluded that a small value of h 1 π cannot be understood unless the current algebra quark masses are increased by about a factor of two over the original Weinberg values, which tends to produce a similar suppression of theoretical estimates in other processes, e.g., the still questioned ∆I = 1/2 rule for flavour changing weak decays. In addition, more precise values for the weak meson-nucleon couplings would permit better theoretical calculation of the proton anapole moment [10,11,12] which, in turn, would improve calculations of the axial vector radiative corrections needed to interpret electron-proton parity violation experiments such as SAMPLE at MIT-Bates, and G-zero at TJNAF.
Experimentally, the most accessible parity violating observable in pp scattering is the longitudinal analyzing power, A z = (σ + − σ − )/(σ + + σ − ), where the + and − signs refer to the helicity state (right or left handed) of the longitudinally polarized incident proton beam, and σ is the scattering cross section. This letter reports the result for A z obtained by experiment 497 at TRIUMF.
A measurement of A z in p-p scattering is sensitive only to the short range interaction mediated by ρ and ω exchanges; the π 0 is its own antiparticle, so parity violating π 0 exchange would also be CP violating and is therefore suppressed by a factor of about 2×10 −3 . Further, the TRIUMF 221 MeV measurement is designed to minimize the effects of ω exchange. This is achieved by choosing the incident energy so that the contribution to A z from the ( 1 S 0 − 3 P 0 ) transition amplitude integrates to zero over the acceptance of the apparatus, leaving the contribution of the ( 3 P 2 − 1 D 2 ) transition, which arises essentially only from ρ exchange [13]. Precise measurements of A z have already been made at 13.6 MeV [14] and at 45 MeV [15]. However, unlike the present measurement of A z , which is proportional primarily to h pp ρ = h 0 ρ + h 1 ρ + h 2 ρ / √ 6, the low energy results are proportional to a linear combination of h pp ρ and h pp ω , where h pp ω = h 0 ω + h 1 ω . By combining the present measurement with the low energy result, h pp ρ and h pp ω can be determined individually. The layout of experiment 497 is shown in Figure 1. A 200 nA proton beam with a longitudinal polarization of 0.75 ± 0.02 is incident on a 0.40 m long liquid hydrogen (LH 2 ) target. Transverse electric field ion chambers (TRIC1 and TRIC2) located immediately upstream and downstream of the target, measure the change in transmission when the helicity of the incident beam is reversed.
The optically pumped polarized ion source (OPPIS) [16] minimizes unwanted helicity correlated modulations of beam properties. Helicity reversals are implemented at OPPIS by changing the frequency of the lasers which optically pump Rb vapor whose polarization is ultimately transferred to the protons of the H − beam. No macroscopic electric or magnetic fields are altered. The polarization of the Rb vapor is measured every spin state and is relayed back to the experiment encoded as a frequency to avoid having helicity correlated levels in the electronics racks. By running the full data acquisition system and ion source, with a current source replacing the main ion chambers, cross talk from the helicity signal was shown to be negligible.
After the ion source, a Wien filter orients the spin direction so that it is vertical in the cyclotron. The 221.3 MeV beam is extracted from the cyclotron and a solenoid -dipole, solenoid -dipole magnet sequence rotates the spin to the longitudinal direction. The magnets can be set to rotate spin-up in the cyclotron to either right handed (+) or left handed (−) helicity at the parity apparatus.
In the last section of beam line, the longitudinally polarized beam passes first through a series of diagnostic devices -a set of two beam intensity profile monitors (IPMs) (reference [17] describes an older version) and a pair of transverse polarization profile monitors (PPMs) [18]. A third IPM is located immediately in front of the LH 2 target, inside the cryostat.
The LH 2 target has a flask of 0.10 m diameter and a length of 0.40 m with flat and parallel end windows. Rapid (5 L/s) circulation of the LH 2 reduces the density gradients to an acceptable level.
The TRICs contain field shaping electrodes plus guard rings to ensure a uniform sense region, 0.15 m wide by 0.15 m high by 0.60 m long between the parallel electrodes. The TRICs are filled with ultra-high purity hydrogen gas and operated at a pressure of about 150 Torr and a high voltage of -8 kV. The entrance and exit windows are located approximately 0.9 m from the center to range out spallation products and thus prevent their entering the active region. False parity violating signals due to the buildup of radioactivity as a result of beam exposure were estimated to be negligible.
The sensitivity to each kind of helicity correlated modulation is measured in separate calibration runs in which each beam parameter (intensity, size, position, transverse polarization) is intentionally modulated at an enhanced level. The sensitivity is then multiplied by the coherent modulation measured during actual data taking and a correction is applied.
Beam position information is derived from the IPM signals, based on secondary emission from thin nickel foil strips placed between thin aluminum foils. The 31 harp signals from each of six planes are individually amplified and digitized to provide the beam intensity profiles in each spin state. The beam centroids at two IPM locations are obtained through integration of the discrete distributions; a corresponding correction signal is used to drive feedback loops to a pair of horizontal and vertical fast, ferrite-cored steering magnets. This position servo holds the beam to within 50µm of the "neutral axis" on which the experiment is insensitive to average transverse polarization components. Sensitivities to helicity-correlated position and size modulations are determined with the beam unpolarized and enhanced modulations introduced using fast, ferrite cored magnets synchronized to the spin sequence.
Transverse polarization components are measured by the PPMs, which are based on p-p elastic scattering using CH 2 blade targets that are scanned through the beam at the beginning of each spin state, immediately prior to the TRIC integration interval. Each PPM contains detector assemblies for 'left', 'right','down', and 'up' scattered protons. The CH 2 blades are 1.6 mm transverse to the incident beam direction and 5.0 mm along the beam direction and move through the beam on a circle of 0.215 m radius with a frequency of 5 revolutions per second. Each PPM has four blades, two which scan the polarization profile in the horizontal direction and two which scan the polarization profile in the vertical direction. By scanning transversely polarized beams horizontally and vertically, the polarization "neutral axis" mentioned above can be found.
To extract A z , measurements in alternating beam helicity are acquired according to an eight state spin cycle. A switching pattern based on the sequence (+ − − + − + +−) or its complement, is used, canceling both linear and quadratic drifts. Each spin state lasts 25 ms, comprising settling time, time for one polarization scan, and a 16.67 ms (1/60 s) TRIC and IPM integration window. The master clock for sequencing the whole experiment, including helicity changes, is derived from optical encoders mounted on the PPM drive shafts. All eight blades of the two synchronized PPMs pass once through the beam in one 200 ms cycle. The 1/60 s integration time is chosen to reject all noise at 60 Hz and its harmonics. To permit a check to be made for unrejected 60 Hz noise, a small controlled phase slip is introduced so that the master clock drifts through one complete cycle of the 60 Hz line every 18 minutes.
The parity detection apparatus attains minimal sensitivity to beam current modulations by precision analog subtraction of the ionization current signals of the two TRICs. To tune the subtraction for minimum sensitivity to coherent intensity modulation, an artificially enhanced (∼ 0.1%) helicity-correlated current modulation can be introduced. Under real data taking conditions, helicity-correlated current modulation ∆I/I = (I + − I − )/(I + + I − ) does not normally exceed a few parts in 10 5 . Periods of enhanced coherent current modulation are also interleaved with the "real" data so that corrections for ∆I/I can be made.
Because the proton energy is on average 27 MeV lower in TRIC2 than in TRIC1, a small change in incident energy changes the signal from TRIC2 more than the signal from TRIC1, and coherent energy modulation appears as a false A z signal. The sensitivity to coherent energy modulation was determined using a RF accelerating cavity placed upstream of IPM1 in the beam line. The measured sensitivity of (2.9±0.3)×10 −8 eV −1 is in excellent agreement with predictions based on the variation of stopping power with energy. Helicity-correlated extracted energy modulations cannot be directly measured at the parity apparatus, so an appropriate average of data taken with the two beam line helicity tunes is used to minimize the effect on A z . In addition, interleaved measurements of intrinsic injected energy modulation at OPPIS together with measurements at the parity apparatus of sensitivity to enhanced energy modulation give independent upper limits to the size of the resulting false asymmetries.
The data were taken in three one month-long running periods, divided into 23 sets of alternating beam line helicity. Each data set contains a series of runs, as well as a large number of control measurements, including polarization neutral axis scans, and measurements of the sensitivity to various helicity correlated modulations. Helicity correlated modulations in beam position (∆x,∆y), beam size (∆σ x ,∆σ y ), beam intensity (∆I/I), transverse polarization coupled to beam position (y * P x ,x * P y ), first moments of transverse polarization ( yP x , xP y ) and energy modulation at the ion source were considered. Figure 2 shows the corrected data for the 23 data sets. The uncertainties shown include all contributions except energy modulation. Table I summarizes the helicity correlated beam properties, the net correction made for each, and the uncertainty in each correction. The uncorrected A z of (1.68 ±0.29) ×10 −7 becomes (0.84 ±0.29(stat.) ±0.17(syst.)) ×10 −7 . The reduced χ 2 ν = 1.08 shown in Table 1 is derived from the 23 corrected asymmetry values assuming A z is a constant and that the uncertainties are as shown in Figure 2 (i.e. not including uncertainty in the energy modulation correction). Uncorrected false A z from energy modulation will have opposite sign in opposite beamline helicities and increase the χ 2 ν . That the χ 2 ν is 1.08 supports the assertion that contributions from uncorrected energy modulation effects are small. An overall systematic uncertainty of ±0.12 has been assigned for energy modulation.
Note that A z was measured in a finite geometry with a thick target and requires a further multiplicative correction of 1.02 ± 0.02 when comparing to theoretical predictions at the ( 1 S 0 − 3 P 0 ) zero crossing energy (225 MeV) and integrated over all angles.
The parity violating longitudinal analyzing power in pp scattering has already attracted considerable theoretical interest, and many calculations have been made [19,20,21,22]. One of the main sources of uncertainty in these calculations is the value of the weak meson nucleon couplings which, up to now, were not sufficiently constrained by experiment.
The relations between A z and the the weak couplings have been recently recalculated by Carlson, et al. [23] using the Argonne v 18 (AV-18) potential [24], the Bonn 2000 (CD-Bonn) [25] strong interaction coupling constants, and including all partial waves up to J=8. Figure  3 shows the resultant limits on the weak meson nucleon couplings h pp ρ and h pp ω imposed by the low energy results [14,15] and the present TRIUMF result. The ±1σ bands are based on quadrature sums of the statistical and systematic errors. Also shown are the DDH "best guess" and "reasonable range" [1].
Although the experimental error of the present experiment is comparable to those at the lower energies, the relation between A z and the weak couplings is such that the width of the error band in the h pp ρ and h pp ω plane is correspondingly larger than those from the low energy measurements. A new experiment is being planned at TRIUMF to improve this situation by significantly reducing the error on A z . Nevertheless, the present TRIUMF measurement has already greatly reduced the acceptable range of both h pp ρ and h pp ω over what was the case when only the low energy measurements were available.
This work was supported in part by the Natural Sciences and Engineering Research Council of Canada; TRIUMF receives federal funding via a contribution agreement through the National Research Council of Canada.