Using information regarding the different amounts of energy lost by different particle types as they travel through drift chamber cells, E614 can distinguish muons from positrons and pions. Muons can be associated with an energy loss (in this context) of 100-175 keV.

For the E614 collaboration to obtain a sample of highly polarized muons (where high polarization here refers to muon spins with large negative z components, the case for the surface muon beam to be used), it seems that different methods used in conjunction will produce optimum results.

Focussing the beam of incoming muons at approximately –150 centimeters relative to the muon stopping target serves as a preliminary measure that can be used to obtain muons having a polarization nearest the ideal (where the ideal polarization is –1.0000).

The fitting of helices to the muon tracks can then be used to make cuts based on the helix radii (the larger the helix radius, the worse the muon polarization), so as to eliminate all but those muons with the most ideal polarization.

It appears that the design of the original detector hampers the determination of the spin-radius correlation via fitting a helix to the detected muon track. The use of a specialized muon detector, placed in front of the original one, to obtain tracking parameters for the muons yields better helices; and therefore, a better determination of the stopped muon polarization.

To allow for an accurate reconstruction of the muon decay process, the E614 experiment requires precise knowledge of the polarization of the stopped muons. This project was to determine first, a procedure by which muons could be discerned from other particles involved in the experiment, then, to find if the muon polarization could be accurately determined from the initial motion of these muons.

Monte Carlo simulations of muons travelling through the E614 detector array were run (using GEANT) to provide the information upon which all of the following results are based. The approach used to differentiate between muons and the other particles was to compare the energy lost by each particle type in dimethyl ether (DME) cells within the drift chambers. This was to find what range of energy loss might exclusively identify muons. Several techniques were explored for the purpose of determining the muon polarization distribution. These include: optimizing the focal position of the incoming beam of muons; fitting helices to muon tracks based on hit information from a varying number of drift chambers in the original detector (and then looking for relationships with which to make cuts); and, fitting helices to muon tracks based on hits in a specially designed muon detector (and then looking for relationships with which to make cuts).

Figure 1 shows the spectrometer with the original detector; Figure 2 shows the same spectrometer with the addition of the muon detector. Note the different positions of the silicon counter and energy degrader in each setup.

Using the five chamber muon detector (see Figure 3, and also Figure 2), Monte Carlo simulations were run using beams of positrons, muons, and pions. The energy loss each particle type experienced as a result of passing through the DME cells of the muon detector was recorded.

Figure 4 shows that, based on energy loss, positrons can be clearly distinguished from muons. Here, the energy lost in all of the cells hit by the passing particle has been summed. It is not apparent whether pions can be cleanly discerned from muons. Figure 5 reveals that statistics for pion energy loss begin at approximately 175 keV. Therefore, E614 may identify muons by recognizing an energy loss within the DME cells of the detector of more than 100 keV, but less than 175 keV. Note that the influences of electronic noise and ADC resolution have not been considered; as well, events in which muons struck the wires within the cells have been excluded from this study.

5.1 CHOOSING FOCAL POSITION

Monte Carlo simulations have shown that the choice of the focal point for the incoming beam of muons has a definite impact on the resulting polarization of these particles at the target¹. Figure 6 shows that focussing the beam at –150 centimeters relative to the experiment center (the muon stopping target) results in muons having the most ideal polarization at the target. This distance corresponds with the approximate position of the magnetic "fringe field" (the area where the magnetic field rises from 0.0 T in the beam line to 2.2 T inside the spectrometer) and agrees with the optimum focal position found through previous studies².

Figure 6 also compares the true mean polarization of the muons and their predicted mean polarization as a function of focal position. The prediction procedure involved extracting hit information from the drift chambers of the muon detector into a file; the ‘hits’ were then smeared with a Gaussian function (sigma = seventy microns) to simulate the drift chamber resolution. Using parameters returned from a helix fitting routine applied to this data, the predicted spin was found:

P = -cos(arctan(rad*akn)) (1)

where P is the predicted spin, rad is the helix radius in centimeters, and akn is the wavenumber in centimeters^-1.

As the true polarization of the muons becomes more ideal, it seems as though the difference between the true and predicted polarization increases. This may be due to the fact that as the muon spin becomes more ideal, the fitting of helices to the muon tracks becomes more difficult because the radii of the helices decrease. This inability to fit proper helices to muons of ideal polarization may render the calculation for the predicted spin invalid, resulting in the trend seen in the comparison of the two curves in Figure 6. It is worth noting that the true polarization is always better than the predicted one; the predicted polarization can serve as a lower limit on the true polarization. Figure 6 also shows that the highest polarization (closest to –1.0000) occurs for both the true and predicted plots with the muon beam focussed at approximately the same focal point. This means that the predicted polarization can be used to tune the muon beam to position the focus in the optimum location.

5.2 MUON TRACKING WITH THE ORIGINAL DETECTOR

5.21 RADIAL CUTS

The existing plan for the E614 detector is to place inside the spectrometer twenty-six drift chambers (see Figure 7).

If helices are fit to muon tracks based on the positions of these particles as they travel through these drift chambers, the radii of these helices can be found. Because the spin of the surface muon is opposite its momentum vector and high polarization refers to muons with large z components in their spins, it follows that highly polarized muons travel in helices with small radii. Therefore, the following correlation exists: the larger the helix radius, the worse the polarization of the muon. Figure 8 shows a plot of muon polarization at the target versus helix radius, based on helices fit using parameters from the first nine of the original detector’s drift chambers. The relationship is rather blurred due to the effect of multiple scattering within the drift chambers. Nonetheless, when systematic radial cuts are applied to the data, the mean polarization at the target does improve, as shown in Figure 9. Plots using helices fit with six or seven chambers have not been included in Figure 9, because the twenty-eight centimeter muon wavelength cannot be accurately fitted with a helix based on the relatively short distance covered by six or seven chambers. Plots using twelve or thirteen chambers have also not been included due to how multiple scattering distorts any useful spin-radius relationship by the time the muons enter these chambers.

Using this technique, it appears that making radial cuts using helices fit with nine or ten chambers will give the best muon polarization at the target.

5.22 CHI-SQUARED CUTS

In an attempt to find other useful relationships with which the muon polarization could be optimized, Monte Carlo simulations were run with the multiple scattering turned off. In addition, the data with which the helices were fit was augmented so as to produce significantly larger helix radii: the angles involved with the muon tracking were increased by a factor of ten.

This "test" run was produced to check if helices actually were being fitted to the data from the drift chambers. Figure 10, a plot showing a relationship between the polarization at the target and the chi-squared values of the fits, was produced under these two special conditions. However, once multiple scattering was turned back on, and the "real" data reinstated, this relationship disappeared, as shown in Figure 11.

Except for hints of the spin-radius correlation, no other useful relationships were seen using helices fit with parameters from the original detector.

3. MUON TRACKING WITH THE ‘IDEAL’ MUON DETECTOR

5.31 RADIAL CUTS

Several problems are apparent regarding the usefulness of the original detector inside the spectrometer as a tool for tracking muons. The stack of six planes at the forefront of the detector (see Figure 7) does not provide any useful information for obtaining the helix fitting parameters (due to its short length relative to the approximately twenty-eight centimeter muon wavelength), yet, it introduces significant multiple scattering. In addition, the spacing of those drift chambers beyond the sixth does not particularly lend itself towards obtaining all the useful parameters of the muon track for the purpose of fitting a helix. As well, the muon energy degrader and silicon counter must be placed downstream of the drift chambers used for tracking the muon (see Figure 1) due to their large multiple scattering influence. This places these items very close to the stopping target, which is not ideal for measuring the eventual positron trajectories (from the decay of the stopped muons).

The addition of the muon detector to the spectrometer (see Figure 3, and also Figure 2) deals with all of these problems. Consisting of five drift chambers that are seven centimeters apart from each other, the muon detector is designed to allow the fitting of the best helix possible, while minimizing multiple scattering. Because of the positioning of the drift chambers in this detector, all useful information regarding the muon track is gained for the helix fit; and, as only five chambers are used, the amount of multiple scattering interfering with the helix fit is greatly diminished. The muon detector also allows for an alternate placement of the energy degrader and silicon counter (see Figure 2), which will not interfere with the tracking of positrons from the muon decay.

Figure 12 shows a plot of muon spin at the target versus helix radius, using parameters from the muon detector. The correlation between large radius and poor polarization is more evident here than in Figure 8, where the original detector was used. After systematic radial cuts are made to the data from the muon detector, it is seen in Figure 13 that cuts using the muon detector result in a much better spin than the same cuts made on data from the original detector. Regardless of whether nine, ten, or eleven chambers of the original detector are used to provide information for fitting the helices, the muon detector dramatically improves on the resulting muon polarization at the target.

Figure 14 shows the statistics remaining after each radial cut is made for the data from both detectors (where nine chambers are used to fit the helix for the plot of the original detector). Clearly, the use of the muon detector does not result in a significant loss of statistics.

The ideal muon detector requires 6.2 centimeters between each drift chamber (see Figure 3); however, E614 has spacers of six centimeters in length readily available. Altering the design of the muon detector to accommodate these materials will not significantly affect the detector’s capacity to optimize the fitting of helices to muon tracks. Figure 15 shows this by comparing plots of polarization at the target versus focal point for the original muon detector design, and for the design with only six centimeters between chambers. Because these plots show similar mean polarization at corresponding focal points, it can be assumed that the resulting polarization distributions (after radial cuts are made) using both designs of the detector will also be similar.

The muon detector serves as a vital tool with which E614 can distinguish between muons and other particles involved in the experiment; muons can be identified with an energy loss of 100-175 keV within the DME cells of this detector. In addition, the muon detector significantly contributes to the selection of highly polarized muons (when combined with the optimized focal point at approximately –150 centimeters relative to the target). Compared to the original detector within the spectrometer, the muon detector is clearly of greater advantage to E614 because of its minimization of the influence of multiple scattering, more relevant drift chamber spacing, and allowance for better placement of the energy degrader and silicon counter.

1. MacDonald, R.P. "Possible Methods for Optimizing Muon Polarization," 1997.

2. Ibid.

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