Undergraduate, Peer-Reviewed Science Journal
|
Issue 1, March 2003 Physical Science & Mathematics A Study of Simulated Measurements of W Boson Helicity in the Decay t 
Wb at the Collider Detector at FermilabBrock Tweedie University of Rochester Advisor: Kevin McFarland, Ph.D. University of Rochester Abstract The interactions
of the top quark will soon be coming under greater scrutiny at the
Collider Dectector at Fermilab (CDF) with Run II of the Tevatron
collider. This investigation gauges CDF's improved ability to measure
the helicity of W bosons produced in top quark decays. Such
measurements will provide a direct indication of the spin structure
of the weak interaction responsible for the top decay process. Simulated
CDF Run II data is used to study the W helicity sensitivity
of the muon momentum in m+jets events,
as limited by both statistical and systematic uncertainties. Optimization
of helicity measurements via appropriate choices of event variables
and data criteria is also addressed.
1 Introduction 
In the Standard Model, charged weak interactions such as the top's decay have a built-in left-right asymmetry that manifests itself in the helicities of the particles produced. The asymmetry is "maximal" for massless fermions in the sense that either the (+) or the (-) helicity state is produced to exclusion. The general trend for all particles is favoritism of (-) helicity for "normal" matter and (+) helicity for antimatter. The quantitative degree of this favoritism has always been observed to be equal between matter and antimatter, indicating a combined charge-parity symmetry for these processes. (Christenson et al (1964) showed that this symmetry is not an exact law of nature, but any violation in top decay is expected to be negligible for the purposes of this study.) In the specific case of the top decay, this means that the products of the process t 
W+b, and its antimatter analog t'
W-b', should display equal and opposite helicities.
This will be assumed in what follows, and further mention of top,
its decay products, or the helicities of those products will implicitly
refer to both the matter and antimatter cases but use the charge and
spin conventions appropriate for the former. Since the bottom quark has a mass of ~ 5 GeV/c2 and the energy scale of the top decay is ~ 175 GeV/c2, it is reasonable to treat bottom as "nearly-massless" in this process. From the discussion above, it is clear that if the Standard Model is correct, then the (-) helicity will dominate. In fact, the (+) helicity state of the bottom quark is predicted to be so rare in this decay that it can be treated as if it never occurs. (The (+) helicity state is suppressed by factors on the order of mb2 / mW2 = 0.003.) In the presence of only (-) helicity bottom quarks, the W cannot have (+) helicity either. A (+) helicity W with a (-) helicity bottom quark would imply a total spin of +3/2 to the right in Figure 1, which violates angular momentum conservation because the top quark is a spin-1/2 particle. The fractions of Ws exhibiting the remaining helicity states, (0) and (-), are then specified by some slightly more complicated arguments involving the specific form of the standard weak force interaction (Gilman and Kauffman 1988). Numerically at part per million precision, the Standard Model values of the fractional occurrences of each helicity state for both the bottom quark and the W boson are as follows:
f-(b) = 1.000 (1) f+(W) = 0.000 f0(W) = mt2 / (2mW2 + mt2} = 0.701 + 0.012 f-(W) = 2mW2 / (2mW2 + mt2) = 0.299 + 0.012 (2) The actual helicity fractions chosen by nature can be measured, with some important restrictions, by the same equipment used to discover top and measure its mass. Such measurements can then be used to check the validity of the Standard Model in the top decay process. The major point of interest here is to test whether the maximal parity asymmetry observed in all other charged weak interactions is still present in the case of the peculiar top quark. In other words, do f+(b) and f+(W) really equal 0 in t
Wb? 1.3 Prospects For Measuring Helicities In t
WbUnlike its parent top quark, the bottom quark produced in the decay does experience the strong force, as do most of its own decay products. The general result is a cascade of strongly-interacting particles dubbed a "jet," in which information on the bottom's original spin is completely lost. Measuring the helicity of the bottom quark is not an option. The prospects for measuring the helicity of the W boson take a bit more work to classify. About 70% of the time, the W decays into a quark and an antiquark that form their own jets. However, the difficulty in determining which quark types produced which jets poses a major problem for extracting precise W helicity information from them, since the helicity can affect different quarks in opposite ways. 10% of the time, the W decays into a t lepton and its neutrino. There are a variety of complications with this decay mode related to the t's subsequent decay. (The t lepton has a variety of decay modes. Most of them are hadronic and hard to trace back to a t in the environment of tt' decay. Regardless of the particular decay, the t always produces at least one unobservable neutrino that carries away information.) That leaves the other 20% of W decays, evenly distributed between decays into electrons or muons and their respective neutrinos, W
eue and W
w mum. The charged leptons produced in these decays
are stable enough to be directly detected and identified. These leptonic
W decay products are the most direct messengers of the W's
helicity, and constitute the main resource for performing a precise
measurment. (Since the fractions f+/0/-(W) have
now been shown to be the relevant quantities for measurement, the
distinguishing "W" label will be dropped in further references.)
The connection between the W's helicity and the W's decay products originates in the parity-violating helicity asymmetries discussed above. When a W decays into a charged lepton and its neutrino, any of which can be considered "nearly-massless" with respect to the W, the helicities of those products in the W's rest frame are almost exclusively negative for matter and almost exclusively positive for antimatter. For a W+, this implies that the W has +1 spin along the charged lepton's direction of motion, as depicted in Figure 2. The W's top-frame spin axis and spin state are preserved in its own rest frame, so the probability density, dP / d(cosa), of the charged lepton decay taking place at polar angle a from the original spin axis is modified by the probability of that state projecting a +1 value onto an axis at an angle a. For a W exhibiting one of the three helicity states, the decay angle distribution will be of one of the following forms:
dP0 / d(cosa) = (3/4) (1 - cos2a) dP- / d(cosa) = (3/8) (1 - cosa)2 (3) 
These are graphed in Figure 3. This kinematic dependence of the electrons and muons on the W's helicity is what makes that helicity measurable, since the effect carries over to variables that are directly observable in the lab. For example, if Ws produced in top decays at the Tevatron exhibited only one of the three helicities, then the momentum (P) distribution of the direct electrons and muons in the laboratory would exhibit one of the three characteristic shapes shown in Figure 4. 
Because (+) helicity Ws tend to decay into charged leptons with low a according to Equations (3), and because low a corresponds to close alignment with the direction of the W in the top rest frame, the leptons produced tend to have higher momentum in that frame. Similarly, leptons from (-) helicity Ws tend to have lower momentum and those from (0) helicity Ws are intermediate. The top is not produced at rest in the laboratory, but the effect persists in the lab frame as evidenced by the figure. For the real sample of Ws produced from top decays, the helicity state is a quantum superposition of the three possible values. In general, such a superposition would be expected to produce nonlinear interference effects in variables sensitive to the W helicity, but they are expected to be negligible in this case (G. Mahlon, private communication). Consequently, the distributions of those variables are actually simple linear superpositions where each helicity state is weighted by the fraction of Ws exhibiting it. The actual decay angle distribution is thus
Measurement of the W helicity fractions therefore consists of observing the distribution of some variable sensitive to the helicity, calculating the single-helicity distributions in that variable, and then finding the fractions (f+,f0,f-) that produce the best linear fit to the data. Because f+ + f0 + f- = 1, only two of the fractions need to be determined in the calculation, and the convention here will be to fit to (f0,f-). 1.4 The Purpose and Methodology of This Study In the first run of the Tevatron, in which the top quark was discovered, the Collider Detector Facility (CDF) collaboration performed the type of measurement described in the previous subsection (Affolder et al 2000). The statistics were so low, however, that the measurement was completely inconclusive unless one of the fractions was assumed to be already known. With f+ fixed to 0, representing the Standard Model's maximal helicity bias, the measurement yielded f0 = 0.91 + 0.39. Though this result is consistent with the Standard Model physics responsible for the f0 = 0.70 prediction, the size of the error does not make that consistency very compelling, nor does the measurement give any indication of the actual weak force helicity bias in the top's decay. With f0 fixed to the Standard Model value 0.70, the measurement yielded f+ = 0.11 + 0.15, which is again consistent with the Standard Model but not at all convincing of its applicability. (The result states that f+ < 0.28 at the 95% confidence level, when it is less than 0.30 by assumption.) In March 2001, the Tevatron began an upgraded run (Run II) which, over the next several years, should provide the first large-scale sample of top quarks for detailed study. In anticipation of the new data that will be acquired, this paper makes preliminary estimates of the quality of several possible W helicity measurements that could be made by the CDF collaboration, with the aim of detailing and minimizing the errors associated with those measurements. The fundamental approach taken here is to make as realistic a facsimile of the Run II data set as possible, apply the measurement procedure introduced in Section 1.3 for a small sample of useful variables, and determine the errors on those measurements. Since the actual W helicity fractions are still essentially unmeasured, Standard Model physics has been assumed and "realistic" should be taken in the sense of representing what would actually be seen in the CDF detector under that physics. (Of course, if the values of the W helicity fractions are correlated with their measurement errors, and those fractions turn out to be highly nonstandard, then the estimates made here may be of limited use. However, such an extreme discrepancy between theory and reality is rather unlikely, and at any rate impossible to anticipate.) The study focuses exclusively on a subsample of the Run II data called "m+jets." These are events where a tt' pair is produced in the Tevatron and, upon the pair's decay into (W+b)(W-b'), one W subsequently decays into mum and the other decays into hadrons. The choice to use just this subsample was based largely on time constraints. Different classes of events useful for W helicity measurements have different sources of error, and a thorough investigation of all of these sources was not possible over the course of this research. The m+jets subsample was the natural place to start because it constitutes approximately half of the total useful data and is easier to fully analyze than the analogous and similarly-sized e+jets subsample, owing to extra detection issues associated with electrons. To estimate the quality of results that will be derived from the entire direct lepton data set, double-sized m+jets samples are used. Pretending that e+jets electrons are actually muons has the effect of unnaturally increasing the quality of the simulated helicity measurements, but the failure to incorporate the final class of direct lepton events, "dilepton," more than offsets this, making the estimate a conservative one. Dilepton events are events where both Ws decay leptonically, and they will constitute the highest-quality tt' subsample, though they will only account for on the order of 10% of the observed direct leptons. To introduce the experimental setting in which the W helicity measurements will be performed, and which this study attempts to simulate, the next section discusses the CDF detector in more detail. Section 3 then outlines the procedures by which simulated detector data is used to estimate the errors on the W helicity measurements. Sections 4 and 5 respectively report the statistical and systematic errors found for a small set of measurements, and Section 6 presents the optimized total errors. Finally, conclusions are presented in Section 7.
2 The CDF Detector 
2.2 Definitions of Detector Variables CDF uses a spherical coordinate system for its detector, with the center of the system corresponding to the center of the detector. The azimuthal angle f is defined in the plane perpendicular to the beampipe. The polar angle q is defined with respect to the beampipe, which serves as the z-axis. Generally, q is replaced by the pseudorapidity, h = -ln(tan(q/2)). Pseudorapidity is a useful variable because particle flux in the detector is approximately uniformly distributed over it. Because the detector is cylindrical, particle momenta are broken-down into parts transverse to and parallel to the beampipe, labeled PT and Pz, respectively. For particles depositing energy in the calorimeters, the relevant quantity is transverse energy (ET) which is the projection of energy onto the transverse plane as if it were a vector aligned with momentum. This quantity is more convenient than total energy for determining which calorimeter data is potentially interesting, especially in the forward part of the detector. Events generated by colliding beams generally take place with very little total transverse motion, so the products have momenta and ET that balance out in the transverse plane. The CDF calorimetry is complete over f and excludes only regions of very high |h| (as indicated by Figure 6), occupied by the plethora of low-ET collision debris that flies down the beampipe in each event. Since this low-angle debris part of the event has very small vector-summed ET, so must the part of the event that passes through the detector in order to keep their sum at approximately 0. Hence, the vector sum of the measured transverse energy of an event should add up to almost 0 unless something is escaping detection in the calorimeters and muon trackers. This is exactly the case for neutrinos, and the "missing" ET (E'T) necessary to bring an event into azimuthal balance can often be a signature of those particles.
3 Procedures for Simulating the Run II CDF Measurements
When this study was performed, the CDF reconstruction software necessary to calculate E'T had not been completed, so special care had to be taken to replicate the E'T > 20 GeV criterion. For events with leptons from W decays, the vector sum of Monte Carlo level neutrino PT stands in for E'T. For events without leptons from W decays, called "non-W" events, no such procedure can be convincingly applied because those events would only realistically pass the E'T criterion due to misreconstructions in the calorimetry. As a workaround, the events are simply weighted by a factor of 1.9 to match the relative non-W background fraction found in the Run I l+jets sample (where l = m or e) (Affolder et al 2001). This procedure has the additional benefit of "including" non-W events from all processes, even though this Monte Carlo only generated them using tt' events. Though the weighting is by no means a perfect substitute for an actual E'T cut and an actual simulation of the non-tt' non-W processes, the number of events is small and their general characteristics should be accurately reflected. In addition to the unsimulated portion of the non-W background, there is one other major class of background events, called "W+jets," that is not represented in the simulated tt' event samples. These include any non-tt' processes that produce a W boson and hadronic jets. A very small fraction of W+jets events pass the m+jets criteria when the W decays into a muon, either directly or via an intermediate t. In fact, that fraction is so small that simulation of W+jets for the study (also using HERWIG) was complicated by the sheer number of events necessary to produce a sizable subsample that passes the selection criteria (where, as with the other events containing leptonic W decays, the Monte Carlo neutrino PT is used for the E'T cut). (Even with Monte Carlo level filtering that only passes events with W mum
and W tut
mumutut, removing
90% of unwanted data at the outset, only about 1 in 1000 events passes
the m+jets criteria. Simulating enough W+jets
events so that just 100 pass the criteria would require ~ 550 hours
of processor time.) The major difficulty in finding W+jets
events that pass the m+jets criteria is the
rarity of the appropriate jet structure, so, to facilitate the inclusion
of W+jets data in the study, the criteria
5 and 6 are replaced with the single, looser criterion "there are
at least three hadronic jets with ET
> 8 GeV and |h| < 2.4." This is meant to preserve
at least the gross features of a sample of muons from non-tt'
Ws produced with four jets. The W+jets
sample generated for the study contains 209 total events that pass
the modified m+jets criteria. These events are
weighted by 0.38 to match the Run I W+jets:
tt' event ratio and introduced into the
10 data samples with random fluctuations generated according to the
Poisson probability distribution. The final composition of the average m+jets data sample, taking into account weightings, is
The influence of the three backgrounds (t+jets, non-W, W+jets) on the measurements will be explored in Sections 4 through 6. The presence of the backgrounds in the combined 10 samples is shown in Figure 9 for the muon PT variable, and their shapes in that variable are shown in more detail in Figure 10. 
3.2 Generation of Single-Helicity Distributions In order to perform measurements of the helicity fractions in the 10 data samples, it is necessary to know what the distributions of detector measurements would be if the Ws were produced exclusively in each of the three helicities, as per Section 1.3. These distributions are meant to represent the probability densities of the various measurements, not the results of a specific experiment like the simulated data samples. In principle, such distributions could have been obtained in the same manner as the simulated data, but using "reprogrammed" W helicities and much larger Monte Carlo samples. However, that procedure was impractical, owing to the difficulty in reprogramming HERWIG to make single-helicity Ws and the finite amount of disk space available for storing the data. (The difficulty was not associated with modifying the HERWIG Fortran code, but with the re-integration of that modified code into a C++ framework.) Instead, the data samples themselves are used to calculate the single-helicity distributions, which will be called "template" distributions. The 10 data samples are combined, and muons originating directly from W decay are weighted by the following value for each of the three helicities, where i is the index of the muon and ai is that muon's polar decay angle from Figure 2:
[0.000*(dP+/d(cosa))cosai + 0.703*(dP0/d(cosa))cosai + 0.297*(dP-/d(cosa))cosai]-1 (5) The numerator of the above equation (5) is any of the three Equations (3) evaluated at cosai, and the denominator is Equation (4), also evaluated at cosai, with the Standard Model fractions that are used to generate the data. (Using mt = 175 GeV/c2 instead of 174.3 GeV/c2 slightly changes the fractions from Equations (2).) Application of the weight reshapes the decay angle distribution to match those of single-helicity Ws, and modifies the distributions of other helicity-sensitive variables accordingly. The distributions for the (+) helicity produced in this manner display much more statistical jitter than the other two because that state was not originally represented in the data. Those distributions are smoothed in intermediate ranges of the variables. The effects of the re-weighting and smoothing are illustrated for the variable PT in Figures 11 and 12. 
3.3 Mathematical Fitting Routine Used To Perform the Measurement The "best fit" of Section 1.3 is performed using a Poisson loglikelihood calculation. Both the "measured" variable distributions of the 10 sample sets and the "calculated" variable distributions of the template sets are defined as histograms like the ones used in previous figures. The likelihood, defined independently for each histogram as a function of f0 and f-, is a quantity related to the probability that a particular measured histogram was generated by physics obeying a candidate superposition (f0,f-) of template distributions. The best fit is the superposition with the greatest likelihood. In this calculation, any given candidate superposition is automatically renormalized to match the number of events in the measured histogram. For a histogram bin i with with measured value ni and candidate superposition distribution value Mi(f0,f-), the Poisson likelihood, Li, of the candidate bin is the probability of observing ni with Mi as it's expectation value.
The 1s statistical error region of a loglikelihood fit consists of all points in the phase space where the value of -2ln L departs no more than 1 from the minimum, as shown in Figure 14 for the same example. The error for the two fractions are the respective projections of the 1s error region onto the two axes. The error for f+ is calculated using the error correlation coefficient between the two free parameters, r0-, which is related to the amount that the 1s region is tilted with respect to the axes.
4 Statistical Errors
For the one-parameter fit, f0 is constant and Dstat f- = Dstat f+, so only the error on f+ needs to be listed.
P and PT are shown to be the best of the three variables in terms of minimizing statistical error, with P being marginally better than PT. 
In light of the discussion of Section 4.1, it is interesting to note that there would be a disproportionate decrease in error if there were no need for a E'T cut. To see the effect, fits are performed on background-free data samples with and without the E'T > 20 GeV criterion. The removal of backgrounds is necessary because they are explicitly included under the assumption of E'T > 20. Of course, the E'T cut is there in the first place to ensure that these backgrounds are small. Comparison of the two sets of results shows that dropping the cut increases the amount of data going into the histograms by only 13%, but uniformly decreases the errors by around 30% for the (+) and (0) fractions in the two-parameter fits, 10% for the (-) fraction, and 20% for the one-parameter fits (as compared to a predicted 6% reduction in all errors from simple N-1/2 scaling). The reason for the large error reductions is the fact that the cut is biased against higher-momentum muons, since they tend to be produced with lower-momentum neutrinos as seen in the laboratory frame. The template distributions used for the PT fits in both studies are shown in Figure 19, illustrating the increase in distinguishability of the distributions at high range when the cut is dropped, especially between (+) and (0). 
5 Systematic Errors 5.1
Calculation of Systematic Errors From Backgrounds 
5.2 Errors From the Non-W and W+jets Background Normalizations At present, the Run II normalization errors for the non-W and W+jets background are unknown. Because the difficulty associated with making calculations for processes that involve the strong force, the contributions of these two backgrounds can be calculated only after Run II data is accumulated. The errors on those calculations will depend on that data, so at present the only way to determine the systematic errors is to make an educated guess based on the Run I experience: 20% for non-W and 30% for W+jets. These will be used in what follows. The errors from normalization of the non-W background are listed below.
And the analogous values for the W+jets background are:
5.3 Errors From the t Background The normalization of the background from t+jets is much better known because it depends on the ratio between the probabilities of W tut
and W mum
decays, which has been measured with 3.3% error (Groom et
al 2000). (Theoretically, this ratio is unity. This is
consistent with the measured value 1.016 +
0.033.) However, the relatively large contribution of t+jets
to the data sets makes this small uncertainty into a non-negligible
source of systematic error. Those errors are:
The fact that the relatively massive t is influenced by the physics of Ws produced in top decay opens the possibility of some unknown mass-related behavior that alters the shape of the t+jets contributions to the variable distributions but leaves the contributions from actual m+jets unaffected. Though this type of scenario is very unlikely, an extra study is performed with an extreme change in the physics of the W
w tut process to test
whether an effect would be seen. As with the normalization studies,
the background is left untouched in the data samples, but now the
template distributions are constructed under the assumption that the
sign of the helicity of the W's decay
products in Figure 2 is reversed when the W
decays into t. In other words, the "wrong-signed"
version of Equation (5) is used on the muons from t
decay for the (+) and (-) distributions. The distinction between the
t+jets background contributions in the two cases
is shown in Figure 21. 
For the two-parameter fit on PT, the result is a +0.028 shift in the average measured f+ and a -0.047 shift in the average measured f0. The shifts for the other two-parameter fits are similarly a couple of times larger than the respective systematic errors from t+jets normalization. The shifts for the one-parameter fits are more on par with their corresponding t+jets errors or are smaller than them. For PT again, the shift in f+ is only +0.0001, but for P the shift is +0.0014. The point here is not to include these as errors in the final results, but to note that unusual t physics can have an influence on the fit results that is greater than the errors from t+jets normalization, and that those results cannot be considered insensitive to such physics when the normalization-based errors are significant. (This statement remains true when the stricter selection criteria of Section 6 are used.) For the simulated data sets analyzed here, statistical errors alone vastly dominate any potential effects from anomalous t physics. Such effects could only be significant for data sets that are several times larger. 5.4 Other Sources of Systematic Error In addition to background normalization, there are a variety of other factors that introduce uncertainty into the construction of the template samples. They include uncertainties in the background distribution shapes, in the top quark mass, in the effects of strong force radiative processes, and in the distribution of quarks and gluons inside of the protons and antiprotons that are collided in the Tevatron. These factors were not studied here due to the difficulty of accurately determining their influence. However, their contribution to the total measurement error is expected to be small compared to the combined effect from the background normalizations. This expectation is supported by the contributions calculated for the Run I one-parameter measurement of f0 (Affolder et al 2000), for which the quadrature sum of the errors from non-W background shape, a conservatively rescaled top quark mass uncertainty, strong force radiation, and quark/gluon distribution is on par with the error from non-W normalization alone. (The top quark mass uncertainty is scaled to 3.0 GeV/c2 from 5.1 GeV/c2 to represent a possible Run II refinement.) 6
Total Errors
These errors differ by at most a few percent from the statistical errors tabulated in Section 4.3. Consequently, even if it were possible to modify the selection criteria to preserve all of the real events and eliminate all of the background events, the improvement of the error would be minuscule. Indeed, strengthening of the minimum PT and maximum |h| criteria show uniform increases in total errors associated with decreased statistics. Loosening the PT criterion, on the other hand, introduces no new real m+jets events in any of the samples (only new background), and loosening the maximum |h| criterion has absolutely no effect, since it was implemented implicitly by the muon detector coverage. Effects of altering the other selection criteria are not explored here, but their application is based on a large body of CDF experience in maximizing measurement quality in Run I. Since very little can be accomplished from trying to optimize the above set of measurement errors, the best errors from that set will be used as-is for the final estimated measurement errors on the approximately 1,000 direct leptons expected from the first stage of Run II. Those best errors belong to P for both the one- and two-parameter measurements, making the final estimates:
6.3 Anticipated Final Sample (10,000 events) The full length of Run II is predicted to see at least a tenfold increase in data over the first stage. This translates to a 10-1/2 scaling of the statistical errors in the W helicity measurement, leading to the following total errors with the default m+jets selection criteria:
Here, the total errors are more like 10-20% greater than the statistical errors alone, making the search for ideal selection criteria less futile than it was with the conservative sample. To determine the ideal minimum PT criterion, that criterion is varied from "PT > 8 GeV/c" to "PT > 24 GeV/c" in increments of 4 GeV/c, and all errors are recalculated for each increment. P remains the best variable throughout this investigation, so its results alone are listed.
The individual statistical and systematic errors under the different minimum PT criteria are tabulated in the appendix. Variation of the |h| criterion (with PT > 8 GeV/c) from "|h| < 1.2" to "|h| < 0.9" in increments of 0.1 causes the statistical errors to increase by up to 5% with no significant changes in systematic errors. Consequently, the default |h| will not be altered. The difference between the errors obtained with the default PT/|h| criteria and the ideal PT/|h| criteria are 1-3% for the two-parameter and 10% for the one-parameter. Thus, only the one-parameter measurement displays even a remotely significant improvement. The best errors for the 10,000-event extrapolation are listed below, with P as the fit variable and PT > 12 GeV/c for the two-parameter measurement and PT > 20 for the one-parameter measurement:
7 Conclusions The estimates calculated in the previous section display, as expected, a large improvement over the Run I measurements. The two-parameter measurement, which formerly yielded no results, will at least match the Run I one-parameter measurement of f+ by the end of the first stage of Run II, and will improve upon the one-parameter measurement of f0 with at least a 40% error reduction. By the end of Run II, the one-parameter measurement of f+ will probably be able to probe for an anomalous departure from maximal parity violation at the scale of a couple percent, with the assumption of no highly unorthodox new physics.More accurate estimates will require full investigation of the errors associated with e+jets and dilepton events, of the utility of the b jet and E'T data, and/or of the contributions from the additional systematics discussed in Section 5.4. After accounting for all of these, it is quite likely that the estimated measurement quality will display further improvements. In addition, of course, such estimates will also benefit from more accurate values for the overall size of the data sample and the errors on the non-W and W+jets background normalizations, which will both be refined as CDF takes data over the next several years. These refinements can be directly applied to the results of this study by simple rescaling of the errors listed in the appendix, which then provides an immediate guide to optimizing the minimum PT criterion for the m +jets subsample in the 8 GeV/c to 24 GeV/c region (lacking the b jet and E'T detector data). Acknowledgements This paper and its author owe a large debt of gratitude to Prof. Kevin McFarland. Kevin took me on as a summer student at the end of my sophomore year, giving me an unsuspected alternative to my initial choice between a summer of complete idleness or a "real" job. Working on this project with him over the past two years has been an equally unsuspected pleasure. Through his patient guidance, I have learned more than I am sure I even currently realize, and see my future path in life with a view far clearer than any undergraduate coursework could have granted me.Kevin's group at CDF has also been instrumental in my learning process. Kirsten Tollefson in particular was of great help during my first weeks at CDF. Ben Kilminster, Tony Vaiciulis, Sarah Demers, Mike Carew, Jedong Lee, Erika Artukovik, Han Yoo, and Wells Wulsin (in no particular order) have all served as invaluable allies in my constant struggle to make the CDF software do what I wanted, and provided the ears necessary for me to brag about when it actually did. My undergraduate colleagues Andrew Blechman and Albert Wang deserve a measure of recognition for this document as well. Andrew has served as a sounding board for many of my ideas on high energy physics and life in general. His friendship, his passion for physics, and his culinary generosity have provided a not-insubstantial part of my motivation for completing this work and staying in this field. Albert works on condensed matter, so I have no comprehension of what he does or why he does not work in my obviously superior field, and vice versa. However, we have a major common ground in pursuing quality work and mocking each other for it. Albert has been a major force in keeping my work in perspective, especially on those 4 a.m. shifts when we were the only two people in the physics building. Finally, I am indebted to the incredibly helpful University of Rochester physics staff. Specific thanks go to Connie Jones, who has performed countless invaluable secretarial feats for me in the processes of performing and presenting this research. Also, Janet Fogg deserves special mention for several helpful conversations and some lighting-fast duplicating.
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||