1
Chapter 1
Introduction
1.1 The pion.
Japanese physicist Hideki Yukawa first presented in 1935 what is now known as the Yukawa potential as a means of mathematically describing the nucleon-nucleon interaction. That potential is written:
(1.1)
where k=mc/.
The potential is a solution of the time independent Klein-Gordon equation:
(1.2)
Yukawa proposed that, like the photons that were responsible for carrying the electromagnetic force, a particle existed which carried the nuclear force. This particle was exchanged between nucleons and was responsible for binding a nucleus together.
The relation between the mass of the force-carrier particle and that force's range can be derived using the uncertainty relationship between energy and time Et~ which leads to
The maximum distance a particle can travel in time tis given by
(1.3)
where the range R would be estimated by the range of the potential of interest. This relation is consistent with the zero mass, infinite range of photons, which mediate the electromagnetic interaction.
The relation (1.3) can also be derived using the assumption that k-1 (k being from (1.1)) should be on the order of the range of the nuclear force (~1 fm),
(1.4)
Yukawa used the relation (1.4) to estimate the mass of a particle mediating the nucleon-nucleon interaction to be about 200 MeV/c2.He named these particles "mesotrons" with "meso"meaning "middle" since the mass of these was between the masses of electrons and nucleons.
By the early 1940's, experiments using cosmic rays indicated the existence of a particle whose mass was ~100 MeV/c2. This was, at first, assumed to be Yukawa's meson. However, the unusually long paths these particles traveled through matter were inconsistent with the predicted, strongly interacting particles. In 1947, C.F. Powell et al. gave experimental evidence of a heavier particle (~150 MeV/c2) which decayed into a lighter one (~100 MeV/c2) [Pow 59]. The heavier particle was then correctly identified as the pion while the lighter particle (which had come to be known as the mu meson) was (eventually) identified as a second-generation member of the lepton family of particles. The term meson now has a more general meaning and is given to any particle constructed of a quark and an anti-quark.
Pions exist in three varieties most easily identified by their electric charge. These are, , and with charges +1, -1, and 0, respectively, in units of the fundamental electric charge e. The pions represent an SU(2) triplet and singlet through combinations of up and down quarks. They are all spin zero pseudoscalars. The is the antiparticle of the and vice versa, while the neutral pion is its own antiparticle. The charged pions have a mass of 139.56995 ± 0.00035 MeV/c2 while the neutral pion has a mass of 134.9764 ± 0.0006 MeV/c2. [PDG 96]
The has a number of decay channels as seen in Table 1.1. The decay channels are just the charge conjugate of those of the. The neutral has several decay modes with the strongest (~98.8%) being into two photons. The pion beta decay project (pibeta) at the Paul Scherrer Institute (PSI) will attempt to make a precise measurement with an uncertainty of less than 0.5% of the e+ decay rate relative to the e+decay rate.
Table 1.1: The decay modes of the+. (The decay modes of the - are the charge conjugates of those for the+.) [PDG 96]
Decay mode / Fraction () / Confidence/ (99.98770 ± 0.00004)%
/ (1.24 ± 0.25 ) x 10-4
/ (1.230 ± 0.004 ) x 10-4
/ (1.61 ± 0.23 ) x 10-7
/ (1.025 ± 0.034 ) x 10-8
/ (3.2 ± 0.5 ) x 10-9
/ <5 x 10-6 / 90%
Lepton Family / (LF) or Lepton number (L) / violating modes
/ <1.5 x 10-3 / 90%
/ <8.0 x 10-3 / 90%
/ <1.6 x 10-6 / 90%
1.2 Experimental motivation
According to the Standard Model (SM), the strong mass eigenstates of the quarks are different from the eigenstates for the weak force. Cabibbo parameterized this difference in 1963 in the form of a matrix that rotated the quark mass eigenstates of the strong force into the weak eigenstates [Cab 63]. Cabibo's parameterization dealt only with four quarks (u, d, s, and c) and used a single parameter known as the Cabibbo angle. In 1973, Kobayashi and Maskawa extended the idea to all six quarks (three generations) and gave an explicit parameterization for what is known as the Cabibbo-Kobayashi-Maskawa quark mixing matrix (CKM) [Kob 73]. In the CKM, only the charge -1/3e quarks (d, s, b) mix by convention as show here:
According to the SM, the CKM is a unitary matrix; thus, adding the elements of any row in quadrature should result in unity. Given the experimental precision with which each of the elements of the CKM has been determined, the top row provides the most stringent test of unitarity.
(1.5)
has been determined from Ke3 decays (e.g. K+e+e) to be 0.2196 ± 0.0023 [PDG 96, Shr 78] . A more recent re-analysis by Barker et al. modifies the value only slightly to 0.2199 ± 0.0017 [Bar 92]. Slightly higher values of have been determined from the study of hyperon decays (e.g. e and n e) [Gar 92] which leads to an overall average of 0.2205 ± 0.0018 [PDG 96].
The value has not yet been determined directly. Values for and however, have been measured and can be used to indicate of the magnitude of . The value can be determined from the semileptonic decay of B mesons produced on the (4S) resonance. The current value, which combines the experimental and theoretical uncertainties, is [PDG 96]:
=0.08 ± 0.02(1.6)
The value can be obtained from B semileptonic decays to charmed mesons (). The current value of is :
=0.041 ± 0.003(1.7)
Combining (1.6) and (1.7) yields a value for on the order of 10-3 (about the same order uncertainty as in ) and is therefore safe to ignore.
The dominant term in (1.5) is which can be determined from both nuclear beta-decay and neutron decay experiments. The results disagree somewhat as described below.
1.2.1 Neutron decay
Neutrons are hadrons comprised of up and down quarks. Neutron decay, however, is a weak process and thus involves the matrix element . Extracting from neutron decay requires not only an experiment to measure the neutron lifetime, but also an experiment to measure the -asymmetry of polarized neutron decays. Data from both such experiments have been used to perform the unitarity test of (1.7) [Tow 95]
which is significantly greater than unity.
1.2.2 Nuclear beta decay
The Fermi theory of beta decay gives for the total decay rate:
where g is related to the weak coupling constant and proportional to the value , Mfi is the nuclear matrix element, and F(Z',p) is the Fermi function. Te and p refer to the kinetic energy of the decay electron and its momentum, respectively. The Fermi integral is defined as:
where Eo and pmax are the maximum available energy and momentum for the electron. In the limit that the emitted electron's mass is negligible with respect to its momentum, the ratio of these two values is a constant represented by:
where is a constant. The value is only constant insofar as the matrix element is constant. For superallowed decays (J), this value is easily calculated:
where represents the isospin of the initial state nucleon. This, however, is not entirely accurate since it assumes that the initial and final states of the nucleus are pure isospin states. Nuclear and charge-dependent effects cause the isospin portion of the nuclear wavefunctions to be slightly mixed due to a presence of an isospin non-conserving term (INC) in the interaction Hamiltonian. This requires a correction to known as the nuclear mismatch. Additionally, radiative corrections must be applied due to the presence of electric charges. The modified value can thus be written,
where (1 + R) represents the radiative corrections and (1 - C) represents the nuclear mismatch correction. The O(Z2) radiative corrections have been well documented ([Sir 87, Jau 87, Sir 86, Bar 92]). The nuclear mismatch correction is not well understood and is very model dependent as is illustrated in Table 1.2.
The pion beta decay process ( e+) is a transition similar to the transitions in superallowed Fermi decays, with J and . No INC term exists for free pions that would require a nuclear mismatch correction C. This makes details of the pion beta decay process much less ambiguous with respect to nuclear beta decays and therefore provides a third method for testing the unitarity of the top row of the CKM. The present measurements of the pion beta decay rate yield a value of 1.025 ± 0.034 [PDG 96], with an uncertainty at a level of ~4% [McF 85]. This is not sufficient to test even the radiative corrections which are already at the level of ~3%.
According to the theory of conserved vector currents (CVC), the vector part of the weak current is not re-normalized by the strong force. The weak vector current is therefore the same in strength for muons, pions, and nucleons. The CVC hypothesis leads to a calculation of the pion beta decay rate of (1.0482 ± 0.0048) x 10-8 with an
1
Table 1.2: Values for the nuclear mismatch correction (in percent) for superallowed beta decays in several nuclei as calculated by various sources.
/ [Bar 94] / [Orm 89] / [Har 90] / [Wil 90] / [Woo 91] / [Tow 95]14O / 0.12 / 0.19 / 0.28 / 0.32 / 0.33 / 0.22
26Alm / 0.05 / 0.24 / 0.33 / 0.48 / 0.62 / 0.31
34Cl / 0.11 / 0.48 / 0.64 / 0.84 / 0.98 / 0.61
38Km / 0.10 / 0.49 / 0.70 / 0.90 / 0.91 / 0.62
42Sc / 0.12 / 0.39 / 0.39 / 0.71 / 0.88 / 0.41
46V / 0.05 / 0.21 / 0.45 / 0.65 / 0.89 / 0.41
50Mn / 0.05 / 0.28 / 0.50 / 0.72 / 0.77 / 0.41
54Co / 0.05 / 0.35 / 0.59 / 0.79 / 1.00 / 0.52
uncertainty of ~0.5% [McF 85].
1.3 Previous measurements
Several previous experiments involving precise measurements of pion decay rates have been performed. Most relevant to the pibeta project are those concerned with e and e+ decays. Specifically, the recent e measurements by G. Czapek et al. in 1993 and by D.I. Britton et al. in 1992 as well as the e+ measurements by W.K. McFarlane et al. in 1985 and P. Depommier et al.in 1968 are discussed in the following sections.
1.3.1 Previous e measurements
Two recent precise measurements of the e decay rate have been made. One by Czapek et al. with results published in 1993 and the other by Britton et al. with the results published in 1992 and then again in 1994. Both of these experiments are discussed in the following sections.
1.3.1.1 Czapek, et al. (1993)
In 1993, results were reported for a measurement of the e branching ratio from data taken at PSI in 1988. The experimental setup (shown in Fig. 1.1) consisted of 132 hexagonal BGO crystals which covered all but 0.2% of 4. A target made of plastic scintillator was used for stopping the pions at the center of the array.
1
Figure 1.1: Experimental setup from [Cza 93]. PM indicates the photomultipliers, BGO indicates the BGO calorimeter S indicates a beam-defining scintillator, and T indicates the active target.
BGO crystals on either side of the target were coupled to the target and served simultaneously as light guides to the target and active members of the calorimeter.
Data were taken using two different triggers simultaneously. One triggered on the rare e decays while the other was a prescaled trigger for measuring the normalization events. The branching ratio was found by cutting on a window in the total energy spectrum (83.5 MeV to 101 MeV pion stopping+decays). The low energy tail was estimated using a GEANT simulation. The value obtained was ([Cza 93].
1.3.1.2 Britton, et al. (1992,1994)
In 1992 [Bri 92] and again in 1994 [Bri 94], results were reported for another measurement of the e branching ratio. The experimental apparatus consisted of a plastic scintillator target, two wire chambers, a large NaI crystal (TINA), and several other beam counters and vetos. A diagram of the experimental apparatus can be seen in Figure 1.2. Pions were stopped in a plastic scintillator target and allowed to decay. Positrons emitted in the direction of calorimeter passed through two wire chambers and four thin, plastic scintillator detectors before entering TINA. The TINA crystal gave extremely good energy resolution as can be seen in Figure 1.3. The branching ratio was found by fitting the timing spectra for e and e events simultaneously. Correction for the low energy tail of the e spectrum that extended under the spectrum arising from the e decay chain was achieved by establishing upper and lower limits on the tail fraction. The value obtained was (1.2265 ± 0.0078) 10-4. The upper limits came from direct-in-beam measurements of the response function of TINA while the lower limits were derived from a e suppressed energy spectrum.
Figure 1.2: The experimental setup from [Bri 92, Bri 94]. The inset shows details of the target assembly. Events where the decay positrons enter the large NaI crystal TINA are recorded.
1.3.2 Previous e+measurements
Two previous precise measurements of the e+ decay rate have been made. The first, which used a stopped pion beam, was done in 1968 by Depommier et al.and is described in section 1.3.2.1. The second, which used in-flight pion decays, was done by McFarlane et al. and is described in section 1.3.2.2.
Figure 1.3: Positron energy spectrum for early times (<30 ns) from [Bri 94]. The two low energy peaks are the zero energy pedestal and the 0.511 MeV spectrum from the annihilation of low energy positrons outside of TINA.
1.3.2.1 Depommier et al. (1968)
The earliest precise measurement of the e+ branching ratio was performed by Depommier et al. and reported in 1968 [Dep 68]. This measurement was done at the CERN synchrocyclotron using stopped pions. Pion beta decay events were identified by the coincidence from a decay in an array of lead glass detectors (see Figure 1.4). The data acquisition system consisted of two oscilloscopes with cameras triggered by this coincidence. Punch tape was also used for storing some digitized
1
Figure 1.4: The experimental setup from [Dep 68]. Both front and side views of the leadglass calorimeter are shown. Pions pass through the carbon block which slows them so that they stop in counter 3. The pions decay and the leadglass calorimeter detects the back-to-back 2 signature of a decay.
information. The experiment yielded a value (1.00 )10-8 for the pion beta decay branching ratio.
1.3.2.2 McFarlane et al. (1985)
The most recent measurement of the e+ branching ratio was reported by McFarlane et al. in 1985 [McF 85]. The experiment was done at LAMPF and measured in-flight decays of pions. Figure 1.5 shows a diagram of the apparatus. The removable CH2 target was only in place for the calibration runs that alternated with the pion-beta-decay runs. This measurement yielded a value of (1.026 ± 0.039) 10-8. The experiment was not an easy one to perform due to the difficult normalization.
Figure 1.5: The experimental setup from [McF 85]. Charged Pions which decay in-flight
into neutral pions can be detected by the subsequent neutral pions decaying into two photons.
1.3.3 Summary
A precise measurement of the pion beta decay rate would provide a third method for determining the Vud element of the CKM providing a more stringent unitarity test ofthe top row. Since pion beta decay represents a transition between two spin zero members of an isotriplet, it is analogous to superallowed nuclear beta decays allowing for a comparison of ƒt values. Additionally, a stringent test of CVC would be made by a measurement of the pion beta decay rate at the <0.5% level of uncertainty. Pion beta decay provides the most direct test of CVC because it is a pure vector transition occurring outside of a nucleus and thus free from the re-normalizing effects of the strong force.
The branching ratio for the e decay has been measured accurately to an uncertainty of <0.4%. There have been, however, only two accurate measurements of the e+ branching ratio. These had uncertainties of >3% [McF 85] and >8% [Dep 68]. The pibeta project will measure the pion beta decay rate using a stopped pion method not unlike the one used in [Dep 68] but with a modern data acquisition system and a calorimeter with much greater angular resolution. The pibeta project anticipates an uncertainty of <0.5% on the initial measurement of the e+ decay rate with hopes of reducing the uncertainty to the level of <0.2%.
This document focuses on a measurement of the e branching ratio and the preparation of the plastic veto array supplied by Arizona State University for the pibeta project. A review of the theoretical background related to the pibeta experiment as well as an overview of the detector apparatus is presented. Results from cosmic ray tomography of three plastic veto detectors are presented. Finally, results from the analysis of pion decay data are given which yielded a measurement of the e branching ratio.
For this work, the author assembled and prepared the plastic veto scintillator staves for the pion beta decay experiment. Data were taken by the author using cosmic rays and three plastic veto scintillator staves. Results of the analysis of that data are presented in Chapter 4. The author participated in performing in-beam tests of several components of the pion beta decay detector in 1994, 1995,1996, and 1997. Analysis done by the author of data acquired in 1996 and 1997 is presented in Chapter 5, resulting in a determination of the e branching ratio.