Chapter 1
Introduction

The novel ideas of the British chemist, John Dalton, as well as the pioneering work of Joseph-Louis Gay-Lussac demonstrated that chemical reactions occurred in specific ratios of ``atoms'' [2]. These ideas developed further through the work of chemist William Prout. Prout observed that the atomic weights of all known chemical elements were nearly integer multiples of the atomic weight of hydrogen and suggested that hydrogen must be the base of all atoms. The russian chemist, Dimitri Mendeleev, arranged all the known elements of his time into an ordered table according to common characteristics of each element demonstrating a definite ``periodicity'' and even predicting certain elements based on this periodicity. The triumphant discoveries of a number of missing elements seemed to indicate that this understanding of the world was indeed correct. The discovery of the electron by Sir Joseph Thomson changed the way these early scientist understood the atom. A half a century later, Ernest Rutherford demonstrated that the elements of the periodic table were composed of ever smaller particles including protons and neutrons at the nucleus around which circled the electrons.

The number of such elementary particles grew in number to more than 100 by 1960. Order was finally brought to this chaotic world of elementary particles through the work of Murray Gell-Mann who suggested that all of these elementary particles were composed of smaller constituents known as ``quarks''. Today, our understanding of the known and conjectured elementary particles consists of quarks, leptons, and ``bosons'' which are classified according to known characteristics into families.

1.1  Elementary Particles

The most fundamental understanding of the physical world divides elementary particles into two distinct types known as fermions (spin-1/2, 3/2, ..., half-integer) and bosons (spin-0, 1, 2, ..., integer). If the fermions, which consist of quarks and leptons, are organized according to certain important theoretical criteria called quantum numbers, the resulting arrangement falls neatly into three sets of particles referred to as ``families'' as shown in Table 1.1 [3].

The e^-, m^-, and t^-, called the ``electron,'' ``muon,'' and ``tau,'' respectively, have a charge of -1 and not only interact through the weak force but also electromagnetically. Here n<sub>e</sub>, n<sub>m</sub>, and n<sub>t</sub> are the so called ``neutrinos'' which carry neutral charge and interact only via the weak bosons, W^±, and Z⁰. The u, d, c, s, b, and t are called ``up,'' ``down,'' ``charm,'' ``strange,'' ``bottom'' and ``top'' quarks, respectively. The u-type quarks (u, c and t) carry a fractional charge of +2/3 and the d-type quarks (d, s and b) carry a fractional charge of -1/3. They interact through all types of interactions intermediated by the weak bosons, photons and gluons. To date, all evidence indicates that these fermions which make up the periodic table consist of quarks and leptons which are both structureless and point-like down to a scale of 10^-17 m. Associated with each fermion are certain properties and symmetry characteristics summarized by ``quantum numbers``.

The quantum numbers used to create the arrangement of elementary particles shown in Table 1.1 include the electric charge, Q, the hypercharge, Y, and the third component of weak isospin, I₃. This theoretical description of the elementary particles treats each family identically due to the inherent symmetries of the formulation and is called the Standard Model (SM). Notable to the SM description of elementary particles is that the mass of each type of particle or ``species'' increases in traversing the families with the exception of the neutrinos, which are conjectured to be massless. Although the Standard Model describes the interactions of all known and conjectured particles such as the t-quark, it does not predict the number of elementary particle families. The number of elementary families which is indicated by the arrangement in Table 1.1 turns out to be exactly three, i.e. N_fam º 3, however this number must be empirically determined through experimentation.

1.2  Fundamental Interactions

The second type of elementary particle are the bosons which mediate the four fundamental interactions between the elementary particles. These four fundamental interactions are shown in Table 1.2 [9] and include the following forces: electromagnetic, weak, strong, and gravitational. Over the past two decades, our understanding of the world of interactions of elementary particles has witnessed a whole series of exciting discoveries including: the weak vector bosons, i.e. W^±and Z⁰  [5], the neutral current interaction [6], and charmed particles [7]. Each of these discoveries have lead to the rapid development and application of local symmetry gauge theories [8] to describe the fundamental interactions of elementary particles.

The interactions mediated by the most basic bosons, the photon, g, and the vector bosons, W^± and Z⁰, are described through a single local symmetry group, SU(2)_L Ä U(1)_Y, referred to as the Glashow-Salam-Weinberg (GSW) [10] or electroweak theory. To date, the GSW Model is the most complete and successful description of all observations in the area of electroweak particle interactions. The addition of a third local symmetry group, SU(3)_C group, where the generators of the theory represent the strong vector bosons, i.e. the eight gluons, g_i where i=1,8, describes the strong interaction and is referred to as quantum chromodynamics (QCD). GSW and QCD taken together make up a single theory called the Standard Model (SM). The model mathematically describes the interactions of the electroweak and strong interactions through the group product of the local symmetries given by SU(3)_C ÄSU(2)_L ÄU(1)_Y. The SM theory describes all known physical phenomena up to 100 GeV very well.

Attempts to extend the SM theory to include the fourth fundamental interaction of gravity have been based on the symmetry group SU(5)_L. Such theories which attempt to include the force of gravity through a consistent quantum field theory are called the Theory of Everything (TOE). TOE's remain complete speculation due to the difficulty in formulating a renormalizable quantum field theory and as yet the graviton has not been observed experimentally. Although a complete mathematical description of the interactions of elementary particles is not complete or substantiated, the pattern of elementary interactions and particles is quite clear. By sequentially including each of the fundamental interactions in a theoretical construction, one goes from broken symmetry and unambiguity of particles to complete symmetry of interactions and ambiguity of particles.

1.3  Neutrino Counting

From Table 1.1, the number of families of elementary particles which populate the universe is exactly three, i.e. N_fam º 3. Since this number is not predicted by the SM description of the fundamental interactions, the question naturally arises if there could be any other number of families not excluding fractions of families. To answer such a fundamental question, it is of the utmost importance to empirically measure the number of elementary families in as many different ways and as accurately as possible. Today, both direct and indirect experimental evidence is mounting and converging toward the exact number of families of indeed three. The most direct way to measure the number of elementary particle families is to count the number of different species within a family, e.g. counting the number of quarks with Q = +2/3 or the number of neutrinos. Since neutrinos are apparently massless, they are ideal for counting and measuring the number of elementary particle families since they would be produced at lower energy thresholds than their massive ``sibling'' particles.

Neutrino Limits - Historical

Historically, the best measurements of the number of elementary light neutrinos, N_n came from cosmology and particle physics. Cosmological considerations of primordial nucleosynthesis placed limits of N_n < 3.3 at the 90% C.L. and N_n < 3.6 at the 95% C.L. on the number of light neutrinos. This limit was imposed by a c² fit to five different measurements of primordial material including: 1) Deuterium, 2) He³, 3) D + He³, 4) Li⁷, and 5) He⁴ and the neutron half life, t_¹/2 (10.35±0.12 min)  [11].

The limits imposed on the number of elementary light neutrinos, N_n, from particle physics are divided into two areas according to the type of collider used. Combining, the e⁺e^- collider experiments of ASP, CELLO, and MAC, a total of 3.9 events are observed whereas 6.8 are expected giving a limit of N_n < 3.9 at the 90% C.L. and N_n < 4.8 at the 95% C.L. for the number of light neutrinos [12]. The results of the p [`(p)] collider experiments of UA1 and UA2 when combined with the recent results from the CDF p [`(p)] collider experiment gives a value of N_n= 2.6±1.1(stat.)±0.6(sys.) for the number of light neutrinos  [13].

All of these measurements have specific theoretical and experimental uncertainties which can be improved upon. The cosmological limits suffer the fate of large uncertainties in the measurements of basic primordial material and lifetimes. The e⁺e^- and p [`(p)] collider experiments operate in reduced energy regimes where the cross-section for the production of either the W^± or the Z⁰ is small and consequently their results suffered from low statistics. In general, all limits imposed by either cosmological or particle physics measurements suffer from the large errors due to low statistics.

Neutrino Limits - LEP

The most precise measurements of the number of elementary light neutrino species comes from the recent measurements by the experiments of the Large Electron Positron collider (LEP) at CERN. The LEP accelerator allows very precise determinations of the mass and width of the neutral weak vector bosons, Z⁰, by scanning the peak of Z⁰ production near Ös » M_Z⁰. The LEP accelerator also allows for the precise measurement of the number of light neutrino species which couple directly to the Z⁰ and have m_n £ M_Z⁰/2 through two different methods of measurement: directly, single photon counting, and indirectly, invisible width.

Invisible Width Method

One method for measuring the number of elementary families which couple directly to the Z0 assumes that the total invisible width, GZ0inv, defined as the total fitted width of the Z0, GZ0tot, minus the observed hadronic, GZ0had, and leptonic, GZ0lept, widths, is the same as the total neutrino width, GZ0n[`(n)]  [14]. This method is known as the invisible width or line shape method and will be discussed in greater detail in Chapter 2. The best measurements using the invisible width method come from the LEP experiments. Each of the four experiments at LEP, namely ALEPH, DELPHI, L3, and OPAL, has performed this measurement as shown in Table 1.3. The clear advantage of the LEP measurements over previous measurements is the gain in statistics resulting from the operation of the LEP collider near Ös » MZ0.

Single Photon Counting

Another complementary method for measuring the number of elementary families makes use of the direct proportion of N_n to the spectrum of the radiated single photon from the decay of the Z⁰ to invisible particles  [19]. This method is called the single photon counting method and is discussed in greater detail in Chapter 2. The best measurements determined using this method are those from the LEP experiments as shown in Table 1.4.

1.4  Thesis Overview

This thesis presents the results of the measurement of the number of elementary neutrinos with mn  £ MZ0/2 using the method of single photon counting. The data analyzed in this thesis has been collected by OPAL detector at LEP during the 1991 run corresponding to Periods 20 to 33. This thesis then presents a combined limit from the 1990 run corresponding to Periods 14 to 19 and the 1991 run. Finally, the invisible width of the Z0, GZ0inv, in the Standard Model is extracted from this number of light neutrinos.

In Chapter 2, the theoretical aspects of the Standard Model and the Method of Neutrino Counting are discussed. Focus is placed on the method of single photon counting to determine the number of elementary light neutrinos, i.e. N_n with M_Z⁰/2. The experimental apparatus consisting of the LEP accelerator and the OPAL detector is described in Chapter 3. The data acquisition system of the OPAL detector is described in Chapter 4. A detailed discussion of the Monte Carlo methods and generators along with the simulation of the OPAL detector are detailed in Chapter 5. The single photon event selection is discussed in Chapter 6. The single photon energy loss and resolution is discussed in Chapter 7. A discussion of the efficiencies for triggering, vetoing and selecting single photon events is given in Chapter 8. The backgrounds to the single photon signal, e⁺e^-® n[`(n)]g, are discussed in Chapter  9. The determination of the efficiency and the backgrounds to the e<sup>+</sup>e<sup>-</sup>® n[`(n)]g signal are essential before the single photon candidates from the data can be compared to Monte Carlo predictions to make a measurement of the number of elementary light neutrinos. The following Chapter 10 discusses the results from the single photon measurement sample using the 1991 data and the combined result with the previous results [21]. Chapter 10 also concludes the thesis and discusses the significance of the measurement presented in this thesis. At the end of this thesis, the reader is provided with a supplementary discussion of the application of gauge theories to high energy physics in  Appendix A, the Standard Model of particle physics in  Appendix B , and radiative corrections in  Appendix C.