Baryon and lepton numbers in particle physics beyond the standard model

The works presented in this thesis explore a variety of extensions of the standard model of particle physics which are motivated by baryon number (B) and lepton number (L), or some combination thereof. In the standard model, both baryon number and lepton number are accidental global symmetries violated only by non-perturbative weak effects, though the combination B-L is exactly conserved. Although there is currently no evidence for considering these symmetries as fundamental, there are strong phenomenological bounds restricting the existence of new physics violating B or L. In particular, there are strict limits on the lifetime of the proton whose decay would violate baryon number by one unit and lepton number by an odd number of units.

The first paper included in this thesis explores some of the simplest possible extensions of the standard model in which baryon number is violated, but the proton does not decay as a result. The second paper extends this analysis to explore models in which baryon number is conserved, but lepton flavor violation is present. Special attention is given to the processes of μ to e conversion and μ → eγ which are bound by existing experimental limits and relevant to future experiments.

The final two papers explore extensions of the minimal supersymmetric standard model (MSSM) in which both baryon number and lepton number, or the combination B-L, are elevated to the status of being spontaneously broken local symmetries. These models have a rich phenomenology including new collider signatures, stable dark matter candidates, and alternatives to the discrete R-parity symmetry usually built into the MSSM in order to protect against baryon and lepton number violating processes.

Rational design of zinc phosphide heterojunction photovoltaics

The prospect of terawatt-scale electricity generation using a photovoltaic (PV) device places strict requirements on the active semiconductor optoelectronic properties and elemental abundance. After reviewing the constraints placed on an "earth-abundant" solar absorber, we find zinc phosphide (α-Zn₃P₂) to be an ideal candidate. In addition to its near-optimal direct band gap of 1.5 eV, high visible-light absorption coefficient (>10⁴ cm^-1), and long minority-carrier diffusion length (>5 μm), Zn₃P₂ is composed of abundant Zn and P elements and has excellent physical properties for scalable thin-film deposition. However, to date, a Zn₃P₂ device of sufficient efficiency for commercial applications has not been demonstrated. Record efficiencies of 6.0% for multicrystalline and 4.3% for thin-film cells have been reported, respectively. Performance has been limited by the intrinsic p-type conductivity of Zn₃P₂ which restricts us to Schottky and heterojunction device designs. Due to our poor understanding of Zn₃P₂ interfaces, an ideal heterojunction partner has not yet been found.

The goal of this thesis is to explore the upper limit of solar conversion efficiency achievable with a Zn₃P₂ absorber through the design of an optimal heterojunction PV device. To do so, we investigate three key aspects of material growth, interface energetics, and device design. First, the growth of Zn₃P₂ on GaAs(001) is studied using compound-source molecular-beam epitaxy (MBE). We successfully demonstrate the pseudomorphic growth of Zn₃P₂ epilayers of controlled orientation and optoelectronic properties. Next, the energy-band alignments of epitaxial Zn₃P₂ and II-VI and III-V semiconductor interfaces are measured via high-resolution x-ray photoelectron spectroscopy in order to determine the most appropriate heterojunction partner. From this work, we identify ZnSe as a nearly ideal n-type emitter for a Zn₃P₂ PV device. Finally, various II-VI/Zn₃P₂ heterojunction solar cells designs are fabricated, including substrate and superstrate architectures, and evaluated based on their solar conversion efficiency.

Part I: Latent heat of vaporization of n-decane. Part II: Heat and mass transfer from a cylinder placed in a turbulent air stream - Sherwood and Frössling numbers as a function of free stream turbulence level and Reynolds number

Part I

The latent heat of vaporization of n-decane is measured calorimetrically at temperatures between 160° and 340°F. The internal energy change upon vaporization, and the specific volume of the vapor at its dew point are calculated from these data and are included in this work. The measurements are in excellent agreement with available data at 77° and also at 345°F, and are presented in graphical and tabular form.

Part II

Simultaneous material and energy transport from a one-inch adiabatic porous cylinder is studied as a function of free stream Reynolds Number and turbulence level. Experimental data is presented for Reynolds Numbers between 1600 and 15,000 based on the cylinder diameter, and for apparent turbulence levels between 1.3 and 25.0 per cent. n-heptane and n-octane are the evaporating fluids used in this investigation.

Gross Sherwood Numbers are calculated from the data and are in substantial agreement with existing correlations of the results of other workers. The Sherwood Numbers, characterizing mass transfer rates, increase approximately as the 0.55 power of the Reynolds Number. At a free stream Reynolds Number of 3700 the Sherwood Number showed a 40% increase as the apparent turbulence level of the free stream was raised from 1.3 to 25 per cent.

Within the uncertainties involved in the diffusion coefficients used for n-heptane and n-octane, the Sherwood Numbers are comparable for both materials. A dimensionless Frössling Number is computed which characterizes either heat or mass transfer rates for cylinders on a comparable basis. The calculated Frössling Numbers based on mass transfer measurements are in substantial agreement with Frössling Numbers calculated from the data of other workers in heat transfer.

An investigation of wind tunnel wall effects at high Mach numbers

This paper presents the results of an investigation of wind tunnel wall interference in a two-dimensional wind tunnel at high Mach numbers. The results are presented in the form of curves of lift coefficient versus the ratio of model chord to tunnel height, as functions of Mach number and angle of attack. The investigation was carried out by the authors at the Guggenheim Aeronautical Laboratory of the California Institute of Technology during the school year 1944-45.

Tests were carried out on the NACA low drag airfoil section 65,1-012 at Mach numbers from .60 to .80, and angles of attack of from 1 to 3 degrees. Models were 1", 2", 4" and 6" chord, giving values of the chord to tunnel height ration of .1 to .6. Schlieren photographs were made of shock waves where they occurred.

Behavior of spherical particles at low Reynolds numbers in a fluctuating translational flow

The behavior of spheres in non-steady translational flow has been studied experimentally for values of Reynolds number from 0.2 to 3000. The aim of the work was to improve our qualitative understanding of particle transport in turbulent gaseous media, a process of extreme importance in power plants and energy transfer mechanisms.

Particles, subjected to sinusoidal oscillations parallel to the direction of steady translation, were found to have changes in average drag coefficient depending upon their translational Reynolds number, the density ratio, and the dimensionless frequency and amplitude of the oscillations. When the Reynolds number based on sphere diameter was less than 200, the oscillation had negligible effect on the average particle drag.

For Reynolds numbers exceeding 300, the coefficient of the mean drag was increased significantly in a particular frequency range. For example, at a Reynolds number of 3000, a 25 per cent increase in drag coefficient can be produced with an amplitude of oscillation of only 2 per cent of the sphere diameter, providing the frequency is near the frequency at which vortices would be shed in a steady flow at the mean speed. Flow visualization shows that over a wide range of frequencies, the vortex shedding frequency locks in to the oscillation frequency. Maximum effect at the natural frequency and lock-in show that a non-linear interaction between wake vortex shedding and the oscillation is responsible for the increase in drag.

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.