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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 06 Dec 2023 14:33:08 +0000Two studies of dynamical calculations in two meson systems
https://resolver.caltech.edu/CaltechETD:etd-03242003-091021
Authors: Beder, Douglas Stanley
Year: 1965
DOI: 10.7907/K3FF-P112
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
This thesis describes dynamical calculations in dispersion theory relating to meson states. The first part discusses the bound state pseudoscalar mesons, utilizing a pole model representation of the binding forces.
In the one-channel pseudoscalar vector calculation, and in a calculation coupling this to the baryon-antibaryon channel, fairly modest forces suffice to produce a tightly bound state. However, the output coupling constants are much larger than those fed into the calculation, so that bootstrap self consistency is not attained. It is also interesting that the baryon-antibaryon channel seems to be a very significant contributor to the dynamical generation of bound state pseudoscalar mesons.
The second part of this work considers electromagnetic mass splittings of mesons. In a dynamical scheme for generating the mesons, mass splittings of the derived multiplets arise both because of mass splittings of the particles participating in the relevant scattering channels, and, because of photon exchanges. A crude inelastic bootstrap calculation of the [rho] vector meson is developed and then subject to electromagnetic perturbations. As a corresponding pseudoscalar meson bootstrap is not available, we can only relate pseudoscalar and vector mass differences here. A rough estimate which results for the [rho] meson is M[...] - M[...] 11 MeV. A yet cruder estimate of the K*(885) mass difference is MK[...] - MK[...][...] 5 MeV. https://thesis.library.caltech.edu/id/eprint/1083The influence of the NN* channel on elastic NN scattering
https://resolver.caltech.edu/CaltechTHESIS:10192015-090318183
Authors: Shepard, Harvey Kenneth
Year: 1966
DOI: 10.7907/5HRF-4A20
<p>The problem of two channels NN and NN*, coupled through unitarity, is studied to see whether sizable peaks can be produced in elastic nucleon-nucleon scattering due to the opening of a strongly coupled inelastic channel. One-pion-exchange (OPE) interactions are calculated to estimate the NN*→NN* and NN→NN* amplitudes. The OPE production amplitudes are used as the sole dynamical input to drive the multichannel ND<sup>-1</sup> equations in the determinental approximation, and the effect on the J = 2+ (<sup>1</sup>D<sub>2</sub>) elastic NN scattering amplitude is studied as the width of the unstable N* and strength of coupling to the inelastic channel are varied. A cusp-type enhancement appears in the NN channel near the NN* threshold but for the known value of the N* width the cusp is so “wooly” that any resulting elastic peak is likely to be too broad and diminished in height to be experimentally prominent. A brief survey of current experimental knowledge of the real part of the <sup>1</sup>D<sub>2</sub> NN phase shift near the NN* threshold is given, and the values are found to be much smaller than the nearly “resonant” phase shifts predicted by the coupled channel model. </p>https://thesis.library.caltech.edu/id/eprint/9225High-energy scattering processes with cuts in the angular momentum plane
https://resolver.caltech.edu/CaltechTHESIS:10192015-141742955
Authors: Reichert, John D.
Year: 1966
DOI: 10.7907/C84N-TD28
<p>The experimental consequence of Regge cuts in the angular momentum plane are investigated. The principle tool in the study is the set of diagrams originally proposed by Amati, Fubini, and Stanghellini. Mandelstam has shown that the AFS cuts are actually cancelled on the physical sheet, but they may provide a useful guide to the properties of the real cuts. Inclusion of cuts modifies the simple Regge pole predictions for high-energy scattering data. As an example, an attempt is made to fit high energy elastic scattering data for pp, ṗp, π<sup>±</sup>p, and K<sup>±</sup>p, by replacing the Igi pole by terms representing the effect of a Regge cut. The data seem to be compatible with either a cut or the Igi pole. </p>https://thesis.library.caltech.edu/id/eprint/9229Radiative Corrections to Neutrino-Electron Processes
https://resolver.caltech.edu/CaltechETD:etd-09182002-113654
Authors: Hebb, Mathilde Jeannette
Year: 1967
DOI: 10.7907/QS3P-0P04
<p>The lowest order electromagnetic radiative corrections to electron-positron annihilation into neutrino and antineutrino and to neutrino scattering by electrons are calculated. The pair annihilation corrections are used to calculate the radiative corrections to stellar neutrino luminosities in the temperature range in which the zero order process gives the dominant contribution. The corrections to the neutrino-electron scattering cross section are those relevant to a proposed experiment detecting scattered electrons with more than a minimum recoil energy whether or not a bremsstrahlung photon is emitted.</p>
<p>The results depend logarithmically on an ultraviolet cut-off in the same way as does the lowest order vacuum polarization diagram of electrodynamics. When the cut-off is taken to be on the order of the nucleon mass the luminosity is enhanced by as much as 10 percent below T ~ 10⁹ °K and depressed by ~1 percent for T > 10⁹ °K. The scattering cross section is depressed by ~4 percent for the incident neutrino energies ~8 - 14 MeV of the proposed experiment.</p>
<p>A characteristic distance, the neutrino charge radius, is associated with a charge distribution of the neutrino and depends on the cut-off. With the cut-off at the nucleon mass the charge radius of the electron neutrino is estimated to be two orders of magnitude smaller than the experimental limit. The possible effects of a charge radius larger than the estimate are also considered. It is found that interference between the electromagnetic and weak couplings could depress both the non-relativistic stellar luminosity and the scattering cross section, but that if the scattering cross section is found to be as large as expected' the luminosity must be also.</p>https://thesis.library.caltech.edu/id/eprint/3609Calculation of the N*(1238) electromagnetic mass differences by S-matrix methods
https://resolver.caltech.edu/CaltechETD:etd-09182002-114335
Authors: Henyey, Frank Stephen
Year: 1967
DOI: 10.7907/8E08-7D21
We calculate the electromagnetic mass differences within the N*(1238) isomultiplet, using the S-matrix theory of perturbations developed by Dashen and Frautschi. An ambiguity in the choice of methods for calculating the effect of one photon exchange, and lack of sufficient data on the rho meson lead to rather large uncertainties in the predicted mass differences. Our results are consistent with experimental determinations of the differences, which also have rather large uncertainties.https://thesis.library.caltech.edu/id/eprint/3610Bootstrap theory and certain properties of the hadron axial vector current
https://resolver.caltech.edu/CaltechETD:etd-12092004-140220
Authors: Chapline, George Frederick
Year: 1967
DOI: 10.7907/PXKT-FG78
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The matrix element [...] is calculated. A similar calculation for [...] is compared with experiment. The relationship of the Goldberger-Treiman relation to the bootstrap principle is discussed. Approximate symmetry predictions for the axial vector current are compared with the S-matrix calculations. Implications of the bootstrap principle for equal time commutators of hadron currents are discussed.https://thesis.library.caltech.edu/id/eprint/4895Calculation of [pi]NN and [pi]NN* resonance shifts, using the Dashen-Frautschi method
https://resolver.caltech.edu/CaltechETD:etd-09252002-121457
Authors: Josephson, Nora Sigrun
Year: 1967
DOI: 10.7907/VKK6-0Y76
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In this thesis the Dashen-Frautschi method is applied to find shifts from SU(2) symmetry of [pi]NN and [pi]NN* coupling constants. Three new features of this type of calculation are discovered. First, we observe that the same A matrix used to connect s channel and u channel residue shifts also relates u channel contributions such as those due to [gamma]N exchange to analogous processes in the s channel. Secondly, under the assumption that all photon masses are the same (for fixed [delta]I), we note that for linear D functions the A matrix has one eigenvalue exactly equal to one (for each [delta]I), but the corresponding component of the driving term vanishes. This result depends essentially only on Clebsch-Gordan and crossing coefficients. The third discovery is that when viewed in a space of larger dimension, eigenvalues near one and "no enhancement" are easy to understand. We also note that when including infrared corrections, residues are not in general proportional to products of coupling constants.
Since the driving terms are approximately orthogonal to the eigenvectors with eigenvalues near one, there is no simple dominant pattern, and thus our numerical results are sensitive to details which are poorly known. We do believe that our calculation gives correct order of magnitude estimates; the observable parts of the [delta]R/R[subscript o]'s are found to be less than one percent. The experimental data are presently unclear but at least do not decisively indicate larger residue shifts than this.
https://thesis.library.caltech.edu/id/eprint/3754Reggeization of Some Unequal Mass Processes Involving Higher Spins: The Reactions πN → VN, πN → VΔ , and γp → π⁺n
https://resolver.caltech.edu/CaltechTHESIS:12212015-131910199
Authors: Jones, Lorella Margaret
Year: 1968
DOI: 10.7907/76Z3-0K96
<p>Recent theoretical developments in the reggeization of inelastic processes involving particles with high spin are incorporated into a model of vector meson production. A number of features of experimental differential cross sections and density matrices are interpreted in terms of this model. </p>
<p>The method chosen for reggeization of helicity amplitudes first separates kinematic zeros and singularities from the parity-conserving amplitudes and then applies results of Freedman and Wang on daughter trajectories to the remaining factors. Kinematic constraints on helicity amplitudes at t = 0 and t = (M – M<sub>Δ</sub>)<sup>2</sup> are also considered.</p>
<p>It is found that data for reactions of types πN→VN and πN→VΔ are consistent with a model of this type in which all kinematic constraints at t = 0 are satisfied by evasion (vanishing of residue functions). As a quantitative test of the parametrization, experimental differential cross sections of vector meson production reactions dominated by pion trajectory exchange are compared with the theory. It is found that reduced residue functions are approximately constant, once the kinematic behavior near t = (M – M<sub>Δ</sub>)<sup>2</sup> has been removed.</p>
<p>The alternative possibility of conspiracy between amplitudes is also discussed; and it is shown that unless conspiracy is present, some amplitudes allowed by angular momentum conservation will not contribute with full strength in the forward direction. An example, γp→π<sup>+</sup>n in which the data for dσ/dt indicate conspiracy, is studied in detail.</p>
https://thesis.library.caltech.edu/id/eprint/9340I. Non-Linear Effects in a Self-Consistent Calculation of SU₃ Symmetry Breaking in Strong Interaction Coupling Constant. II. Direct-Channel Reggeization of Strong Interaction Scattering Amplitudes
https://resolver.caltech.edu/CaltechTHESIS:01292016-161457738
Authors: Creekmore, Stephen Paul
Year: 1969
DOI: 10.7907/EZ5N-Q104
<p>The thesis is divided into two parts. Part I generalizes a self-consistent calculation of residue shifts from SU<sub>3</sub> symmetry, originally performed by Dashen, Dothan, Frautschi, and Sharp, to include the effects of non-linear terms. Residue factorizability is used to transform an overdetermined set of equations into a variational problem, which is designed to take advantage of the redundancy of the mathematical system. The solution of this problem automatically satisfies the requirement of factorizability and comes close to satisfying all the original equations.</p>
<p>Part II investigates some consequences of direct channel Regge poles and treats the problem of relating Reggeized partial wave expansions made in different reaction channels. An analytic method is introduced which can be used to determine the crossed-channel discontinuity for a large class of direct-channel Regge representations, and this method is applied to some specific representations.</p>
<p>It is demonstrated that the multi-sheeted analytic structure of the Regge trajectory function can be used to resolve apparent difficulties arising from infinitely rising Regge trajectories. Also discussed are the implications of large collections of "daughter trajectories." </p>
<p>Two things are of particular interest: first, the threshold behavior in direct and crossed channels; second, the potentialities of Reggeized representations for us in self-consistent calculations. A new representation is introduced which surpasses previous formulations in these two areas, automatically satisfying direct-channel threshold constraints while being capable of reproducing a reasonable crossed channel discontinuity. A scalar model is investigated for low energies, and a relation is obtained between the mass of the lowest bound state and the slope of the Regge trajectory.</p>
https://thesis.library.caltech.edu/id/eprint/9553The complex angular momentum theory of the production of three particles in collisions of two strongly interacting particles at high energy
https://resolver.caltech.edu/CaltechTHESIS:08072015-083927734
Authors: Luxton, Gary
Year: 1970
DOI: 10.7907/RSEM-GC04
<p>The problem of the continuation to complex values of the angular
momentum of the partial wave amplitude is examined for the simplest
production process, that of two particles → three particles. The
presence of so-called "anomalous singularities" complicates the procedure
followed relative to that used for quasi two-body scattering
amplitudes. The anomalous singularities are shown to lead to exchange
degenerate amplitudes with possible poles in much the same way as
"normal" singularities lead to the usual signatured amplitudes. The
resulting exchange-degenerate trajectories would also be expected to
occur in two-body amplitudes.</p>
<p>The representation of the production amplitude in terms of the
singularities of the partial wave amplitude is then developed and
applied to the high energy region, with attention being paid to the
emergence of "double Regge" terms. Certain new results are obtained
for the behavior of the amplitude at zero momentum transfer, and some
predictions of polarization and minima in momentum transfer distributions
are made. A calculation of the polarization of the ρ<sup>o</sup> meson in
the reaction π <sup>-</sup> p → π <sup>-</sup> ρ<sup>o</sup>p at high energy with small momentum transfer
to the proton is compared with data taken at 25 Gev by W. D. Walker and
collaborators. The result is favorable, although limited by the statistics
of the available data.</p>https://thesis.library.caltech.edu/id/eprint/9084Two Topics in Elementary Particle Physics: I. Crossing as a Group and Elimination of Exotic Channels. II. Real Parts of Meson-Nucleon Forward Scattering Amplitude
https://resolver.caltech.edu/CaltechTHESIS:08242015-093245359
Authors: Yahil, Amos
Year: 1970
DOI: 10.7907/51R2-EF81
<p>I. Crossing transformations constitute a group of permutations
under which the scattering amplitude is invariant. Using Mandelstem's
analyticity, we decompose the amplitude into irreducible representations
of this group. The usual quantum numbers, such as isospin or
SU(3), are "crossing-invariant". Thus no higher symmetry is generated
by crossing itself. However, elimination of certain quantum numbers
in intermediate states is not crossing-invariant, and higher symmetries
have to be introduced to make it possible. The current
literature on exchange degeneracy is a manifestation of this statement.
To exemplify application of our analysis, we show how, starting with
SU(3) invariance, one can use crossing and the absence of exotic
channels to derive the quark-model picture of the tensor nonet. No
detailed dynamical input is used.</p>
<p>II. A dispersion relation calculation of the real parts of forward
π<sup>±</sup>p and K<sup>±</sup>p scattering amplitudes is carried out under the assumption
of constant total cross sections in the Serpukhov energy range.
Comparison with existing experimental results as well as predictions
for future high energy experiments are presented and discussed.
Electromagnetic effects are found to be too small to account for the
expected difference between the π<sup>-</sup>p and π<sup>+</sup>p total cross sections at
higher energies.</p>https://thesis.library.caltech.edu/id/eprint/9113A Dual Quark Model with Spin
https://resolver.caltech.edu/CaltechTHESIS:04202018-125942170
Authors: Ellis, Stephen Dean
Year: 1971
DOI: 10.7907/G3AD-N729
<p>A dual quark model is developed from the usual Veneziano model
by explicitly including the Dirac spin of the quarks. Resonances
appear without the parity doubling and new ghosts present in previous
models with spin. This is accomplished by eliminating the contributions
of the negative parity components (MacDowell-twins) of the
spin quarks 1/2 through the introduction of fixed J-plane cuts. The
resonances belong to an SU<sub>6</sub> symmetric spectrum identical, on the
leading trajectory, with that of the usual static symmetrical quark
model. All resonances couple via SU<sub>6w</sub> x O<sub>2Lz</sub> symmetric vertices
and the model factorizes with essentially the same degeneracy as the
usual Veneziano model. As a consequence of requiring these two
features the model acquires further new structure which is studied
in detail in terms of the asymptotic behavior of the model. This
new structure leads to unavoidable "background" contributions to
the imaginary parts of the amplitudes not present in previous dual
models. This situation is examined and interpreted in the language
of Finite Energy Sum Rules.</p>
<p>In order to test the basic features of the model explicit
calculations are made for the case of pion-nucleon scattering in
the Regge limit. To make the numerical work easier a somewhat
simplified version of the model is used. Although the results of
the calculations are suggestive of reasonable J-plane structure for
the various amplitudes, i.e., the location of Regge pole-fixed cut
interference is reasonable from the standpoint of the data, the
overall kinematic behavior of the amplitudes is definitely not
compatible with what is measured. However, it is noted that this
kinematic behavior depends strongly on those details of the model
which were simplified in the present study. If such models are to
be unambiguously and successfully tested against data, future studies
must treat these details more completely and realistically, including
both unitarity and symmetry breaking effects.</p>https://thesis.library.caltech.edu/id/eprint/10823A relativistic quark model with harmonic dynamics
https://resolver.caltech.edu/CaltechETD:etd-05022005-085218
Authors: Ravndal, Finn
Year: 1971
DOI: 10.7907/XRTB-V265
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
A relativistic equation to represent the symmetric quark model of hadrons with harmonic interaction is constructed. This gives straight and parallel Regge trajectories and a hadron spectrum which easily can accommodate all known resonances. From the equation we derive vector and axial vector currents for baryons and mesons. The vector current matrix elements of baryons are compared to known magnetic moments, photoproduction amplitudes and inelastic electron proton cross sections. Good agreement is obtained when the theoretical results are modified by an empirical form factor. Besides this form factor, the results depend on no free parameters. Using the same form factor, we calculate radiative decay rates of vector mesons and parameters of K[...] decay, which agree fairly well with experiment. Assuming that the amplitude for emission of a pseudoscalar meson from a hadron is proportional to the divergence of the axial vector current, we calculate most of the known strong decay rates. These results depend on one new coupling constant and a smooth, empirical form factor. More than half of the calculated baryon rates agree well with experiment. The reasons for the many disagreements are discussed. All except one of the meson rates come out close to their experimental values. The angular distributions of the decay B(1235) [...] and A[...](1070) [...] are well described in this model.
https://thesis.library.caltech.edu/id/eprint/1574Elimination of parity doubled states from Regge amplitudes
https://resolver.caltech.edu/CaltechTHESIS:02172016-144723161
Authors: Carlitz, Robert David
Year: 1971
DOI: 10.7907/S57M-PV50
The common belief that fermions lying on linear Regge trajectories
must have opposite-parity partners is shown to be false.
The mechanism by which these experimentally nonexistant states are
eliminated from the theory depends on the presence of fixed Regge
cuts in fermion exchange amplitudes. Thus it is predicted that
fermion Regge trajectories are always accompanied by fixed Regge
cuts. More generally, if particles may be classified as composites
of spin-1/2 (fermion) quarks, fixed cuts are expected to be present
in boson exchange amplitudes as well. This result is demonstrated
in the framework of the Van Hove model and a few further experimental
consequences are discussed.https://thesis.library.caltech.edu/id/eprint/9562Elimination of Parity Doublets in Regge Amplitudes
https://resolver.caltech.edu/CaltechTHESIS:03022016-141707222
Authors: Kislinger, Mark Brecher
Year: 1971
DOI: 10.7907/EGCH-VT65
<p>In Part I, the common belief that fermions lying on linear
trajectories must have opposite-parity partners is shown to be
false. Reggeization of a sequence of positive-parity fermion
resonance is carried out in the Van Hove model. As a consequence
of the absence of negative-parity states, the partial-wave amplitudes
must have a fixed cut in the J plane. This fixed cut, in
conjunction with the moving Regge pole, provides a new parametrization
for fermion-exchange reactions, which is in qualitative
agreement with the data.</p>
<p>In Part II, the spin structure of three particle vertices is
determined from the quark model. Using these SU(6)<sub>W</sub> vertices in
the Van Hove model, we derive a Reggeized scattering amplitude. In
addition to Regge poles there are necessarily fixed Regge cuts in
both fermion and boson exchange amplitudes. These fixed cuts are
similar to those found in Part I, and may be viewed as a consequence
of the absence of parity doubled quarks. The magnitudes of the pole
and cut terms in an entire class of SU(6) related reactions are
determined by their magnitudes in a single reaction. As an example
we explain the observed presence or absence of wrong-signature
nonsense dips in a class of reactions involving vector meson exchange.</p>https://thesis.library.caltech.edu/id/eprint/9600The statistical bootstrap model
https://resolver.caltech.edu/CaltechTHESIS:04112016-091846124
Authors: Hamer, Christopher John
Year: 1972
DOI: 10.7907/W6Y3-4E90
<p>A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm<sup>-3</sup> e<sup>βom</sup> at high masses.</p>
<p>In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.</p>
<p>A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β<sub>o</sub> required in all these applications is consistently around [120 MeV]<sup>-1</sup> corresponding to a "resonance volume" whose radius is very close to ƛ<sub>π</sub>. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.</p>
https://thesis.library.caltech.edu/id/eprint/9668I. Baryon-antibaryon phase transition at high temperature. II. Inclusive virtual photon-hadron reactions in the parton model
https://resolver.caltech.edu/CaltechTHESIS:03022016-151750147
Authors: Cisneros, Arturo
Year: 1973
DOI: 10.7907/ZTWX-TK91
<p> Part I</p>
<p> Present experimental data on nucleon-antinucleon scattering allow a study of the possibility of a phase transition in a nucleon-antinucleon gas at high temperature. Estimates can be made of the general behavior of the elastic phase shifts without resorting to theoretical derivation. A phase transition which separates nucleons from antinucleons is found at about 280 MeV in the approximation of the second virial coefficient to the free energy of the gas.</p>
<p>Part II</p>
<p> The parton model is used to derive scaling laws for the hadrons observed in deep inelastic electron-nucleon scattering which lie in the fragmentation region of the virtual photon. Scaling relations are obtained in the Bjorken and Regge regions. It is proposed that the distribution functions become independent of both
q<sup>2</sup> and ν where the Bjorken and Regge regions overlap. The quark density functions are discussed in the limit x→1 for the nucleon octet and the pseudoscalar mesons. Under certain plausible assumptions it is found that only one or two quarks of the six types of quarks and antiquarks have an appreciable density function in the
limit x→1. This has implications for the quark fragmentation functions near the large momentum boundary of their fragmentation region. These results are used to propose a method of measuring the proton and neutron quark density functions for all x by making measurements on inclusively produced hadrons in electroproduction
only. Implications are also discussed for the hadrons produced in electron-positron annihilation.</p> https://thesis.library.caltech.edu/id/eprint/9601Baryon Number Generation and Mass Relations in SO(10) Unified Models
https://resolver.caltech.edu/CaltechTHESIS:01302018-144721271
Authors: Harvey, Jeffrey Alan
Year: 1981
DOI: 10.7907/mv0x-zk52
<p>Two topics are discussed in this thesis. The first is the calculation of cosmological baryon number generation in the early universe. These calculations are performed for a variety of SU(5) and SO(10) unified models. The effects of superheavy fermions and charge conjugation symmetry are discussed in the context of SO(10) models. The second section contains an analysis of natural fermion mass and mixing angle relations in a grand unified model based on SO(10). These relations are used to study neutrino masses and oscillations. Appreciable mixing is found only between μ and τ neutrinos. Spinor representations of the Lorentz group and of SO(10) are described in two appendices.</p>https://thesis.library.caltech.edu/id/eprint/10657Some Topics in Grand Unified Models and the Cosmological Baryon Asymmetry
https://resolver.caltech.edu/CaltechTHESIS:03132018-141623091
Authors: Reiss, David Benjamin
Year: 1981
DOI: 10.7907/7629-m351
<p>In part I of this thesis some of the parameters relevant to the production of a cosmological baryon number asymmetry are considered in the context of grand unified models. General expressions for the average baryon number generated in the free decays of bosons are derived . The CP violation necessary for the generation of a baryon excess is discussed for a variety of <i>SU</i>(5) models. The kinematics of baryon number production in an illustrative <i>SO</i>(10) model is discussed in detail. In part II a viable <i>SO</i>(10) model is constructed which reproduces the phenomenological fermion mass and mixing angle values. A detailed discussion of the beta function for this model is presented. This analysis includes the effects of scalars.</p>https://thesis.library.caltech.edu/id/eprint/10774Topics in Grand Unified Theories: i) The Naturalness Problem. ii) Monopoles and Fermion Number Violation
https://resolver.caltech.edu/CaltechTHESIS:10232019-171800698
Authors: Sathiapalan, Balachandran
Year: 1983
DOI: 10.7907/m0cj-7n28
<p>This dissertation consists of two parts. The first part contains a discussion of the 'fine-tuning' and 'naturalness ' problems in grand unified theories. It is argued that, while it is impossible to solve these problems in conventional theories which contain scalars, supersymmetric theories that require no fine tuning can be constructed. In these theories the problem reduces to that of obtaining a light Higgs doublet at the tree level, without any unnatural adjustment of parameters. A realistic supersymmetric grand unified theory that has this feature is constructed. It is based on the gauge group SO(10). Supersymmetry is explicitly broken through terms of dimension two.</p>
<p>The second part is an analysis of the interaction of fermions with a non-Abelian ('t Hooft-Polyakov) monopole. Monopoles are invariably present in grand unified theories, and recent studies with massless isospin half fermions have shown that monopoles catalyse fermion number violation. We show that this phenomenon can be described in simple terms using the language of instanton physics. This description also permits a straightforward extension of previous results to arbitrary fermion representations. The importance of half-integer winding numbers is stressed. An explicit calculation is done in the case of isovector fermions.</p>https://thesis.library.caltech.edu/id/eprint/11854Topics in Supersymmetry Theory: 1. A Superspace Action for Ten-Dimensional Supersymmetric Yang-Mills Theory in Terms of Four-Dimensional Superfields; 2. Gauge Groups for Type-I Superstrings
https://resolver.caltech.edu/CaltechTHESIS:10232019-170411829
Authors: Sagnotti, Augusto
Year: 1983
DOI: 10.7907/qrfw-nf31
This thesis is an account or most of the work that I did in Supersymmetry and Supergravity over the last two years. It deals with two major topics. the construction of a new superspace action for ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields. and the classification of the gauge groups allowed at the classical level in the type-I superstring theory. In addition, it contains a discussion of work that I did showing the uniqueness of supergravity in eleven dimensions and the uniqueness of the free Rarita-Schwinger action for massless and massive spin-³/₂ fields.https://thesis.library.caltech.edu/id/eprint/11853Finiteness in Supersymmetric Theories
https://resolver.caltech.edu/CaltechTHESIS:11262018-165108335
Authors: Marcus, Neil
Year: 1984
DOI: 10.7907/4t2f-t947
<p>A two loop calculation in the N = 4 supersymmetric Yang Mills theory is performed in various dimensions. The theory is found to be two-loop finite in six dimensions or less, but infinite in seven and nine dimensions. The six-dimensional result can be explained by a formulation of the theory in terms of N = 2 superfields. The divergence in seven dimensions is naively compatible with both N=2 and N=4 superfield power counting rules, but is of a form that cannot be written as an on-shell N=4 superfield integral. The hypothesized N=4 extended superfield formalism therefore either does not exist, or at least has weaker consequences than would have been expected. By analogy, four-dimensional supergravity theories are expected to be infinite at three loops.</p>
<p>Some general issues about the meaning of finiteness in nonrenormalizable theories are discussed. In particular, the use of field redefinitions, the generalization of wavefunction renormalizations to nonrenormalizable theories, and whether counterterms should be used in calculations in "finite" theories are studied. It is shown that theories finite to n loops can have at most simple-pole divergences at n + 1 loops.</p>
<p>A method for simplifying the calculation of infinite parts of Feynman diagrams is developed. Based on the observation that counterterms are local functions, all integrals are reduced to logarithmically divergent ones with no dependence on masses or external momenta. The method is of general use, and is particularly effective for many-point Green functions at more than one loop.</p>https://thesis.library.caltech.edu/id/eprint/11284Yang-Mills Theory in Six-Dimensional Superspace
https://resolver.caltech.edu/CaltechTHESIS:06042014-113206988
Authors: Koller, Jeffrey George
Year: 1984
DOI: 10.7907/RP3T-S865
<p>The superspace approach provides a manifestly supersymmetric formulation of supersymmetric theories. For N= 1 supersymmetry one can use either constrained or unconstrained superfields for such a formulation. Only the unconstrained formulation is suitable for quantum calculations. Until now, all interacting N>1 theories have been written using constrained superfields. No solutions of the nonlinear constraint equations were known.</p>
<p>In this work, we first review the superspace approach and its relation to conventional component methods. The difference between constrained and unconstrained formulations is explained, and the origin of the nonlinear constraints in supersymmetric gauge theories is discussed. It is then shown that these nonlinear constraint equations can be solved by transforming them into linear equations. The method is shown to work for N=1 Yang-Mills theory in four dimensions. </p>
<p>N=2 Yang-Mills theory is formulated in constrained form in six-dimensional superspace, which can be dimensionally reduced to four-dimensional N=2 extended superspace. We construct a superfield calculus for six-dimensional superspace, and show that known matter multiplets can be described very simply. Our method for solving constraints is then applied to the constrained N=2 Yang-Mills theory, and we obtain an explicit solution in terms of an unconstrained superfield. The solution of the constraints can easily be expanded in powers of the unconstrained superfield, and a similar expansion of the action is also given. A background-field expansion is provided for any gauge theory in which the constraints can be solved by our methods. Some implications of this for superspace gauge theories are briefly discussed. </p>
https://thesis.library.caltech.edu/id/eprint/8477Supergravity Theory from Ten Dimensions
https://resolver.caltech.edu/CaltechTHESIS:01312019-162531115
Authors: Romans, Larry James
Year: 1985
DOI: 10.7907/wt9n-gm39
<p>This work is concerned with the study of several ten-dimensional field theories intimately associated with superstring theories, and possibilities for obtaining realistic four-dimensional theories from them.</p>
<p>Three chapters follow the N = 2b supergravity from ten to five, then to four dimensions . First of all, compactifications to five dimensions on various manifolds are studied. Then the entire mass spectrum for the compactification on S<sup>5</sup> is derived using techniques of harmonic analysis on spheres. A particular set of modes corresponds to a gauged maximal super gravity theory in five dimensions; this theory, with Yang-Mills group SO(6), is constructed in detail. By a process similar to analytic continuation, noncompact versions of this theory are also obtained, gauging all the semisimple real forms of SO(6). One particular form, with gauge group SO*(6) ≈ SU(3,1), compactifies to fiat four-dimensional spacetime and offers attractive phenomenological possibilities.</p>
<p>The final chapter is concerned with candidates for effective low-energy theories for N = 1 superstrings with gauge group SO(32) or E<sub>8</sub> x E<sub>8</sub>. These effective theories contain curvature squared terms, and require unusual gravitational interactions to cancel anomalies. The field equations are derived and found to admit compactifications to fiat four dimensional spacetime, with the possibility of accommodating many phenomenological considerations.</p>https://thesis.library.caltech.edu/id/eprint/11373Interactions of Strings Compactified on Orbifolds
https://resolver.caltech.edu/CaltechTHESIS:08012017-135315454
Authors: Hamidi, Shahram
Year: 1987
DOI: 10.7907/gvyt-8e89
<p>It is very important to understand the process of string compactification before one can extract any reliable phenomenology. We consider an exactly solvable method of string compactification, in which the internal space is an orbifold. We compute various interaction amplitudes and describe how other amplitudes can be calculated.</p>
<p>Multi-valued string variables are handled by formulating the amplitudes on covering spaces where they become single-valued. In the computation of the amplitudes, stretched string intermediate states give rise to expressions that are non-perturbative from the non-linear sigma model point of view.</p>
<p>We also discuss, in the context of Z orbifold, the "blowing up" of the fixed points of an orbifold, to give rise to a Calabi-Yau manifold. The resulting Calabi-Yau manifold is shown to be non-perturbatively stable.</p>https://thesis.library.caltech.edu/id/eprint/10358Listening to the Ear
https://resolver.caltech.edu/CaltechTHESIS:09072011-150449036
Authors: Shera, Christopher A.
Year: 1992
DOI: 10.7907/VAK9-MK96
Otoacoustic emissions demonstrate that the ear creates sound while listening to sound, offering a promising acoustic window on the mechanics of hearing in awake, listening human beings. That window is clouded, however, by an incomplete knowledge of wave reflection and transmission, both forth and back within the cochlea and through the middle ear. This thesis "does windows,"
addressing wave propagation and scattering on both sides of the middle ear. A summary of highlights follows.
Measurements of the cochlear input impedance in cat are used to identify a new symmetry in cochlear mechanics-termed
"tapering symmetry" after its geometric interpretation in simple models-that guarantees that the wavelength of the traveling wave changes slowly with position near the stapes.
Waves therefore propagate without reflection through the basal turns of the cochlea. Analytic methods for solving the cochlear wave equations using a perturbative scattering
series are given and used to demonstrate that, contrary to common belief, conventional cochlear models exhibit
negligible internal reflection whether or not they accurately represent the tapering symmetries of the inner ear. Frameworks for the systematic "deconstruction" of eardrum and middle-ear transduction characteristics are developed and applied to the analysis of noninvasive measurements of middle-ear and cochlear mechanics. A simple
phenomenological model of inner-ear compressibility that correctly predicts hearing thresholds in patients with missing or disarticulated middle-ear ossicles is developed and used to establish an upper bound on cochlear
compressibility several orders of magnitude smaller than that provided by direct measurements. Accurate measurements of stimulus frequency evoked otoacoustic emissions are performed and used to determine the form and frequency variation of the cochlear traveling-wave ratio
noninvasively. Those measurements are inverted to obtain the spatial distribution of mechanical inhomogeneities
responsible for evoked emission. Although current models require that the periodicities found in emission spectra and threshold hearing curves originate in a corresponding corrugation in the mechanics of the cochlea, it is shown that the observed spectral periodicities can arise spontaneously through the dynamics of wave propagation and reflection and that the organ of Corti, as suggested by the anatomy, need manifest no particular translational
symmetries.https://thesis.library.caltech.edu/id/eprint/6653