Advisor Feed
https://feeds.library.caltech.edu/people/Wise-M-B/advisor.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 20:19:52 +0000Chiral Perturbation Theory and the Weak Interaction
https://resolver.caltech.edu/CaltechTHESIS:08042017-160047213
Authors: Bijnens, Johan Lambert
Year: 1985
DOI: 10.7907/64qa-xw17
<p>We study the interface between the standard six-quark model and the observed low-energy weak phenomena. The main processes discussed are weak decays of kaons and hyperons. We study first the low-energy effective weak Hamiltonian at the quark level. This is derived using the renormalization group in leading logarithmic approximation.</p>
<p>Then some properties of this effective weak Hamiltonian that can be derived using chiral perturbation theory are studied. A review of chiral perturbation theory is included.</p>
<p>This formalism is used to study the relation between K̅<sup>0</sup>K<sup>0</sup> mixing and a ΔI = 3/2 decay. We find that the logarithmic corrections to this relation are large, making it unreliable. The same formalism is used to discuss a relation between Kππ, Kπ and K-vacuum matrix elements used in most attempts to compute the Kππ matrix element relevant for the ΔI = 1/2 rule. The domain of validity of this relation is determined.</p>
<p>A review of inclusion of baryons in chiral perturbation theory is given and
one-loop corrections to the Gell-Mann-Okubo relation; semileptonic hyperon decays and nonleptonic S and P wave decays are calculated. All corrections are small except the nonleptonic P wave decays and one S wave decay. The corrections to the Lee-Sugawara relation are large as a consequence of the latter.</p>
<p>Some predictions beyond chiral perturbation theory can be made within the soliton model of baryons. F/D ratios are predicted for hyperon magnetic moments, semileptonic decays and nonleptonic S wave decays in this model.</p>https://thesis.library.caltech.edu/id/eprint/10363On the BRST Invariance of String Theory
https://resolver.caltech.edu/CaltechETD:etd-01052005-142036
Authors: Rey, Soo-Jong
Year: 1988
DOI: 10.7907/MDK4-NY02
<p>Radiative corrections to string scattering amplitude generate, in general, BRST anomalies due to the massless particle tadpole, the on-shell external two-point function singularities, and the intermediate unphysical cut singularities. It is proved that they originate from the boundaries of moduli space. Unitarity, analyticity, and BRST invariance are restored only after we add appropriate local counterterms to the scattering amplitudes. We show that counterterms have physical interpretations as the Fischler-Susskind mechanism, the mass renormalization, and the contact interactions respectively.</p>
https://thesis.library.caltech.edu/id/eprint/31Quantum Aspects of Gravity
https://resolver.caltech.edu/CaltechETD:etd-06072007-083631
Authors: Gupta, Arun Kumar
Year: 1990
DOI: 10.7907/bq7r-ps67
We study here some models of quantum gravity. In Euclidean quantum gravity, some of the possible consequences of including topology changes in the path integral are studied in the semiclassical approximation. The effects of wormhole interactions on the semiclassical sum are considered. The effects of wormholes in the Yang-Mills-Einstein system on the phase structure of these theories is discussed. Also, we perform the computation of some partition and correlation functions in conformal gauge, in a two dimensional model of quantum gravity, i.e., the sub-critical Polyakov string.https://thesis.library.caltech.edu/id/eprint/2501Flavor SU(3) predictions for charmed baryon and B-meson decays
https://resolver.caltech.edu/CaltechTHESIS:07292014-081524505
Authors: Savage, Martin J.
Year: 1990
DOI: 10.7907/xg6c-7v36
The predictions of the SU(3) flavor symmetry of the strong interactions for the
weak decay of charmed baryons and B-mesons are detailed. It is hoped that comparison
between these predictions and experiment will shed some light on the underlying
dynamics involved in these weak decays. Although only a few decay modes of the
charmed baryons and B-mesons have been studied experimentally it is hoped that the
next generation of B-factories and even Z-decays at LEP will provide enough events
to test these predictions.
https://thesis.library.caltech.edu/id/eprint/8617The Persistence of Charm in the Relentless Decay of Beauty
https://resolver.caltech.edu/CaltechETD:etd-09162005-162439
Authors: Adler, Mark
Year: 1990
DOI: 10.7907/91HF-NW14
<p>The results of calculations of semileptonic B<sup>±</sup><sub>c</sub> meson exclusive decay channels using the quark potential model are presented. These results are compared with estimations made using the spectator model. The polarization of charmonia states resulting from b → c decay are also calculated, providing a more detailed experimental check of the model.</p>https://thesis.library.caltech.edu/id/eprint/3566Aspects of heavy quark physics
https://resolver.caltech.edu/CaltechETD:etd-09142005-104947
Authors: Boyd, Charles Glenn
Year: 1991
DOI: 10.7907/BZR0-2W44
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The [...] Wisgur corrections to semileptonic decay form factors for the [...] system are enumerated, and a general theorem on the vanishing of all [...] corrections at threshold is derived. The contribution of charged higgs scalars to the neutron electric dipole moment in multi-higgs models is also examined, and found to be near present experimental limits.
https://thesis.library.caltech.edu/id/eprint/3528QCD Effects in Weak Radiative β-Meson Decays
https://resolver.caltech.edu/CaltechETD:etd-09042008-110831
Authors: Springer, Roxanne Patricia
Year: 1991
DOI: 10.7907/ewdz-7q49
The effective Hamiltonian for B-meson decays of the form B → X<sub>xγ</sub>, where X<sub>s</sub> is a strange hadron, is found in the minimal Standard Model with strong interaction effects included. Renormalization group techniques are used to scale the coefficients of the operators in the effective Hamiltonian to find the inclusive decay rate for hard photon (E<sub>γ</sub> ~ 2GeV) emission, to leading logarithmic approximation.
https://thesis.library.caltech.edu/id/eprint/3329Renormalization corrections in heavy colored scalar effective field theory
https://resolver.caltech.edu/CaltechTHESIS:01082013-134838904
Authors: Sharma, Murali
Year: 1993
DOI: 10.7907/k333-2a97
<p>Recently, QCD processes involving a heavy quark at energ1es much
smaller than its mass have been examined in an effective field theory approach. In this
'heavy quark theory', the mass of the quark is taken to infinity while its four velocity is
held fixed. The effective theory has a large set of symmetries because of the decoupling of
the flavor (when the kinematic dependence on masses is removed) and spin of the heavy
quark from its interactions with the light degrees of freedom . As a consequence, several
matrix elements of the theory are determined in terms of a single function, the Isgur-Wise
function. Being nonperturbative in character, this function is not fully calculable. However,
it has a calculable logarithmic dependence on the masses of the heavy particles, arising
from QCD effects in the full theory. </p>
<p>Some extensions of the standard model contain heavy color triplet scalars.
It is instructive therefore to consider the analogous effective field theory for scalars. In
processes where pair production does not occur, the statistics of the heavy particles are
irrelevant, and their interactions are identical with those of quarks. Thus there is a 'superflavor
symmetry' that interchanges quarks and scalars, and a flavor symmetry between
scalars. Again, these symmetries determine several matrix elements involving scalars up
to the same Isgur-Wise function. In this thesis, the logarithmic mass dependence of the
operators ϕ_2^†ϕ_1, ϕ_2^† (ὶð^µ ϕ_1), and (ὶð^µ ϕ_2) ^† ϕ_1 is calculated. The latter two operators
mix under renormalization. </p>
https://thesis.library.caltech.edu/id/eprint/7380Perturbative corrections to the ratio Γ(B → D ρ^-)/ Γ(B → D π^-).
https://resolver.caltech.edu/CaltechTHESIS:12042012-092409874
Authors: Haas, George D. A.
Year: 1993
DOI: 10.7907/dwt2-3r04
<p>QCD interactions involving a heavy quark with energy much smaller than its
mass can be understood in the context of an effective field theory in which the
heavy quark velocity is held fixed while its mass is taken to infinity. Nonleptonic
decays of hadrons containing a heavy quark further simplify when gluons
exchanged carry small momenta compared to the heavy quark mass.</p>
<p>Under these assumptions the ratio of rates for B → D ρ^- and B → D π^- is
investigated. The reliability of these assumptions is tested by calculating first
order, one loop QCD corrections, assuming reasonable momentum distributions for
the quarks inside the light mesons.</p>https://thesis.library.caltech.edu/id/eprint/7301Quantum effective field theories in heavy quark physics and phase transitions in cosmology
https://resolver.caltech.edu/CaltechTHESIS:04182012-104107815
Authors: Lee, Clarence L. Y.
Year: 1994
DOI: 10.7907/tr7n-vw39
<p>This thesis is concerned with aspects of quantum effective field theories, effective
actions, and their applications. New spin-flavor symmetries of the strong interactions,
which arise in the limit of very large quark masses, can be incorporated into a heavy
quark effective field theory (HQEFT). A general method for deriving the effective
Lagrangian of this theory to any order in 1/m_Q (where m_Q is the heavy quark mass)
is developed; it is used to calculate terms up to order 1/m^3_Q. The renormalization of
terms in the Lagrangian to order 1/m^2_Q is performed. Such operators break these new
symmetries and consequently are important corrections to the leading-order predictions.
HQEFT can be combined with chiral perturbation theory into a heavy meson
chiral perturbation theory (HMChPT) which describes the low-momentum interactions
of hadrons containing a heavy quark with pseudo-Goldstone bosons. HMChPT
is used to investigate the semi-leptonic four-body decay of B and D mesons into final
states with at least one Goldstone boson. Such processes may be utilized to test
the above heavy quark symmetries. The remainder of this dissertation deals with the
evaluation of effective actions and their implications. A method to efficiently compute
the one-loop effective action at zero and finite temperatures is elucidated. In a first
order cosmological phase transition, the decay rate and the temperature at which it
occurs depends on the free energy of a critical bubble configuration. Since this free
energy is related to the effective action but is usually approximated with an effective
potential, the calculational method developed above is used to study the validity of
of this approximation. The corrections are found to be important for quantitative
work.</p>
https://thesis.library.caltech.edu/id/eprint/6943Applications of heavy quark symmetry and long distance contributions to weak decays
https://resolver.caltech.edu/CaltechETD:etd-10152007-125922
Authors: Lu, Ming
Year: 1995
DOI: 10.7907/6DV4-ZZ66
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Heavy quark chiral perturbation theory is used to predict the form factors for [...] and [...] decays. We also look at the long distance contributions to some hyperon and kaon weak decays which are important for CP violation or extracting information of CKM matrix.
https://thesis.library.caltech.edu/id/eprint/4098Heavy hadrons in the large Nc limit
https://resolver.caltech.edu/CaltechETD:etd-09172007-144702
Authors: Chow, Chi-Keung
Year: 1995
DOI: 10.7907/7qz6-sg17
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In the heavy quark and large [...] limit, heavy baryons can be identified as bound states of heavy mesons and light baryons. The binding potential can be calculated under chiral perturbation theory, and is simple harmonic when [...]. The spectra and properties of these bound states agree reasonably well with the observed heavy baryons. In this framework, some non-perturbative quantities, like the orbital excitation energy and the slope of the Isgur-Wise form factor, can be evaluated. Moreover, the same universal Isgur-Wise form factor describes the semileptonic decays [...] and [...]. The formalism can also be used to study the spectra, stabilities and decay modes of exotic multiquark states.https://thesis.library.caltech.edu/id/eprint/3584Effective Field Theories in the Study of K_L → π^+π^-e^+e^- and Heavy Quark Fragmentation
https://resolver.caltech.edu/CaltechTHESIS:08072017-112244341
Authors: Elwood, John Kenneth
Year: 1997
DOI: 10.7907/vzrw-t659
This thesis examines several situations in which effective field theories may be
used to generate perturbative predictions for nonperturbative phenomena. The
decay mode K<sub>L</sub> → π<sup>+</sup>π<sup>-</sup>e<sup>+</sup>e<sup>-</sup> is analyzed in great detail using chiral perturbation theory, and the form factors for the decay are determined, along with the sizes of
various CP violating observables. One of these variables turns out to be quite sizeable,
approaching 20% for appropriate cuts on the lepton pair invariant mass. Fragmentation
of a c quark to the excited charmed baryon doublet Λ*<sub>c</sub> is also studied within the
framework of a chiral theory, and various decay distributions are expressed in terms
of nonperturbative fragementation parameters. A perturbative calculation of related fragmentation
parameters is also briefly discussed.https://thesis.library.caltech.edu/id/eprint/10370Aspects of Heavy Quark Physics
https://resolver.caltech.edu/CaltechTHESIS:07242017-112524631
Authors: Gremm, Martin
Year: 1998
DOI: 10.7907/yfze-b589
<p>We discuss the use of two QCD based effective field theories in determining parameters
of the standard model. Heavy Quark Effective theory provides a framework for
studying the weak decays of the B meson. We calculate the B → X<sub>c</sub>lv decay rate
to second nonvanishing order in the HQET expansion and compare the theoretical
prediction to experimental data. This allows us to determine the b and c pole quark
masses and the weak mixing angle V<sub>cb</sub>.</p>
<p>Nonrelativistic QCD is an effective field theory in which bound states of two heavy
quarks can be analyzed conveniently. We use this approach to compute the leading
relativistic corrections to the decay of S-wave quarkonia. These corrections can be
expressed in terms of the leading order result and the quark pole mass. Including
color octet contributions and the first relativistic corrections, we extract the value
of α<sub>s</sub> from low energy data. We also show that the color octet contributions to the
decay rates are not negligible.</p>https://thesis.library.caltech.edu/id/eprint/10350Applications of Chiral Symmetry
https://resolver.caltech.edu/CaltechTHESIS:08022017-141551703
Authors: Davoudiasl, Hooman
Year: 1998
DOI: 10.7907/dv4e-6748
We study some applications of the chiral symmetry of quantum chromodynamics in
treating phenomena involving hadrons at low energies, where perturbative methods
are not valid. We begin by introducing the concepts of global symmetry breaking
and the consequent generation of Goldstone bosons. It is shown how these concepts
are realized through chiral symmetry breaking and provide an understanding of some
of the features of strong interactions at low energies. This leads us to the chiral
perturbation theory effective Lagrangian for the low energy interactions of the light
pseudo-scalars. We use this effective Lagrangian, and the considerations that led to
it, as the basis of our approach in studying three different problems. First, we find
the rates for the τ lepton decays τ → Vπv<sub>τ</sub>, where V stands for ρ, K* or w, and
extract the magnitude of the ρwπ coupling, |g2<sup>(ρ)</sup>| = 0.6. Next, we use this coupling
to find the decay rate for D<sup>0</sup> → K*<sup>0</sup>π<sup>-</sup>e<sup>+</sup>V<sub>e</sub> in a certain kinematic regime. This rate depends on the DD<sup>*</sup>π coupling and our results can provide and extraction of this coupling, given data on this decay. The third problem we address is that of finding
solutions that represent the qualitative behavior of the disoriented chiral condensate
in the non-linear sigma model O(p<sup>4</sup>). We show that these solutions do not become
singular at short distances where the O(p<sup>2</sup>) solutions begin to diverge.https://thesis.library.caltech.edu/id/eprint/10361Quarkonia Production in Nonrelativistic Quantum Chromodynamics
https://resolver.caltech.edu/CaltechTHESIS:08072017-152935193
Authors: Leibovich, Adam Keith
Year: 1998
DOI: 10.7907/ezh4-nr37
Color-singlet production of quarkonia has failed to correctly predict the cross sections
of ψ's produced at the Tevatron. Gluon fragmentation has been identified the dominant
source of high energy prompt quarkonia at hadron colliders. Fragmentation
approximations break down, however, when a quarkonium's transverse momentum
becomes comparable to its mass. We review the NRQCD formalism, which is an
effective field that improves upon the color-singlet calculations. As an example of
color-singlet calculation, we calculate in closed form the complete O(α<sup>2</sup><sub>s</sub>) color-singlet
differential cross section for e<sup>+</sup>e<sup>-</sup> → γ<sup>*</sup> → ψq + X scattering. The cross section
reduces at high energies to a heavy quark fragmentation form. We find that the energy
scale at which the approximate fragmentation result becomes reliable exceeds the ψq
mass by more than an order of magnitude. We also discuss the color-singlet model's
predictions for direct J/ψ angular and energy distributions at CLEO. For production
at a pp collider, we identify a large class of color-octet diagrams that mediate quarkonia
production at all energies and reduce to the dominant set of gluon fragmentation
graphs in the high p⊥ limit. They contribute to quarkonia differential cross sections at
the same order as color-singlet diagrams and bring theoretical predictions for γ and ψ
production at the Tevatron into agreement with experimental measurements. Using
recent CDF data, we extract numerical values for bottomonia and charmonia color-octet
matrix elements which are consistent with NRQCD scaling rules. We calculated the polarization of ψ'
due to pp → QQ[<sup>2S+1</sup>L<sub>J</sub><sup>(8)</sup>]X → ψ<sup>(λ)</sup>X color-octet quarkonia
production at order α<sup>3</sup><sub>s</sub> which could be used as a test of NRQCD. We find that at
low transverse momenta the ψ' is unpolarized due to the contributions proportional
to the L = S = 0 and L = s = 1 color-octet matrix elements. As p⊥ increases,
the ψ' mesons become 100% polarized, as predicted by fragmentation calculations.
Polarization due to lowest order color-singlet production is also considered, which
qualitatively has a similar shape to the color-octet production. https://thesis.library.caltech.edu/id/eprint/10371Applications of Chiral Perturbation Theory in Reactions with Heavy Particles
https://resolver.caltech.edu/CaltechTHESIS:08082017-105330690
Authors: Stewart, Iain W.
Year: 1999
DOI: 10.7907/w8fe-ww63
Effective field theory techniques are used to describe the interaction of heavy hadrons
in a model independent way. Predictability is obtained by exploiting the symmetries
of QCD. Heavy hadron chiral perturbation theory is reviewed and used to describe
D* decays. The phenomenologically important D*Dπ coupling is extracted from data
working to first order in the chiral and heavy quark symmetry breaking parameters.
A method is described for determining |V<sub>ub</sub>| from exclusive semileptonic B and D
decays with 10% uncertainty. An effective field theory for two-nucleon systems is
then discussed. The large S-wave scattering lengths necessitate expanding around a
non-trivial fixed point. A detailed discussion of the interplay between renormalization
and the power of counting is given. In power counting pion interactions with nucleons
it is useful to consider three classes of pion: potential, radiation, and soft. A power
counting for massive radiation is developed. Finally, it is shown that the leading terms
in the effective theory for nucleon-nucleon interactions are invariant under Wigner's
SU(4) spin-isospin symmetry in the infinite scattering length limit.https://thesis.library.caltech.edu/id/eprint/10373Brane Models and the Hierarchy Problem
https://resolver.caltech.edu/CaltechTHESIS:06242010-150733171
Authors: Goldberger, Walter D.
Year: 2001
DOI: 10.7907/zmfm-yd07
It has been recently proposed that higher-dimensional field theory models in the presence of extended defects ("branes") may play a role in addressing the gauge hierarchy problem. In this thesis we consider several aspects of such field theories. First we perform the Kaluza-Klein reduction of a bulk scalar field propagating in the scenario of Randall and Sundrum, which consists of a region of five-dimensional anti-deSitter space bounded by two three-branes. We then propose a simple mechanism, based on the dynamics of a bulk scalar field, for stabilizing the modulus field (the "radion") corresponding to the size of the compact dimension in the Randall-Sundrum scenario. Some implications of this stabilization mechanism for low-energy phenomenology are described. Next, we investigate the one-loop quantum corrections to the radion effective potential. We show that for large brane separation, the quantum effects are power suppressed and therefore have a negligible effect on the bulk dynamics once a classical stabilization mechanism is in place. Finally, we study the ultraviolet divergence structure of field theory in the presence of branes and find that brane-localized divergences arise both at the classical and quantum level. We show how to interpret the classical divergences by the usual regularization and renormalization procedure of quantum field theory.https://thesis.library.caltech.edu/id/eprint/5959SU(3) Chiral Symmetry in Non-Relativistic Field Theory
https://resolver.caltech.edu/CaltechETD:etd-08172001-054126
Authors: Ouellette, Stephen Michael
Year: 2001
DOI: 10.7907/JN2B-5X12
Applications imposing SU(3) chiral symmetry on non-relativistic field theories are considered. The first example is a calculation of the self-energy shifts of the spin-3/2 decuplet baryons in nuclear matter, from the chiral effective Lagrangian coupling octet and decuplet baryon fields. Special attention is paid to the self-energy of the Delta baryon near the saturation density of nuclear matter. We find contributions to the mass shifts from contact terms in the effective Lagrangian with coefficients of unknown value. As a second application, we formulate an effective field theory with manifest SU(2) chiral symmetry for the interactions of K and eta mesons with pions at low energy. SU(3) chiral symmetry is imposed on the effective field theory by a matching calculation onto three-flavor chiral perturbation theory. The effective Lagrangian for the pi-K and pi-eta sectors is worked out to order Q^4; the effective Lagrangian for the K-K sector is worked out to order Q^2 with contact interactions to order Q^4. As an application of the method, we calculate the K-K s-wave scattering phase shift at leading order and compare with chiral perturbation theory. We conclude with a discussion of the limitations of the approach and propose new directions for work where the matching calculation may be usefulhttps://thesis.library.caltech.edu/id/eprint/3148Probing Physics and the Standard Model and Beyond with Electroweak Baryogenesis and Effective Theories of the Strong Interactions
https://resolver.caltech.edu/CaltechETD:etd-05272005-162229
Authors: Lee, Christopher
Year: 2005
DOI: 10.7907/GJPE-HN05
<p>We address in this thesis two primary questions aimed at improving our ability to calculate reliably in the Standard Model of particle physics and probing possible new particles which may exist beyond it.</p>
<p>First, we embark on an attempt to account for the abundance of matter in the present Universe if earlier in its history matter and antimatter were equally abundant. We explore whether baryogenesis at the electroweak phase transition could successfully account for the observed density of baryons in the Universe, using the closed-time-path (CTP) formalism of quantum field theory to calculate the buildup and relaxation of particle densities during the phase transition. For our model of the new particles and sources of CP violation necessary to account for the baryon asymmetry of the Universe, we adopt the Minimal Supersymmetric Extension of the Standard Model (MSSM). We look for regions of the parameter space in the MSSM that could give rise to sufficiently large baryon asymmetry without violating constraints on these parameters from existing experiments, in particular, constraints on masses of Higgs and supersymmetric particles from accelerator searches and precision electroweak tests, and on CP-violating parameters of the MSSM from searches for electric dipole moments of elementary particles.</p>
<p>Next, we explore how to get around our ignorance of the dynamics of strongly interacting particles in the nonperturbative regime of Quantum Chromodynamics (QCD) by the clever use of effective field theories. Two applications are explored: the decay of Z bosons to hadronic jets using soft-collinear effective theory (SCET) and the radiative decays of quarkonia to light hadrons using SCET and non-relativistic QCD (NRQCD). These tools facilitate the proof of factorization of decay rates into perturbatively-calculable and nonperturbative parts. Universality of the latter among different observables provides predictive power even in our ignorance of the details of the nonperturbative physics.</p>https://thesis.library.caltech.edu/id/eprint/2160Heavy Pentaquarks in the Diquark Model and the Large Nc Expansion
https://resolver.caltech.edu/CaltechETD:etd-05232005-174621
Authors: Wessling, Margaret Ellen
Year: 2005
DOI: 10.7907/6812-4G64
<p>Recent experimental evidence for the Θ⁺(1540) has given rise to much theoretical interest in exotic baryons. The Θ⁺ is a baryon that has strangeness S=+1, meaning that it contains an anti-strange quark. Thus it cannot be constructed from three quarks, unlike all other known baryons; it needs at least an extra quark-antiquark pair. It is usually modeled as a pentaquark state in the 10 bar representation of flavor SU(3), with flavor content s̅uudd.</p>
<p>This thesis considers possible heavy pentaquarks, in which the antiquark is charmed or bottom rather than strange. In the context of the diquark model of Jaffe and Wilczek, it is argued that negative-parity pentaquarks of this type may be lighter than their positive-parity counterparts, and hence are likely to be stable against strong decay. Estimates are made for their masses, and their weak decays are discussed. Isospin relations are found between the decay rates for different possible decay channels.</p>
<p>Negative-parity heavy pentaquarks are also considered in a less model-dependent way, in the context of a 1/Nc expansion, where Nc is the number of colors. Heavy quark effective theory is also employed. Mass relations are found between the mass splittings of heavy pentaquarks and those of nonexotic baryons, and SU(3)-breaking corrections to these relations are computed. The results could be helpful in interpreting experimental data if heavy pentaquarks are observed.</p>https://thesis.library.caltech.edu/id/eprint/1976Topics in Heavy Particle Effective Theories
https://resolver.caltech.edu/CaltechETD:etd-05262006-125115
Authors: Dorsten, Matthew Paul
Year: 2006
DOI: 10.7907/2SCF-KR56
<p>This thesis gives several applications of effective field theory to processes involving heavy particles. The first is a standard application of heavy quark effective theory to exclusive B decays. It involves two sum rules giving constraints on the curvature of the B→D Isgur-Wise function. This thesis calculates order alpha corrections to these constraints, increasing the accuracy of the resultant constraints on the physical form factors.</p>
<p>The second application involves matching SCETI onto SCET<sub>II</sub> at one loop. Keeping the external fermions off their mass shell does not regulate all IR divergences in both theories. The work described here gives a new prescription to regulate infrared divergences in SCET. Using this regulator, we show that soft and collinear modes in SCET<sub>II</sub> are sufficient to reproduce all the infrared divergences of SCET<sub>I</sub>. We explain the relationship between IR regulators and an additional mode proposed for SCET<sub>II</sub>.</p>
<p>Next we consider top production at large energies. The production process is characterized by three disparate energy scales: the center-of-mass energy (E), the mass (m), and the decay width (Gamma). At the scale E we match onto massive soft-collinear effective theory (SCET). The SCET current is run from E to m, thereby summing Sudakov logarithms of the form log<sup>n</sup>(m/E), where n=2,1. At the scale m, the top quark mass is integrated out by matching SCET jet functions onto a boosted version of heavy quark effective theory (bHQET). The jet functions in bHQET are then run from m to Gamma, summing powers of single logarithms of the ratio m/Gamma.</p>
<p>Under certain assumptions factorization formulas can be derived for differential distributions in processes involving highly energetic jets, such as jet energy distributions. As a final topic, we show how to test these assumptions using semileptonic or radiative decays of heavy mesons, by relating the jet P⁺ distribution derived under these assumptions to other differential distributions in these decays, which are better understood.</p>https://thesis.library.caltech.edu/id/eprint/2109Topics in Theoretical Particle Physics and Cosmology beyond the Standard Model
https://resolver.caltech.edu/CaltechETD:etd-06022006-145211
Authors: Jenkins, Alejandro
Year: 2006
DOI: 10.7907/9VSJ-XW82
<p>We review our understanding of spin-1 and spin-2 massless particles as mediators of long-range forces. We discuss how a quantum description of such particles that is compatible with Lorentz covariance leads to gauge invariance, a mathematical redundancy in the description of the physics. We discuss the Weinberg-Witten theorem, which underlines the need for gauge invariance in relativistic theories with massless mediators of higher spin.</p>
<p>This leads us to consider a class of models in which long-range interactions are mediated by the Goldstone bosons of spontaneous Lorentz violation. Since the Lorentz symmetry is realized non-linearly in the Goldstones, these models could evade the Weinberg-Witten theorem and the need for gauge invariance. In the case of gravity, the broken symmetry would protect the theory from having non-zero cosmological constant, while the compositeness of the graviton could provide a solution to the perturbative non-renormalizability of gravity.</p>
<p>Next we consider the phenomenology of spontaneous Lorentz violation and the experimental limits thereon. We find the general low-energy effective action of the Goldstones of this kind of symmetry breaking minimally coupled to gravity. We compare this effective theory to the ghost condensate that has been proposed in the literature as a model for gravity in a Higgs phase. We compute the modification to Newton's law from this mechanism and discuss observational limits on this kind of Lorentz violation from solar system tests of gravity and from gravitational Cherenkov radiation of cosmic rays.</p>
<p>We then summarize the cosmological constant problems and show that models in which a scalar field causes super-acceleration of the universe generally exhibit instabilities connected to violation of the null-energy condition. We discuss how the equation of state evolves in a universe where the dark energy is caused by a ghost condensate. We comment on the anthropic argument for a small cosmological constant and how it is weakened if the inflaton self-coupling varies over the landscape of possible universes.</p>
<p>Finally, we discuss the reverse sprinkler, a problem in elementary fluid mechanics that had eluded a definitive treatment for decades.</p>https://thesis.library.caltech.edu/id/eprint/2403Constraints on Physics Beyond the Standard Model and its Observable Effects
https://resolver.caltech.edu/CaltechETD:etd-05282007-034337
Authors: Kile, Jennifer E.
Year: 2007
DOI: 10.7907/KSBC-RD46
<p>In this work, we describe three analyses, all of which involve physics beyond the Standard Model. The first two discussed here are closely related; they use effective operator analyses to constrain the contributions of physics beyond the SM to observable processes. The third project involves the investigations of a particular extra-dimensions model which addresses the cosmological constant problem.</p>
<p>The first project which we will discuss uses the scale of neutrino mass to place model-independent constraints on the coefficients of the chirality-changing terms in the muon decay Lagrangian. We list all of the dimension-six effective operators which contribute to muon decay and Dirac mass for the neutrino. We then calculate the one-loop contributions that each of these operators makes to neutrino mass. Taking a generic element of the neutrino mass matrix to be of order ~ 1 eV, we derive limits on the contributions of these operators to the muon Michel parameters which are approximately four orders of magnitude more stringent than the current experimental results, and well below near-future experimental sensitivity. We also find two chirality-changing operators, which, due to their flavor structure, are unconstrained by neutrino mass yet contribute to muon decay. However, as these two operators differ from those constrained by neutrino mass only by their flavor indices, we naively expect their contributions to also be small; if their effects instead turn out to be observable, this may be an indication of beyond-the-Standard-Model physics with an interesting flavor structure.</p>
<p>In the second analysis, we again perform an effective operator analysis, this time applied to Higgs production at a linear collider. Here we include all dimension-six operators containing fermions which contribute to Higgs production. We again include operators that contain right-handed Dirac neutrinos. We obtain limits on these operators from electroweak precision observables, the scale of neutrino mass, and limits on neutrino magnetic moments, and use these limits to constrain the contributions of these operators to the Higgs production cross-section. Although we find that all operators containing right-handed neutrinos contribute negligibly to Higgs production, we do find three operators containing only SM fields which could have observable contributions at an e⁺e⁻ linear collider.</p>
<p>Lastly, we discuss the characteristics of a particular extra-dimensions model originally proposed by Carroll and Guica [54]. This model has two extra dimensions compactified into a sphere, a bulk magnetic field, and a bulk cosmological constant. In this model, the cosmological constant seen by a four-dimensional observer can be set to zero by fine-tuning the bulk magnetic field against the bulk cosmological constant. If branes with a tension are added at each of the poles of the two-sphere, solutions with zero four-dimensional cosmological constant are still possible, but the compactified dimensions must acquire a deficit angle which depends on the brane tension. However, the brane tension does not affect the fine-tuning relationship between the bulk cosmological constant and the bulk magnetic field. This feature led to the hope that, after this fine-tuning, the model might self-tune, keeping the four-dimensional cosmological constant zero regardless of what happens to the brane tension by adjusting the deficit angle. We speculated that this self-tuning property would imply a massless scalar mode in the perturbed Einstein's equations; as there exist very stringent limits on scalar-tensor theories of gravity, a massless scalar mode would make this model incompatible with observation. We conducted a search for such modes, and found none which satisfied the boundary conditions. This finding led us to speculate that this model does not, in fact, have a self-tuning property.</p>https://thesis.library.caltech.edu/id/eprint/2201Unusual Signs in Quantum Field Theory
https://resolver.caltech.edu/CaltechETD:etd-05242007-141715
Authors: O'Connell, Dónal
Year: 2007
DOI: 10.7907/FEFB-JZ53
Quantum field theory is by now a mature field. Nevertheless, certain physical phenomena remain difficult to understand. This occurs in some cases because well-established quantum field theories are strongly coupled and therefore difficult to solve; in other cases, our current understanding of quantum field theory seems to be inadequate. In this thesis, we will discuss various modifications of quantum field theory which can help to alleviate certain of these problems, either in their own right or as a component of a greater computational scheme. The modified theories we will consider all include unusual signs in some aspect of the theory. We will also discuss limitations on what we might expect to see in experiments, imposed by sign constraints in the customary formulation of quantum field theory.https://thesis.library.caltech.edu/id/eprint/2022Topics in Theoretical Particle Physics and Cosmology
https://resolver.caltech.edu/CaltechETD:etd-05222007-105100
Authors: Salem, Michael Phillip
Year: 2007
DOI: 10.7907/BQ6Q-DA17
<p>We first delve into particle phenomenology with a study of soft-collinear effective theory (SCET), an effective theory for Quantum Chromodynamics for when all particles are approximately on their light-cones. In particular, we study the matching of SCET(I) involving ultrasoft and collinear particles onto SCET(II) involving soft and collinear particles. We show that the modes in SCET(II) are sufficient to reproduce all of the infrared divergences of SCET(I), a result that was previously in contention.</p>
<p>Next we move into early universe cosmology and study alternative mechanisms for generating primordial density perturbations. We study the inhomogeneous reheating mechanism and extend it to describe the scenario where the freeze-out process for a heavy particle is modulated by sub-dominant fields that received fluctuations during inflation. This scenario results in perturbations that are comparable to those generated by the original inhomogeneous reheating scenarios. In addition, we study yet another alternative to single field inflation whereby the curvature perturbation is generated by interactions at the end of inflation, as opposed to when inflaton modes exit the horizon. We clarify the circumstances under which this process can dominate over the standard one and we show that it may result in a spectrum with an observable level of non-Gaussianities.</p>
<p>We then turn to studies of the landscape paradigm, which hypothesizes that the observed universe is just one among a multitude of possibilities that are realized in separate causal regions. Such a landscape has been used to explain the smallness of the cosmological constant, at least when only it scans across the landscape. We study the scenario where both the cosmological constant and the strength of gravity, parameterized by the effective Planck mass, scan across the landscape. We find that selection effects acting on the cosmological constant are significantly weaker in this scenario and we find the measured value of the Planck mass to be exponentially unlikely under certain plausible assumptions about the landscape. Finally, we study some other models of the landscape as part of a possible explanation for quark-sector flavor parameters in the Standard Model. In this picture quark Yukawa couplings result from overlap integrals involving quark and Higgs wavefunctions in compactified extra dimensions, and the values we measure result from random selection from a landscape of possibilities. We find that many of the salient features of the measured flavor parameters are typical of the landscape distribution.</p>https://thesis.library.caltech.edu/id/eprint/1953Neutrina Mass Implications for Physics Beyond the Standard Model
https://resolver.caltech.edu/CaltechETD:etd-05312007-144931
Authors: Wang, Peng
Year: 2007
DOI: 10.7907/4AGY-DF85
We begin by working out an effective field theory valid below some new physics scale for Dirac neutrinos and Majorana neutrinos, respectively. For Dirac neutrinos, we obtain a complete basis of effective dimension four and dimension six operators that are invariant under the gauge symmetry of the Standard Model. As for Majorana neutrinos, we come up with a complete basis of effective dimension five and dimension seven operators that are invariant under the gauge symmetry of the Standard Model. Using the effective theory, we derive model-independent, "naturalness" upper bounds on the magnetic moments of Dirac neutrinos and Majorana neutrinos generated by physics above the scale of electroweak symmetry breaking. In the absence of fine-tuning of effective operator coefficients, for Dirac neutrinos, we find that current information on neutrino mass implies that the bound on neutrino magnetic moments is several orders of magnitude stronger than those obtained from analyses of solar and reactor neutrino data and astrophysical observations. As for Majorana neutrinos, the magnetic moment contribution to the mass is Yukawa suppressed. The bounds we derive for magnetic moments of Majorana neutrinos are weaker than present experimental limits if neutrino magnetic moments are generated by new physics at around 1 TeV, and surpass current experimental sensitivity only for new physics scales >10-100 TeV. The discovery of a neutrino magnetic moment near present limits would thus signify that neutrinos are Majorana particles. Then, we use the scale of neutrino mass to derive model-independent naturalness constraints on possible contributions to muon decay Michel parameters. We show that -- in the absence of fine-tuning -- the most stringent bounds on chirality-changing operators relevant to muon decay arise from one-loop contributions to neutrino mass. The bounds we obtain on their contributions to the Michel parameters are four or more orders of magnitude stronger than bounds previously obtained in the literature. We also show that, if neutrinos are Dirac fermions, there exist chirality-changing operators that contribute to muon decay but whose flavor structure allows them to evade neutrino mass naturalness bounds. We discuss the implications of our analysis for the interpretation of muon decay experiments. Finally, we use the upper limit on the neutrino mass to derive model-independent naturalness constraints on some non-Standard-Model interactions of beta decays. In the absence of fine-tuning of effective operator coefficients, our results yield constraints on scalar and tensor weak interactions one or more orders of magnitude stronger than a recent global fit after combined with the current experimental limits. We also show that, if neutrinos are Majorana fermions, there exist four-fermion operators that contribute to beta decay but whose flavor structure allows them to evade neutrino mass naturalness bounds. Constraints on the beta decay parameters by CKM Unitarity, ratio of positive pion decays, and pion beta decays are discussed as well.https://thesis.library.caltech.edu/id/eprint/2342Supersymmetry: From Baryogenesis at the Electroweak Phase Transition to Low-Energy Precision Experiments
https://resolver.caltech.edu/CaltechETD:etd-06102009-114711
Authors: Tulin, Sean Michael
Year: 2009
DOI: 10.7907/HYKE-VY04
<p>Electroweak-scale supersymmetry is one of the most popular extensions of the Standard Model and has many important implications for nuclear physics, particle physics, and cosmology. First, supersymmetric electroweak baryogenesis may explain the origin of the matter-antimatter asymmetry in the universe. In this scenario, electroweak symmetry is broken in the early universe by a first-order phase transition, when bubbles of broken phase nucleate and expand, eventually consuming the unbroken phase. Charge density is generated within the expanding bubble wall and diffuses into the unbroken phase. Through inelastic collisions in the plasma, this charge is partially converted into left-handed quark and lepton charge, which in turn leads to the production of baryon number through weak sphaleron transitions.
In this work, we study these charge transport dynamics, from its generation within the bubble wall, to the final baryon asymmetry.</p>
<p>We evaluate which collisions are important for baryogenesis, and what is their impact upon the final baryon asymmetry. Our main result is that bottom and tau Yukawa interactions, previously neglected, can play a crucial role, affecting the magnitude and sign of baryon asymmetry. We investigate how this works in detail in the Minimal Supersymmetric Standard Model (MSSM); we suggest that these interactions may be even more important in gauge-singlet extensions of the MSSM. Second, low-energy precision measurements of weak decays may provide interesting signals of supersymmetry. We study in detail the supersymmetric radiative corrections to (i) leptonic pion decay branching ratios, and (ii) muon and beta decay coefficients. A deviation from the Standard Model predictions would imply strong departures from the minimal, commonly-assumed, theoretical assumptions about supersymmetry breaking.</p> https://thesis.library.caltech.edu/id/eprint/5268Lorentz Symmetry Breaking in a Cosmological Context
https://resolver.caltech.edu/CaltechTHESIS:05252010-135506831
Authors: Gresham, Moira I.
Year: 2010
DOI: 10.7907/9G69-3Z95
This thesis is comprised primarily of work from three independent papers, written in collaboration with Sean Carroll, Tim Dulaney, and Heywood Tam. The original motivation for the projects undertaken came from revisiting the standard assumption of spatial isotropy during inflation. Each project relates to the spontaneous breaking of Lorentz symmetry---in early Universe cosmology or in the context of effective field theory, in general. Chapter 1 is an introductory chapter that provides context for the thesis. Chapter 2 is an investigation of the stability of theories in which Lorentz invariance is spontaneously broken by fixed-norm vector "aether" fields. It is shown that models with generic kinetic terms are plagued either by ghosts or by tachyons, and are therefore physically unacceptable. Chapter 3 is an investigation of the phenomenological properties of the one low-energy effective theory of spontaneous Lorentz symmetry breaking found in the previous chapter to have a globally bounded Hamiltonian and a perturbatively stable vacuum---the theory in which the Lagrangian takes the form of a sigma model. In chapter 4 cosmological perturbations in a dynamical theory of inflation in which an Abelian gauge field couples directly to the inflaton are examined. The dominant effects of a small, persistent anisotropy on the primordial gravitational wave and curvature perturbation power spectra are found using the "in-in" formalism of perturbation theory. It is found that the primordial power spectra of cosmological perturbations gain significant direction dependence and that the fractional direction dependence of the tensor power spectrum is suppressed in comparison to that of the scalar power spectrum. https://thesis.library.caltech.edu/id/eprint/5837Complex Phenomena in Social and Financial Systems: From Bird Population Growth to the Dynamics of the Mutual Fund Industry
https://resolver.caltech.edu/CaltechTHESIS:08112010-110422842
Authors: Schwarzkopf, Yonathan
Year: 2011
DOI: 10.7907/6Y9G-WM75
<p>This work explores different aspects of the statics and dynamics of the mutual fund industry. In addition, we answer a major question in the field of complex systems; the anomalous growth fluctuations observed for systems as diverse as breeding birds, city population and GDP.</p>
<p>We study how much control is concentrated in the hands of the largest mutual funds by studying the size distribution empirically. We show that it indicates less concentration than, for example, personal income. We argue that the dominant economic factor that determines the size distribution is market efficiency and we show that the mutual fund industry can be described using a random entry, exit and growth process.</p>
<p>Mutual funds face diminishing returns to scale as a result of convex trading costs yet there is no persistence nor a size dependence in their performance. To solve this puzzle we offer a new framework in which skillful profit maximizing fund managers compensate for decreasing performance by lowering their fees. We show that mutual fund behavior depends on size such that bigger funds charge lower fees and trade less frequently in more stocks. We present a reduced form model that is able to describe quantitatively this behavior.</p>
<p>We conclude with an investigation of the growth of mutual funds due to investor funds flows. We show that funds exhibit the same unusual growth fluctuations that have been observed for phenomena as diverse as breeding bird populations, the size of U.S. firms, the GDP of individual countries and the scientific output of universities. To explain this we propose a remarkably simple additive replication model. To illustrate how this can emerge from a collective microscopic dynamics we propose a model based on stochastic influence dynamics over a scale-free contact network.</p>
https://thesis.library.caltech.edu/id/eprint/5988Beyond the Standard Cosmology: Anisotropic Inflation and Baryophilic Dark Matter
https://resolver.caltech.edu/CaltechTHESIS:05122011-161711413
Authors: Dulaney, Timothy Ryan
Year: 2011
DOI: 10.7907/ZSV6-RF08
<p>This thesis discusses two topics in cosmology that resulted in two independent publications. The first topic concerns persistent anisotropy during inflation and the second topic concerns a model of baryophillic dark matter.</p>
<p>The motivation for the project contained within chapter one came from indications in the cosmic microwave background data that seemed to suggest that there may be a cosmologically preferred direction. Moira Gresham and I derived quantitative predictions about the signals one would observe in Cosmic Microwave Background data if isotropy is not assumed during inflation. We considered a particular example of a dynamical theory of anisotropic inflation that is characterized by a scalar field which is nonminimally coupled to an isotropy breaking abelian gauge field, thereby slowing the decay of the gauge field energy density.</p>
<p>The motivation for the project contained within chapter two came from the observation that the global symmetries B (baryon number) and L (lepton number) of the standard model Lagrangian must be broken by higher-dimensional operators at a very high scale. Pavel F. Perez, Mark B. Wise and I analyzed a model that explained the protection of these accidental global symmetries by promoting B and L to gauge symmetries. This model has a natural dark matter, candidate and we discuss the experimental constraints on the parameters in the theory.</p>
<p>Unexpected results are found in each chapter. For example, in chapter two, we find that the anisotropic contribution to the tensor power spectrum is suppressed with respect to that of the scalar power spectrum and, in chapter three, we show that a baryon asymmetry can be generated even within a model that has baryon number as a gauge symmetry.</p> https://thesis.library.caltech.edu/id/eprint/6390Charged Pion Contribution to the Anomalous Magnetic Moment of the Muon
https://resolver.caltech.edu/CaltechTHESIS:05212013-160540441
Authors: Engel, Kevin Thomas
Year: 2013
DOI: 10.7907/M463-8Z93
The model dependence inherent in hadronic calculations is one of the dominant sources of uncertainty in the theoretical prediction of the anomalous magnetic moment of the muon. In this thesis, we focus on the charged pion contribution and turn a critical eye on the models employed in the few previous calculations of $a_\mu^{\pi^+\pi^-}$. Chiral perturbation theory provides a check on these models at low energies, and we therefore calculate the charged pion contribution to light-by-light (LBL) scattering to $\mathcal{O}(p^6)$. We show that the dominant corrections to the leading order (LO) result come from two low energy constants which show up in the form factors for the $\gamma\pi\pi$ and $\gamma\gamma\pi\pi$ vertices. Comparison with the existing models reveal a potentially significant omission - none include the pion polarizability corrections associated with the $\gamma\gamma\pi\pi$ vertex. We next consider alternative models where the pion polarizability is produced through exchange of the $a_1$ axial vector meson. These have poor UV behavior, however, making them unsuited for the $a_\mu^{\pi^+\pi^-}$ calculation. We turn to a simpler form factor modeling approach, generating two distinct models which reproduce the pion polarizability corrections at low energies, have the correct QCD scaling at high energies, and generate finite contributions to $a_\mu^{\pi^+\pi^-}$. With these two models, we calculate the charged pion contribution to the anomalous magnetic moment of the muon, finding values larger than those previously reported: $a_\mu^\mathrm{I} = -1.779(4)\times10^{-10}\,,\,a_\mu^\mathrm{II} = -4.892(3)\times10^{-10}$.https://thesis.library.caltech.edu/id/eprint/7732Baryon and Lepton Numbers in Particle Physics beyond the Standard Model
https://resolver.caltech.edu/CaltechTHESIS:05022014-140735377
Authors: Arnold, Jonathan Mark
Year: 2014
DOI: 10.7907/74JV-BN09
<p>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.</p>
<p>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.</p>
<p>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.</p>https://thesis.library.caltech.edu/id/eprint/8211Baryon Number Violation beyond the Standard Model
https://resolver.caltech.edu/CaltechTHESIS:04082014-225653991
Authors: Fornal, Bartosz
Year: 2014
DOI: 10.7907/R0MY-VR06
This thesis describes simple extensions of the standard model with new sources of baryon number violation but no proton decay. The motivation for constructing such theories comes from the shortcomings of the standard model to explain the generation of baryon asymmetry in the universe, and from the absence of experimental evidence for proton decay. However, lack of any direct evidence for baryon number violation in general puts strong bounds on the naturalness of some of those models and favors theories with suppressed baryon number violation below the TeV scale. The initial part of the thesis concentrates on investigating models containing new scalars responsible for baryon number breaking. A model with new color sextet scalars is analyzed in more detail. Apart from generating cosmological baryon number, it gives nontrivial predictions for the neutron-antineutron oscillations, the electric dipole moment of the neutron, and neutral meson mixing. The second model discussed in the thesis contains a new scalar leptoquark. Although this model predicts mainly lepton flavor violation and a nonzero electric dipole moment of the electron, it includes, in its original form, baryon number violating nonrenormalizable dimension-five operators triggering proton decay. Imposing an appropriate discrete symmetry forbids such operators. Finally, a supersymmetric model with gauged baryon and lepton numbers is proposed. It provides a natural explanation for proton stability and predicts lepton number violating processes below the supersymmetry breaking scale, which can be tested at the Large Hadron Collider. The dark matter candidate in this model carries baryon number and can be searched for in direct detection experiments as well. The thesis is completed by constructing and briefly discussing a minimal extension of the standard model with gauged baryon, lepton, and flavor symmetries.https://thesis.library.caltech.edu/id/eprint/8184Scattering in N=4 Super Yang Mills and N=8 Supergravity
https://resolver.caltech.edu/CaltechTHESIS:05222017-201555383
Authors: Herrmann, Enrico
Year: 2017
DOI: 10.7907/Z94J0C49
<p>The scattering amplitudes of planar N = 4 super-Yang-Mills theory (sYM) exhibit a number of remarkable analytic structures, including dual conformal symmetry, logarithmic singularities of integrands, and the absence of poles at infinite loop momentum. None of these properties are apparent from our usual formulation of quantum field theory in terms of Lagrangians and Feynman rules. In the past years, the hidden features inspired a dual formulation for scattering amplitudes that is not built on the two pillars of locality and unitarity. Instead, a new geometric formulation in terms of Grassmannians and the amplituhedron emerged, which is based on the key analytic properties of scattering amplitudes in the planar sector of $\N=4$ super-Yang-Mills theory. Starting from geometric concepts, the amplituhedron geometry derives all properties of scattering amplitudes in said theory, including locality and factorization. From a practical perspective, expanding the amplitude in terms of a local diagrams, the amplituhedron construction implies that scattering amplitudes in planar N=4 super-Yang-Mills are fully specified by a surprisingly simple subset of all unitarity cuts. Concretely, integrands are uniquely (up to an overall constant) fixed by demanding their vanishing on all spurious singularities.</p>
<p>Extending an initial proposal by Arkani-Hamed, Bourjaily, Cachazo, and Trnka, we conjecture that the same analytic structures extend beyond the planar limit of N=4 super-Yang-Mills. Furthermore we show that the $\dlog$ and \emph{no pole at infinity} constraints give the key integrand level analytic information contained in dual conformal symmetry in the planar sector. While it is presently unclear how to extend either dual conformal symmetry or the amplituhedron picture beyond the planar sector, our results suggest that related concepts might exist and await discovery.</p>
<p>In order to support our conjectures, we have analyzed several nontrivial multi-loop multi-leg amplitudes. For the nonplanar three-loop four-point and two-loop five point $\N = 4$ super-Yang-Mills amplitudes, we explicitly construct a complete basis of diagram integrands that has only logarithmic singularities and no poles at infinity. We also give examples at three loops showing how to make the logarithmic singularity properties manifest by writing explicit dlog forms. We give additional evidence at four and five loops supporting the nonplanar logarithmic singularity conjecture. Our investigations show that the singularity structures of planar and nonplanar integrands in N = 4 super-Yang-Mills are strikingly similar. Finally, we express the complete amplitude in terms of our special basis diagrams, with the coefficients determined by the vanishing conditions on the amplitude. By successfully carrying out this procedure, we provide nontrivial evidence that the “zero conditions” also carry over into the nonplanar sector. Our analysis suggests that the concept of the amplituhedron can be extended to the nonplanar sector of N = 4 super-Yang-Mills theory and one might hope to ultimately reformulate more general quantum field theories in a geometric language.</p>
<p>Using the marvelous squaring relation between Yang-Mills and gravity theories discovered by Bern, Carrasco, and Johansson (BCJ), we relate our newly gained knowledge on the Yang-Mills side to properties of gravity. We conjecture that to all loop orders, while N = 8 supergravity has poles at infinity, at least at four points it has only logarithmic singularities at finite locations. We provide nontrivial evidence for these conjectures. We describe the singularity structure of N = 8 supergravity at three loops and beyond.</p>
<p>In order to approach a geometric formulation for scattering in gravitational theories, we retrace the initial steps taken in planar N=4 super-Yang-Mills in the gravitational setting. In particular, we study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only dlog-factors, in gravity we find a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for $\N=8$ supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present.</p>https://thesis.library.caltech.edu/id/eprint/10193The Union of Quantum Field Theory and Non-Equilibrium Thermodynamics
https://resolver.caltech.edu/CaltechTHESIS:05312018-124004005
Authors: Bartolotta, Anthony Leo
Year: 2018
DOI: 10.7907/F7VT-7X41
<p>Quantum field theory is the language used to describe nature at its most fundamental scales; while thermodynamics is a framework to describe the collective behavior of macroscopic systems. Recent advances in non-equilibrium thermodynamics have enabled this framework to be applied to smaller systems operating out of thermal equilibrium. This thesis is concerned with both quantum field theory and non-equilibrium thermodynamics independently and with their intersection.</p>
<p>First, a purely phenomenological application of quantum field theory is explored in the context of the upcoming Mu2E experiment. This experiment will look for rare decays which would indicate the presence of physics beyond the Standard Model. Using the language of effective field theories, a next-to-leading order analysis of the conversion rate is performed.</p>
<p>The focus then shifts to an apparent paradox in the Bayesian interpretation of statistical mechanics. For a Bayesian observer making measurements of an open system, the Shannon entropy decreases, in apparent violation of the Second Law of Thermodynamics. It is shown that rather than utilizing the entropy, which can decrease under Bayesian updates, the Second Law for a Bayesian observer can be rephrased in terms
of a cross-entropy which is always non-negative.</p>
<p>Finally, the intersection of quantum field theory and non-equilibrium thermodynamics is examined. Using quantum work fluctuation theorems, an investigation of how these frameworks can be applied to a driven quantum field theory is performed. For a time-dependent variant of λφ<sup>4</sup> , analytic expressions for the work distribution functions at one-loop order are derived. These expressions are shown to satisfy the quantum Jarzynski equality and Crooks fluctuation theorem.</p>https://thesis.library.caltech.edu/id/eprint/10981Aspects of Quasi-Single Field Inflation
https://resolver.caltech.edu/CaltechTHESIS:05282019-112333132
Authors: McAneny, Michael Trevor
Year: 2019
DOI: 10.7907/4RBP-Q623
<p>A simple extension of single-field slow roll inflation is called quasi-single field inflation (QSFI). In quasi-single field inflation, the inflaton is coupled to one or more scalar fields with masses of order Hubble constant during inflation, <i>H</i>, called isocurvatons. Depending on the interactions between the inflaton and the isocurvatons, the observable consequences of such a theory can vary dramatically. This thesis is primarily concerned with analyzing how these interactions affect cosmological observables.</p>
<p>We begin by discussing QSFI with one isocurvaton. In particular, we study the non-perturbative limit of a kinetic interaction coupling the inflaton to the isocurvaton. In this non-perturbative limit, the kinetic interaction results in isocurvaton mode functions that oscillate yet decay quickly after horizon crossing. This oscillatory, decaying behavior is reflected in the primordial non-Gaussianity and other observables.</p>
<p>Then, we study the perturbative limit of the aforementioned kinetic interaction. Instead of quickly decaying, oscillating mode functions as in the non-perturbative limit, the mode functions in the perturbative limit decay slowly and do not oscillate. Due to this slow decay, the primordial bispectrum is enhanced in the squeezed limit. This enhanced squeezed limit can result in large contributions to galactic halo correlations at long wavelengths. We explore these long wavelength enhancements to galactic halo correlations in detail.</p>
<p>We then discuss how quantum loops of isocurvatons in QSFI can significantly contribute to galactic halo correlations at long wavelengths. In fact, we show that loops can give the most important contributions at long wavelengths in certain models.</p>
<p>Finally, we consider theories with multiple isocurvatons. Such theories may consist of interactions coupling the isocurvatons to eachother. These interactions can result in slowly decaying yet oscillating late-time behavior for the isocurvaton mode functions. This combines the two characteristic features from the non-perturbative (oscillating) and perturbative (slowly-decaying) single isocurvaton QSFI models discussed above. These features could result in an oscillatory bispectrum that is enhanced in the squeezed limit. Oscillations in the galactic halo power spectrum at long wavelengths may then be indicative of such multi-isocurvaton models.</p>https://thesis.library.caltech.edu/id/eprint/11552Imprints of Massive Scalars on Primordial Non-Gaussianities
https://resolver.caltech.edu/CaltechTHESIS:06112019-185424559
Authors: Ridgway, Alexander Karas
Year: 2019
DOI: 10.7907/0FD0-GY68
<p>In this thesis, we modify the standard single-field inflation scenario by adding additional massive scalars to the inflationary field content. Due to the breaking of time translational invariance by the inflaton background, the inflaton can interact with these extra scalars through a kinetic mixing term. If these scalars have self- interactions, then their kinetic mixings with the inflaton induce potentially large primordial non-gaussianities in the scalar curvature fluctuations, which could be observed in the cosmic microwave background (CMB) and large-scale structure (LSS). We derive expressions for these non-Gaussianities in the limits the scalar masses are much larger than or much smaller than the Hubble constant during inflation and compute their contributions to dark matter halo correlation functions.</p>https://thesis.library.caltech.edu/id/eprint/11738