Technicolor

In technicolor theories the scalar sector of the Standard Model is replaced by a strongly interacting sector. Although the Standard Model has been exceptionally successful, the scalar sector causes theoretical problems that make these theories seem an attractive alternative. I begin my thesis by considering QCD, which is the known example of strong interactions. The theory exhibits two phenomena: confinement and chiral symmetry breaking. I find the low-energy dynamics to be similar to that of the sigma models. Then I analyze the problems of the Standard Model Higgs sector, mainly the unnaturalness and triviality. Motivated by the example of QCD, I introduce the minimal technicolor model to resolve these problems. I demonstrate the minimal model to be free of anomalies and then deduce the main elements of its low-energy particle spectrum. I find the particle spectrum contains massless or very light technipions, and also technibaryons and techni-vector mesons with a high mass of over 1 TeV. Standard Model fermions remain strictly massless at this stage. Thus I introduce the technicolor companion theory of flavor, called extended technicolor. I show that the Standard Model fermions and technihadrons receive masses, but that they remain too light. I also discuss flavor-changing neutral currents and precision electroweak measurements. I then show that walking technicolor models partly solve these problems. In these models, contrary to QCD, the coupling evolves slowly over a large energy scale. This behavior adds to the masses so that even the light technihadrons are too heavy to be detected at current particle accelerators. Also all observed masses of the Standard Model particles can be generated, except for the bottom and top quarks. Thus it is shown in this thesis that, excluding the masses of third generation quarks, theories based on walking technicolor can in principle produce the observed particle spectrum.

Neutrinos and Thermal Leptogenesis

One of the unanswered questions of modern cosmology is the issue of baryogenesis. Why does the universe contain a huge amount of baryons but no antibaryons? What kind of a mechanism can produce this kind of an asymmetry? One theory to explain this problem is leptogenesis. In the theory right-handed neutrinos with heavy Majorana masses are added to the standard model. This addition introduces explicit lepton number violation to the theory. Instead of producing the baryon asymmetry directly, these heavy neutrinos decay in the early universe. If these decays are CP-violating, then they produce lepton number. This lepton number is then partially converted to baryon number by the electroweak sphaleron process. In this work we start by reviewing the current observational data on the amount of baryons in the universe. We also introduce Sakharov's conditions, which are the necessary criteria for any theory of baryogenesis. We review the current data on neutrino oscillation, and explain why this requires the existence of neutrino mass. We introduce the different kinds of mass terms which can be added for neutrinos, and explain how the see-saw mechanism naturally explains the observed mass scales for neutrinos motivating the addition of the Majorana mass term. After introducing leptogenesis qualitatively, we derive the Boltzmann equations governing leptogenesis, and give analytical approximations for them. Finally we review the numerical solutions for these equations, demonstrating the capability of leptogenesis to explain the observed baryon asymmetry. In the appendix simple Feynman rules are given for theories with interactions between both Dirac- and Majorana-fermions and these are applied at the tree level to calculate the parameters relevant for the theory.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Benchmark scenarios for the NMSSM

We discuss constrained and semi--constrained versions of the next--to--minimal supersymmetric extension of the Standard Model (NMSSM) in which a singlet Higgs superfield is added to the two doublet superfields that are present in the minimal extension (MSSM). This leads to a richer Higgs and neutralino spectrum and allows for many interesting phenomena that are not present in the MSSM. In particular, light Higgs particles are still allowed by current constraints and could appear as decay products of the heavier Higgs states, rendering their search rather difficult at the LHC. We propose benchmark scenarios which address the new phenomenological features, consistent with present constraints from colliders and with the dark matter relic density, and with (semi--)universal soft terms at the GUT scale. We present the corresponding spectra for the Higgs particles, their couplings to gauge bosons and fermions and their most important decay branching ratios. A brief survey of the search strategies for these states at the LHC is given.

Charge transport in a Tomonaga-Luttinger liquid: Effects of pumping and bias

We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, pointlike impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the dc and ac components of the current have power-law dependences on the bias and pumping frequencies with an exponent 2K-1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current grows large for special values of the bias. For noninteracting electrons with K=1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.

Low energy properties of the SU(m|n) supersymmetric Haldane–Shastry spin chain

The ground state and low energy excitations of the SU(m|n) supersymmetric Haldane–Shastry spin chain are analyzed. In the thermodynamic limit, it is found that the ground state degeneracy is finite only for the SU(m|0) and SU(m|1) spin chains, while the dispersion relation for the low energy and low momentum excitations is linear for all values of m and n. We show that the low energy excitations of the SU(m|1) spin chain are described by a conformal field theory of m non-interacting Dirac fermions which have only positive energies; the central charge of this theory is m/2. Finally, for ngreater-or-equal, slanted1, the partition functions of the SU(m|n) Haldane–Shastry spin chain and the SU(m|n) Polychronakos spin chain are shown to be related in a simple way in the thermodynamic limit at low temperatures.

Graphene-like two-dimensional ionic boron with double dirac cones at ambient condition

Recently, partially ionic boron (γ-B28) has been predicted and observed in pure boron, in bulk phase and controlled by pressure [Nature, 457 (2009) 863]. By using ab initio evolutionary structure search, we report the prediction of ionic boron at a reduced dimension and ambient pressure, namely, the two-dimensional (2D) ionic boron. This 2D boron structure consists of graphene-like plane and B2 atom pairs, with the P6/mmm space group and 6 atoms in the unit cell, and has lower energy than the previously reported α-sheet structure and its analogues. Its dynamical and thermal stability are confirmed by the phonon-spectrum and ab initio molecular dynamics simulation. In addition, this phase exhibits double Dirac cones with massless Dirac fermions due to the significant charge transfer between the graphene-like plane and B2 pair that enhances the energetic stability of the P6/mmm boron. A Fermi velocity (vf) as high as 2.3 x 106 m/s, which is even higher than that of graphene (0.82 x 106 m/s), is predicted for the P6/mmm boron. The present work is the first report of the 2D ionic boron at atmospheric pressure. The unique electronic structure renders the 2D ionic boron a promising 2D material for applications in nanoelectronics.

Combined Tevatron upper limit on gg->H->W+W- and constraints on the Higgs boson mass in fourth-generation fermion models

We combine results from searches by the CDF and D0 collaborations for a standard model Higgs boson (H) in the process gg->H->W+W- in p=pbar collisions at the Fermilab Tevatron Collider at sqrt{s}=1.96 TeV. With 4.8 fb-1 of integrated luminosity analyzed at CDF and 5.4 fb-1 at D0, the 95% Confidence Level upper limit on \sigma(gg->H) x B(H->W+W-) is 1.75 pb at m_H=120 GeV, 0.38 pb at m_H=165 GeV, and 0.83 pb at m_H=200 GeV. Assuming the presence of a fourth sequential generation of fermions with large masses, we exclude at the 95% Confidence Level a standard-model-like Higgs boson with a mass between 131 and 204 GeV.

Search for New Bottomlike Quark Pair Decays QQ̅ →(tW∓)(t̅ W±) in Same-Charge Dilepton Events

We report the most restrictive direct limits on masses of fourth-generation down-type quarks b′, and quarklike composite fermions (B or T5/3), decaying promptly to tW∓. We search for a significant excess of events with two same-charge leptons (e, μ), several hadronic jets, and missing transverse energy. An analysis of data from pp̅ collisions with an integrated luminosity of 2.7  fb-1 collected with the CDF II detector at Fermilab yields no evidence for such a signal, setting mass limits mb′, mB>338  GeV/c2 and mT5/3>365  GeV/c2 at 95% confidence level.

Search for New Bottomlike Quark Pair Decays QQ̅ →(tW∓)(t̅ W±) in Same-Charge Dilepton Events

We report the most restrictive direct limits on masses of fourth-generation down-type quarks $b^{\prime}$, and quark-like composite fermions ($B$ or $T_{5/3}$), decaying promptly to $t W^{\mp}$. We search for a significant excess of events with two same-charge leptons ($e$, $\mu$), several hadronic jets, and missing transverse energy. An analysis of data from $p\overline{p}$ collisions with an integrated luminosity of 2.7 fb$^{-1}$ collected with the CDF II detector at Fermilab yields no evidence for such a signal, setting mass limits $m_{b^{\prime}}, m_{B} >$ 338 $\mathrm{GeV}/c^2$ and $m_{T_{5/3}} >$ 365 $\mathrm{GeV}/c^2$ at 95% confidence level.

Coherent quasiparticle approximation cQPA and nonlocal coherence

We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are shown to encode the information of the quantum coherence between particles and antiparticles, left and right moving chiral states and/or between different flavour states. Analogously to the usual derivation of the Boltzmann equation, we impose this extended phase space structure on the full interacting theory. This extension of the quasiparticle approximation gives rise to a self-consistent equation of motion for a density matrix that combines the quantum mechanical coherence evolution with a well defined collision integral giving rise to decoherence. Several applications of the method are given, for example to the coherent particle production, electroweak baryogenesis and study of decoherence and thermalization.

Fate of the superconducting ground state on the Moyal plane

It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is smaller compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt. (C) 2010 Elsevier B.V. All rights reserved.

Non-Abelian chiral gauge theories in two dimensions

An anomalous multiflavor chiral theory, with the gauge group SU(N), is studied using non-Abelian bosonization. The theory can be made gauge invariant by introducing Wess-Zumino fields and it is particularly simple if the Jackiw-Rajaraman parameter equals 2. In the strong-coupling limit, the low-energy effective theory only contains light unconfined fermions which interact weakly.

Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Patterning Nanoroads and Quantum Dots on Fluorinated Graphene

Using ab initio methods we have investigated the fluorination of graphene and find that different stoichiometric phases can be formed without a nucleation barrier, with the complete “2D-Teflon” CF phase being thermodynamically most stable. The fluorinated graphene is an insulator and turns out to be a perfect matrix-host for patterning nanoroads and quantum dots of pristine graphene. The electronic and magnetic properties of the nanoroads can be tuned by varying the edge orientation and width. The energy gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO) of quantum dots are size-dependent and show a confinement typical of Dirac fermions. Furthermore, we study the effect of different basic coverage of F on graphene (with stoichiometries CF and C4F) on the band gaps, and show the suitability of these materials to host quantum dots of graphene with unique electronic properties.