Signals of composite particles at the LHC

Composite particles generated by an unknown strong dynamics can be responsible for the ElectroWeak Symmetry Breaking (EWSB) and can substitute the Standard Model (SM) Higgs boson in keeping perturbative unitarity in the longitudinal WW scattering up to a cut-off \Lambda\approx 4\pi v. These new states can be sufficiently light to be observed at the Large Hadron Collider (LHC) and they can even be the first manifestation of new physics at the LHC. Their couplings among themselves and with the SM particles, can be described using reasonable effective Lagrangians and Chiral Perturbation Theory. In the first part of this thesis different possibilities for a strongly interacting EWSB are discussed in details with particular attention to the roles of unitarity in the longitudinal WW scattering and of ElectroWeak Precision Tests (EWPT). Higgsless models with composite vectors and scalars, based on the SU(2)_{L}\times SU(2)_{R}/SU(2)_{L+R} custodial symmetry, are discussed in the context of ElectroWeak Chiral Lagrangians and the phenomenology of the pair productions is studied for the high energy and high luminosity phase of the LHC. In the second part of the thesis the possible signals of single particle production at the early LHC, with 7 TeV of center of mass energy and 1-5 fb^{-1} of integrated luminosity, are treated with a phenomenological Lagrangian approach. The final states containing at least one photon emerge as the most promising channels for an early discovery already with tens of inverse picobarns of integrated luminosity. Finally, in the last part of this work, the role of a composite iso-singlet vector in Dark Matter models is discussed and the related LHC phenomenology is studied, giving particular attention to the Z\gamma final state.Comment: Ph.D. Thesis defended on 27 September 2011 at the University of Pis

New Approaches to Naturalness in the LHC Era: From a Radiative Top Yukawa to a Light Composite Higgs

The puzzling lightness of the Higgs boson, when one considers the Standard Model as an effective field theory to be completed, has driven much of the particle physics research over the last decades. Two paradigms have emerged as solutions to this puzzle: supersymmetry and compositeness. The absence of signals at the LHC pushes these solutions into regions of evermore fine-tuning. We present three novel approaches aimed at explaining the absence of these signatures. The first one, exploiting the large contribution of the top Yukawa to the Higgs mass, proposes a non-symmetry-based solution in which the top Yukawa only obtains its sizeable value in the IR and we discuss its new phenomenological signatures. Secondly, we present a minimal model of 5D warped gauge-Higgs grand unification, study its compelling flavor structure and analyse the resulting constraints. Although these constraints push the model to high scales, additional scalars that reside below the Kaluza-Klein states may provide accessible experimental signatures. Finally, we provide a novel model of composite Higgs generating the Higgs potential at subleading order using a remarkable property of group representations. The model is analysed and can evade existing bounds with little tuning. New light particles are predicted with unusual decays in which naturalness at the LHC may be hidden

Quaternion Algebras

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout

The moduli space of matroids

In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are compatible with the respective matroid theories. Moreover, fuzzy rings are ordered blueprints and lie in the intersection of tracts with ordered blueprints; we call the objects of this intersection pastures. In the second part, we construct moduli spaces for matroids over pastures. We show that, for any non-empty finite set $E$, the functor taking a pasture $F$ to the set of isomorphism classes of rank-$r$ $F$-matroids on $E$ is representable by an ordered blue scheme $Mat(r,E)$, the moduli space of rank-$r$ matroids on $E$. In the third part, we draw conclusions on matroid theory. A classical rank-$r$ matroid $M$ on $E$ corresponds to a $\mathbb{K}$-valued point of $Mat(r,E)$ where $\mathbb{K}$ is the Krasner hyperfield. Such a point defines a residue pasture $k_M$, which we call the universal pasture of $M$. We show that for every pasture $F$, morphisms $k_M\to F$ are canonically in bijection with $F$-matroid structures on $M$. An analogous weak universal pasture $k_M^w$ classifies weak $F$-matroid structures on $M$. The unit group of $k_M^w$ can be canonically identified with the Tutte group of $M$. We call the sub-pasture $k_M^f$ of $k_M^w$ generated by ``cross-ratios' the foundation of $M$,. It parametrizes rescaling classes of weak $F$-matroid structures on $M$, and its unit group is coincides with the inner Tutte group of $M$. We show that a matroid $M$ is regular if and only if its foundation is the regular partial field, and a non-regular matroid $M$ is binary if and only if its foundation is the field with two elements. This yields a new proof of the fact that a matroid is regular if and only if it is both binary and orientable.Comment: 83 page

The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability

The dilatation generator measures the scaling dimensions of local operators in a conformal field theory. In this thesis we consider the example of maximally supersymmetric gauge theory in four dimensions and develop and extend techniques to derive, investigate and apply the dilatation operator. We construct the dilatation operator by purely algebraic means: Relying on the symmetry algebra and structural properties of Feynman diagrams we are able to bypass involved, higher-loop field theory computations. In this way we obtain the complete one-loop dilatation operator and the planar, three-loop deformation in an interesting subsector. These results allow us to address the issue of integrability within a planar four-dimensional gauge theory: We prove that the complete dilatation generator is integrable at one-loop and present the corresponding Bethe ansatz. We furthermore argue that integrability extends to three-loops and beyond. Assuming that it holds indeed, we finally construct a novel spin chain model at five-loops and propose a Bethe ansatz which might be valid at arbitrary loop-order! We illustrate the use of our technology in several examples and also present two key applications for the AdS/CFT correspondence.Comment: PhD thesis (revised), 230 pages. Contains previously unpublished results. v2,v3: minor changes, references added, v4: corrections in table 2.1, eqs. (2.146,3.26,4.43,4.115,4.116) and below (3.23,3.28