Flavour Physics and CP Violation in the Standard Model and Beyond

We present the invited lectures given at the Third IDPASC School which took place in Santiago de Compostela in January 2013. The students attending the school had very different backgrounds, some of them were doing their Ph.D. in experimental particle physics, others in theory. As a result, and in order to make the lectures useful for most of the students, we focused on basic topics of broad interest, avoiding the more technical aspects of Flavour Physics and CP Violation. We make a brief review of the Standard Model, paying special attention to the generation of fermion masses and mixing, as well as to CP violation. We describe some of the simplest extensions of the SM, emphasising novel flavour aspects which arise in their framework.Comment: Invited talk at the Third IDPASC School 2013, January 21st - February 2nd 2013, Santiago de Compostela, Galiza, Spain; 36 pages, 8 figures, 2 tables; version with few misprints correcte

The Higgs System in and Beyond the Standard Model

After the discovery of the Higgs boson particle on the 4th of July of 2012 at the Large Hadron Collider, sited at the european CERN laboratory, we are entering in a fascinating period for Particle Physics where both theorists and experimentalists are devoted to fully understand the features of this new particle and the possible consequences for High Energy Physics of the Higgs system both within and beyond the Standard Model of fundamental particle interactions. This paper is a summary of the lectures given at the third IDPASC school (Santiago de Compostela, Feb. 2013, Spain) addressed to PhD students, and contains a short introduction to the main basic aspects of the Higgs boson particle in and beyond the Standard Model.Comment: 62 pages, 31 figures, Lectures of the IDPASC School at Santiago de Compostela, Spain, February 201

The Standard Model of Electroweak Interactions

In this chapter, we summarize the structure of the standard EW theory and specify the couplings of the intermediate vector bosons W\ub1, Z and of the Higgs particle with the fermions and among themselves, as dictated by the gauge symmetry plus the observed matter content and the requirement of renormalizability

Higgs Messengers

We explore the consequences of the Higgs fields acting as messengers of supersymmetry breaking. The hidden-sector paradigm in the gauge mediation framework is relaxed by allowing two types of gauge-invariant, renormalizable operators that are typically discarded: direct coupling between the Higgses and supersymmetry breaking singlets, and Higgs-messenger mixing terms. The most important phenomenological consequence is a flavor-dependent shift in sfermion masses. This is from a one-loop contribution, which we compute for a general set of weak doublet messengers. We also study a couple of explicit models in detail, finding that precision electroweak constraints can be satisfied with a spectrum significantly different from that of gauge mediation.Comment: 20 pages, 5 figure

Gauge Theories and the Standard Model

This chapter, Chaps. 3 and 4 present a self-contained introduction to the Standard Model of fundamental interactions, which describes in the unified framework of gauge quantum field theories all of the fundamental forces of nature but gravity: the strong, weak, and electromagnetic interactions. This set of chapters thus provides both an introduction to the Standard Model, and to quantum field theory at an intermediate level. The union of the three chapters can be taken as a masters\u2019 level course reference, and it requires as a prerequisite an elementary knowledge of quantum field theory, at the level of many introductory textbooks, such as Vol. 1 of Aitchison-Hey, or, at a somewhat more advanced level, Maggiore. The treatment is subdivided into three parts, each corresponding to an individual chapter, with more advanced field theory topics introduced along the way as needed. Specifically, this chapter presents the general structure of the Standard Model, its field content, and symmetry structure. This involves an introduction to non-abelian gauge theories both at the classical and quantum level. Also, it involves a discussion of spontaneous symmetry breaking and the Higgs mechanism, that play a crucial role in the architecture of the Standard Model, and their interplay with the quantization of gauge theories. Chapter 3 then presents the electroweak sector of the Standard Model. This requires introducing the concepts of CP violation and mixing, and of radiative corrections. Finally, Chap. 4 presents the strong sector of the theory, which requires a more detailed treatment of renormalization and the renormalization group

Phenomenological Consequences of sub-leading Terms in See-Saw Formulas

Several aspects of next-to-leading (NLO) order corrections to see-saw formulas are discussed and phenomenologically relevant situations are identified. We generalize the formalism to calculate the NLO terms developed for the type I see-saw to variants like the inverse, double or linear see-saw, i.e., to cases in which more than two mass scales are present. In the standard type I case with very heavy fermion singlets the sub-leading terms are negligible. However, effects in the percent regime are possible when sub-matrices of the complete neutral fermion mass matrix obey a moderate hierarchy, e.g. weak scale and TeV scale. Examples are cancellations of large terms leading to small neutrino masses, or inverse see-saw scenarios. We furthermore identify situations in which no NLO corrections to certain observables arise, namely for mu-tau symmetry and cases with a vanishing neutrino mass. Finally, we emphasize that the unavoidable unitarity violation in see-saw scenarios with extra fermions can be calculated with the formalism in a straightforward manner.Comment: 22 pages, matches published versio

True Neutrality as a New Type of Flavour

A classification of leptonic currents with respect to C-operation requires the separation of elementary particles into the two classes of vector C-even and axial-vector C-odd character. Their nature has been created so that to each type of lepton corresponds a kind of neutrino. Such pairs are united in families of a different C-parity. Unlike the neutrino of a vector type, any C-noninvariant Dirac neutrino must have his Majorana neutrino. They constitute the purely neutrino families. We discuss the nature of a corresponding mechanism responsible for the availability in all types of axial-vector particles of a kind of flavour which distinguishes each of them from others by a true charge characterized by a quantum number conserved at the interactions between the C-odd fermion and the field of emission of the corresponding types of gauge bosons. This regularity expresses the unidenticality of truly neutral neutrino and antineutrino, confirming that an internal symmetry of a C-noninvariant particle is described by an axial-vector space. Thereby, a true flavour together with the earlier known lepton flavour predicts the existence of leptonic strings and their birth in single and double beta decays as a unity of flavour and gauge symmetry laws. Such a unified principle explains the availability of a flavour symmetrical mode of neutrino oscillations.Comment: 19 pages, LaTex, Published version in IJT

Constraining General Two Higgs Doublet Models by the Evolution of Yukawa Couplings

We study how general two Higgs doublet models can be constrained by considering their properties under renormalization group evolution of the Yukawa couplings. We take into account both the appearance of a Landau pole as well as off-diagonal Yukawa couplings leading to flavour changing neutral currents in violation with experimental constraints at the electroweak scale. We find that the latter condition can be used to limit the amount of Z2 symmetry breaking allowed in a given model.Comment: 28 pages, 10 figures, added discussion of evolution from high to low scales, to be published in JHE

Flavor violating leptonic decays of τ and μ leptons in the Standard Model with massive neutrinos

We have revisited the computations of the flavor violating leptonic decays of the τ and μ leptons into three lighter charged leptons in the Standard Model with massive neutrinos. We were driven by a claimed unnaturally large branching ratio predicted for the τ − → μ − l + l − (l = μ, e) decays (Pham, Eur Phys J C 8:513 1999), which was at odds with the corresponding predictions for the μ − → e−e−e+ processes (Petcov, Sov J Nucl Phys 25:340 1977). In contrast with the prediction in [17], our results are strongly suppressed and in good agreement with the approximationmade in Ref. [15], where masses and momenta of the external particles were neglected in order to deal with the loop integrals. However -as a result of keeping external momenta and masses in the computation of the dominant penguin and box diagrams- we even find slightly smaller branching fractions. Therefore, we confirm that any future observation of such processes would be an unambiguous manifestation of new physics beyond the Standard Model.Finally, we also acknowledge support from Conacyt through projects FOINS-296-2016 (Fronteras de la Ciencia), and 236394 and 250628 (Ciencia Básica)

On Composite Two Higgs Doublet Models

We investigate composite two Higgs doublet models realized as pseudo Goldstone modes, generated through the spontaneous breaking of a global symmetry due to strong dynamic at the TeV scale. A detailed comparative survey of two possible symmetry breaking patterns, SU(5) -> SU(4) x U(1) and SU(5) x SU(4), is made. We point out choices for the Standard Model fermion representations that can alleviate some phenomenological constraints, with emphasis towards a simultaneous solution of anomalous Zb\bar{b} coupling and Higgs mediated Flavor Changing Neutral Currents. We also write down the kinetic lagrangian for several models leading to Two Higgs Doublets and identify the anomalous contributions to the T parameter. Moreover, we describe a model based on the breaking $SO(9)/SO(8)$ in which there is no tree-level breaking of custodial symmetry, discussing also the possible embeddings for the fermion fields.Comment: 17 pages. Mistake corrected, added one section on a T- and flavor safe model based on SO(9)/SO(8). Matches published versio