Search

We explore the phenomenology of Weinberg's $Z_2\times Z_2$ symmetric three-Higgs-doublet potential, allowing for spontaneous violation of CP due to complex vacuum expectation values. An overview of all possible ways of satisfying the stationary-point conditions is given, with one, two or three non-vanishing vacuum expectation values, together with conditions for CP conservation in terms of basis invariants. All possible ways of satisfying the conditions for CP conservation are given. Scans of allowed parameter regions are given, together with measures of CP violation, in terms of the invariants. The light states identified in an earlier paper are further explored in terms of their CP-violating couplings. Loop-induced CP violation in $WWZ$ couplings, as well as charge-asymmetric scattering are also commented on., Comment: 45 pages, 19 figures

We explore three-Higgs-doublet models that may accommodate scalar Dark Matter where the stability is based on an unbroken $U(1)$-based symmetry, rather than the familiar $\mathbb{Z}_2$ symmetry. Our aim is to classify all possible ways of embedding a $U(1)$ symmetry in a three-Higgs-doublet model. The different possibilities are presented and compared. All these models contain mass-degenerate pairs of Dark Matter candidates due to a $U(1)$ symmetry unbroken (conserved) by the vacuum. Most of these models preserve CP. In the CP-conserving case the pairs can be seen as one being even and the other being odd under CP or as having opposite charges under $U(1)$. Not all symmetries presented here were identified before in the literature, which points to the fact that there are still many open questions in three-Higgs-doublet models. We also perform a numerical exploration of the $U(1) \otimes U(1)$-symmetric 3HDM, this is the most general phase-invariant (real) three-Higgs-doublet model. The model contains a multi-component Dark Matter sector, with two independent mass scales. After imposing relevant experimental constraints we find that there are possible solutions throughout a broad Dark Matter mass range, 45-2000 GeV, the latter being a scan cutoff., Comment: 103 pages, 5 figures, v2: added references, minor text changes

We review the theory and phenomenology of isosinglet vector-like quarks (VLQs). In recent years, interest in VLQs has been increasing, due to their contributions to new physics effects that can be tested in experiments at LHC and High-Luminosity LHC. The similarities of models with isosinglet VLQs and the seesaw framework in the leptonic sector are pointed out. The existence of VLQs leads to flavour-changing neutral currents at tree level and deviations from unitarity of the CKM matrix, introducing rich phenomenological implications. These new effects are naturally suppressed by the masses of the new quarks, that are constrained to be above the electroweak scale. In addition, striking new effects can be achieved with the inclusion of an extra complex scalar singlet. Such a minimal extension of the SM can give rise to new sources of CP violation with profound theoretical implications, allowing for a solution to the strong CP problem and a possible explanation for the baryon asymmetry of the Universe. We list and explain strong motivations to consider this class of models. We also briefly review how models with VLQs can be matched to the SM effective field theory (SMEFT). A detailed analysis of flavour observables that can be affected by the presence of VLQs is presented. Current bounds from collider searches of VLQs are summarized. We point out that the discovery of VLQs can be within the reach of present or future colliders being planned., Comment: 121 pages, 7 figures, 7 tables. Work intended as a review. Comments and references added; typos corrected. New appendix on UV completions; section 2.3 expanded. Matches version published in Physics Reports

CP violation plays a very important role in nature with implications both for Particle Physics and for Cosmology. Accounting for the observed matter anti-matter asymmetry of the Universe requires the existence of new sources of CP violation beyond the Standard Model. In models with an extended scalar sector CP violation can emerge either explicitly, i.e., at the Lagrangian level, or spontaneously. In the context of multi-Higgs extensions of the Standard Model imposing the existence of a scalar basis where all couplings are real is a sufficient condition for CP to be explicitly conserved. We discuss a three-Higgs-doublet model with an underlying $S_3$ symmetry, allowing in principle for complex couplings. In this framework it is possible to have either spontaneous or explicit CP violation in the scalar sector, depending on the regions of parameter space corresponding to the different possible vacua of the $S_3$ symmetric potential. We list all possible vacuum structures allowing for CP violation in the scalar sector specifying whether it can be explicit or spontaneous. It is by now established that CP is violated in the flavour sector and that the Cabibbo-Kobayashi-Maskawa matrix is complex. In order to understand what are the possible sources of CP violation in the Yukawa sector we analyse the implications of the different available choices of representations for the quarks under the $S_3$ group. This classification is based strictly on the exact $S_3$-symmetric scalar potential with no soft symmetry breaking terms. The scalar sector of one such model was explored numerically. After applying the theoretical and the most important experimental constraints the available parameter space is shown to be able to give rise to light neutral scalars at the $\mathcal{O}(\text{MeV})$ scale., Comment: 42 pages, 2 figures, V2: version consistent with JHEP

Models with an extended scalar electroweak sector are well motivated. Such models could accommodate a dark matter candidate if there is an additional scalar representation with a vanishing vacuum expectation value and, in addition, there are no couplings between fermions and the dark matter candidate. The most natural way to have these conditions implemented is to consider models where an underlying symmetry is imposed. Governed by this, we consider a three-Higgs-doublet model with an $S_3$ symmetry. Within this framework there are different implementations which could possibly accommodate a dark matter candidate. The family of $S_3$-symmetric three-Higgs-doublet implementations arises due to different vacua and, as a result, different minimisation conditions. In this framework the dark matter candidate falls into the class of weakly interacting massive particles. The dark matter candidate is associated with an $\mathbb{Z}_2$ symmetry which survives spontaneous symmetry breaking and is a remnant of the $S_3$ symmetry. We explore two cases, they share many aspects of the Type-I two-Higgs-doublet model plus an inert SU(2) doublet. The main difference between these two cases is the presence of an irremovable phase, which leads to CP violation in one of the implementations. The two candidate cases differ from other previously studied models with three scalar doublets by the fact that they do not allow for heavy dark matter candidates, $\mathcal{O}(500)\text{ GeV}$. Valid dark matter regions were identified as $m_\mathrm{DM} \in [52.5,\,89]~\text{GeV}$ for a model without CP violation and $m_\mathrm{DM} \in [6.5,\,44.5]~\text{GeV}$ for a model with CP violation. In the present work we refine the parameter space by applying additional checks to our previous work coming from LHC data and from indirect detection data., Comment: 8 pages, 5 figures, to be published in the Proceedings of DISCRETE 2022: 8th Symposium on Prospects in the Physics of Discrete Symmetries, 7-11 November, 2022, Baden-Baden, Germany

The $\mathbb Z_2\times \mathbb Z_2$-symmetric 3HDM potential, sometimes called Weinberg's 3HDM potential, can accommodate both explicit and spontaneous CP violation as well as natural flavour conservation and is hence relevant for studies of CP violation coming from a realistic extended Higgs sector. The model has an interesting regime, controlled by a single parameter, where it acquires an approximate global $U(1) \times U(1)$ symmetry which causes CP violating effects to be small and two pseudo-Goldstone bosons to be present in the scalar spectrum. From parameter space scans, we find that, in a realistic implementation featuring an SM-like Higgs boson, this model predominantely leads to the existence of light additional Higgs bosons with a mass lower than the SM-like Higgs boson.

We study the potential of Weinberg's $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric three-Higgs-doublet model (3HDM). The potential is designed to accommodate CP violation in the scalar sector within a gauge theory, while at the same time allowing for natural flavour conservation. This framework allows for both explicit and spontaneous CP violation. CP can be explicitly violated when the coefficients of the potential are taken to be complex. With coefficients chosen to be real, CP can be spontaneously violated via complex vacuum expectation values (vevs). In the absence of the terms leading to the possibility of CP violation, either explicit or induced by complex vevs, the potential has two global U(1) symmetries. In this case, spontaneous symmetry breaking would in general give rise to massless states. In a realistic implementation, those terms must be included, thus preventing the existence of Goldstone bosons. A scan over parameters, imposing the existence of a neutral state at 125 GeV that is nearly CP-even shows that, in the absence of fine-tuning, the scalar spectrum contains one or two states with masses below 125 GeV that have a significant CP-odd component. These light states would have a low production rate via the Bjorken process and could thus have escaped detection at LEP. At the LHC the situation is less clear. While we do not here aim for a full phenomenological study of the light states, we point out that the $\gamma\gamma$ decay channel would be challenging to measure because of suppressed couplings to $WW$., Comment: Minor changes, some references added. Matches Phys. Rev. D version

In this talk we emphasise the importance of vector-like quarks (VLQs) and their potential to solve some of the open questions of the Standard Model. These are, in some sense minimal extensions of the Standard Model, that can be probed in the next round of experiments. We also make an analogy between vector-like quarks(VLQs) and right-handed neutrinos, emphasising that in both cases some of the flavour dogmas of the SM are violated in a controlled way., Comment: Contribution to 7th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2020-2021), 29th November - 3rd December 2021, Bergen, Norway

Models with an extended scalar electroweak sector can have vanishing vacuum expectation values in a basis where an underlying symmetry is imposed. Such extensions are very well motivated. If a symmetry prevents couplings between fermions and additional scalars, such scalars could become viable dark matter candidates if some additional criteria are satisfied. We catalogue $S_3$-symmetric three-Higgs-doublet models, also allowing for softly broken $S_3$-symmetric scalar potential terms, based on whether a specific model could possibly accommodate a dark matter candidate. The variety of the $S_3$-symmetric family models arises due to different possibilities to arrange vacuum expectation values. Such models can have vacua with one or two vanishing vacuum expectation values. In our study we assume that the dark matter candidate is stabilised by the $\mathbb{Z}_2$ symmetry. The $\mathbb{Z}_2$ symmetry is a remnant of $S_3$ symmetry which survived spontaneous symmetry breaking, and not superimposed over $S_3$. We explore two models; with an without CP violation. These models have a single dark and two active scalar sectors. The active sectors behave in many aspects like a Type-I two-Higgs-doublet model. The dark matter candidate masses, in two cases, are different from the known (previously studied) models with three scalar doublets. After investigating the models in detail, identifying parameters compatible with both theoretical and experimental constraints, we found that the dark matter candidate mass could be within the range of $[52.5,\,89]~\text{GeV}$ or $[6.5,\,44.5]~\text{GeV}$ for a model with CP violation., Comment: 6 pages, 3 figures, to be published in the Proceedings of DISCRETE 2020-2021: 7th Symposium on Prospects in the Physics of Discrete Symmetries, 29th November - 3rd December 2021, Bergen, Norway; v2: Minor changes

In spite of the success of the Standard Model of Particle Physics, there are some theoretical predictions which are not yet fully established experimentally as well as some experimental observations which cannot be fitted within its theoretical framework, thus requiring physics beyond the Standard Model. One of these is a hypothetical non-luminous form of matter - dark matter. Models with an extended scalar electroweak sector yield plausible dark matter candidates. In this paper we study a specific model, C-III-a, from a family of $S_3$-symmetric three-Higgs-doublet models. The model consists of two active SU(2) doublets and an inert one. The latter is inert due to a $\mathbb{Z}_2$ symmetry that survives the breaking of $S_3$, and would accommodate a dark matter particle. We explore the model numerically, based on theoretical and experimental constraints. After applying a number of successive checks over the parameter space we found a viable dark matter mass region in the range $[6.5;\,44.5]~\text{GeV}$. This region is drastically different from the Higgs-like dark matter states that have been proposed: the well-known Inert Doublet Model and models with three scalar doublets, with one or two inert doublets. Furthermore, the C-III-a model allows for spontaneous CP violation., Comment: 40 pages, 12 figures. v2: PRD version, minor clarifications. arXiv admin note: text overlap with arXiv:2108.07026

We perform a comprehensive analysis of a version of the 3-Higgs doublet model whose scalar potential is invariant under a global $\Delta(27)$ discrete symmetry and where the three scalar doublets are chosen to transform as a triplet under this discrete group. For each of the known tree-level minima we study the mass spectra and use the oblique parameters $STU$ as well as perturbative unitarity to constrain the parameter space of the model. We then discuss phenomenological consequences of some leading order flavour mixing quark Yukawa couplings by considering the flavour violation process $b \to s \gamma$. We show that perturbative unitarity significantly constrains parameters of the model while, conversely, the beyond the Standard Model contributions to the $b \to s \gamma$ decay are automatically tamed by the symmetry., Comment: 27 pages, 3 figures; version published in JHEP

We propose a minimal extension of the Standard Model where an up-type vector-like quark, denoted $T$, is introduced and provides a simple solution to the CKM unitarity problem. We adopt the Botella-Chau parametrization in order to extract the $4\times 3$ quark mixing matrix which contains the three angles of the $3\times 3$ CKM matrix plus three new angles denoted $\theta_{14}$, $\theta_{24}$, $\theta_{34}$. It is assumed that the mixing of $T$ with standard quarks is dominated by $\theta_{14}$. Imposing a recently derived, and much more restrictive, upper-bound on the New Physics contributions to $\epsilon_{K}$, we find, in the limit of exact $\theta_{14}$ dominance where the other extra angles vanish, that $\epsilon_{K}^{\text{NP}}$ is too large. However, if one relaxes the exact $\theta_{14}$ dominance limit, there exists a parameter region, where one may obtain $\epsilon_{K}^{\text{NP}}$ in agreement with experiment while maintaining the novel pattern of $T$ decays with the heavy quark decaying predominantly to the light quarks $d$ and $u$. We also find a reduction in the decay rate of $K_L\rightarrow \pi^o \nu\bar{\nu}$., Comment: 33 pages, 8 figures, 1 table

Models with two or more scalar doublets with discrete or global symmetries can have vacua with vanishing vacuum expectation values in the bases where symmetries are imposed. If a suitable symmetry stabilises such vacua, these models may lead to interesting dark matter candidates, provided that the symmetry prevents couplings among the dark matter candidates and the fermions. We analyse three-Higgs-doublet models with an underlying $S_3$ symmetry. These models have many distinct vacua with one or two vanishing vacuum expectation values which can be stabilised by a remnant of the $S_3$ symmetry which survived spontaneous symmetry breaking. We discuss all possible vacua in the context of $S_3$-symmetric three-Higgs-doublet models, allowing also for softly broken $S_3$, and explore one of the vacuum configurations in detail. In the case we explore, only one of the three Higgs doublets is inert. The other two are active, and therefore the active sector, in many aspects, behaves like a two-Higgs-doublet model. The way the fermions couple to the scalar sector is constrained by the $S_3$ symmetry and is such that the flavour structure of the model is solely governed by the $V_\text{CKM}$ matrix which, in our framework, is not constrained by the $S_3$ symmetry. This is a key requirement for models with minimal flavour violation. In our model there is no CP violation in the scalar sector. We study this model in detail giving the masses and couplings and identifying the range of parameters that are compatible with theoretical and experimental constraints, both from accelerator physics and from astrophysics., Comment: 50 pages, 14 figures, V2: typos fixed, some plots changed, V3: minor text edits, V4: version consistent with JHEP

We point out that hints of deviations from unitarity in the first row of the CKM matrix may be explained by the presence of a single vector-like top. We study how the stringent experimental constraints arising from CP Violation in the kaon sector and from meson mixing such as $D^0$-$\overline{D}^0$, $K^0$-$\overline{K}^0$ and $B^0_{d,s}$-$\overline{B}^0_{d,s}$ can be satisfied in the proposed framework. In order for the deviations from unitarity to be of the required size while keeping the theory perturbative, the new top quark should have a mass $m_T \lesssim 7$ TeV which could be probed in upcoming experiments at the energy frontier., Comment: 24 pages, 4 figures, 2 tables; comments and references added

In this paper we analyse in detail an $S_3$-symmetric three-Higgs-doublet model with a specific vacuum configuration. This analysis allows us to illustrate important features of models with several Higgs doublets, such as the possibility of having spontaneous CP violation. We start with a real potential and pick a particularly interesting complex vacuum configuration, which does not violate CP before adding soft breaking terms to the potential. We study the r\^ ole played by different soft symmetry breaking terms. These are essential for our choice of vacuum in order to remove unwanted massless scalars which arise from the spontaneous breaking of an accidental continuous symmetry. We list scalar sector and scalar-gauge sector-couplings for the particular case we consider in detail in this work. Results presented in this paper will be useful for model building, in particular for implementations of models with $S_3$ symmetry and spontaneous CP violation, extensions of the fermionic sector with realistic Yukawa couplings and for Dark Matter studies., Comment: 33 pages. v2: PRD version, Minor clarifications. References added. Title compliant with APS style

We consider seesaw type-I models including at least one (mostly-)sterile neutrino with mass at the eV scale. Three distinct situations are found, where the presence of light extra neutrinos is naturally justified by an approximately conserved lepton number symmetry. To analyse these scenarios consistently, it is crucial to employ an exact parametrisation of the full mixing matrix. We provide additional exact results, including generalised versions of the seesaw relation and of the Casas-Ibarra parametrisation, valid for every scale of seesaw. We find that the existence of a light sterile neutrino imposes an upper bound on the lightest neutrino mass. We further assess the impact of light sterile states on short- and long-baseline neutrino oscillation experiments, emphasise future detection prospects, and address CP Violation in this framework via the analysis of CP asymmetries and construction of weak basis invariants. The proposed models can accommodate enough active-sterile mixing to play a role in the explanation of short-baseline anomalies., Comment: 40 pages, 3 figures, 4 tables

Symmetries play a very important r\^ole in Particle Physics. In extended scalar sectors, the existence of symmetries may permit the models to comply with the experimental constraints in a natural way, and at the same time reduce the number of free parameters. There is a strong interplay among internal symmetries of the scalar potential, its CP properties and mass degeneracies of the physical scalars. Some of these aspects were discussed in this talk., Comment: 8 pages, to be published in the Proceedings of DISCRETE2018: 6th Symposium on Prospects in the Physics of Discrete Symmetries, 26-30 Nov 2018. Vienna, Austria

We explore some aspects of models with two and three SU(2) scalar doublets that lead to mass degeneracies among some of the physical scalars. In Higgs sectors with two scalar doublets, the exact degeneracy of scalar masses, without an artificial fine-tuning of the scalar potential parameters, is possible only in the case of the inert doublet model (IDM), where the scalar potential respects a global U(1) symmetry that is not broken by the vacuum. In the case of three doublets, we introduce and analyze the replicated inert doublet model, which possesses two inert doublets of scalars. We then generalize this model to obtain a scalar potential, first proposed by Ivanov and Silva, with a CP4 symmetry that guarantees the existence of pairwise degenerate scalar states among two pairs of neutral scalars and two pairs of charged scalars. Here, CP4 is a generalized CP symmetry with the property that $({\rm CP}4)^n$ is the identity operator only for integer $n$ values that are multiples of 4. The form of the CP4-symmetric scalar potential is simplest when expressed in the Higgs basis, where the neutral scalar field vacuum expectation value resides entirely in one of the scalar doublet fields. The symmetries of the model permit a term in the scalar potential with a complex coefficient that cannot be removed by any redefinition of the scalar fields within the class of Higgs bases (in which case, we say that no real Higgs basis exists). A striking feature of the CP4-symmetric model is that it preserves CP even in the absence of a real Higgs basis, as illustrated by the cancellation of the contributions to the CP violating form factors of the effective ZZZ and ZWW vertices., Comment: 52 pages, 2 figures, second revised version with new material, as published by JHEP

We emphasise that even in the extreme chiral limit where only the top and bottom quarks acquire mass, quark mixing is physically meaningful. This implies that the natural value of $|V_{13}|^2 + |V_{23}|^2$ is of order one, which is to be compared to its experimental value of order $10^{-3}$ . We show how this fine-tuning problem of the Standard Model can be solved through an extension of the Standard Model where vector-like quarks and a complex singlet are introduced, together with a flavour symmetry. The mixings of the light quarks are generated through the mixing of the vector-like quarks with the standard quarks., Comment: 8 pages. Talk given at Corfu Summer Institute 2017, School and Workshops on Elementary Particle Physics and Gravity, September 2017. To appear in conference proceedings

In this talk we present a powerful tool applied to the study of Leptonic Physics. This tool is based on the construction of Weak Basis invariant relations associated to different properties of leptonic models. The rationale behind these constructions is the fact that fermion mass matrices related through weak basis transformations look different but lead to the same physics. Such invariants can be built, for instance, with the aim to test leptonic models for different types of CP violation. These invariants are also relevant beyond such tests and have been applied to the study of implications from zero textures appearing in the leptonic mass matrices. In this case an important question is, how can a flavour model corresponding to a set of texture zeros be recognised, when written in a different weak basis, where the zeros are not explicitly present. Another important application is the construction of invariants sensitive to the neutrino mass ordering and the $\theta_{23}$ octant., Comment: 7 pages, no figures. Invited talk given at 18th Lomonosov Conference on Elementary Particle Physics (Moscow, Russia, August 24-30, 2017)

We discuss how one can identify CP violation (and conservation) in multi-Higgs-doublet potentials. After a brief review of CP violation in the 2HDM, we refer to the fact that for NHDM with $N \geq 3$ the well known methods useful in the case $N = 2$ have not been generalized in order to provide a set of well defined necessary and sufficient conditions for CP conservation. We then present a simple method, proposed by the authors, to be used in such cases. Two non-trivial examples based on an $S_3$-symmetric three-doublet model are analyzed by means of this new method., Comment: 10 pages. Talk given at Corfu Summer Institute 2017, School and Workshops on Elementary Particle Physics and Gravity, September 2017. To appear in conference proceedings

We address the question of deviations from $3\times 3$ unitarity of the leptonic mixing matrix showing that, contrary to conventional wisdom, one may have significant deviations from unitarity in the framework of type I seesaw mechanism. In order for this scenario to be feasible, at least one of the heavy neutrinos must have a mass at the TeV scale, while the other two may have much larger masses. We present specific examples where deviations from $3\times 3$ unitarity are sufficiently small to conform to all the present stringent experimental bounds but are sufficiently large to have the potential for being detectable at the next round of experiments., Comment: 17 pages, 4 figures, 3 tables

We point out that leptonic weak-basis invariants are an important tool for the study of the properties of lepton flavour models. In particular, we show that appropriately chosen invariants can give a clear indication of whether a particular lepton flavour model favours normal or inverted hierarchy for neutrino masses and what is the octant of $\theta_{23}$. These invariants can be evaluated in any conveniently chosen weak-basis and can also be expressed in terms of neutrino masses, charged lepton masses, mixing angles and CP violation phases., Comment: 10 pages, no figures

We point out that in the Standard Model (SM) there is no explanation why $|V_{23}|^2 + |V_{13}|^2$ is of order $10^{-3}$. A framework is described for explaining this small mixing, involving the introduction of vector-like quarks. A symmetry is introduced so that at a first stage $V_{CKM} = 1\>\!\!\!\mathrm{I}$ and only the third generation of quarks acquires a mass. It is shown that when interactions of vector-like quarks are taken into account a realistic quark mass spectrum is generated together with a correct $V_{CKM}$ matrix., Comment: 10 pages, no figures. Prepared for the proceedings of DISCRETE2016: the Fifth Symposium on Prospects in the Physics of Discrete Symmetries, 28 November-3 December 2016, University of Warsaw, Poland, to appear in the Journal of Physics: Conference Series (JPCS)

The talk summarises work done by the authors consisting of a detailed study of the possible vacua in models with three Higgs doublets with $S_3$ symmetry and without explicit CP violation. Different vacua require special regions of the parameter space which were analysed in our work. We establish the possibility of spontaneous CP violation in this framework and we also show which complex vacua conserve CP. In our work we discussed constraints from vacuum stability. The results presented here are relevant for model building., Comment: 11 pages, no figures. Prepared for the proceedings of DISCRETE2016: the Fifth Symposium on Prospects in the Physics of Discrete Symmetries, 28 November-3 December 2016, University of Warsaw, Poland, to appear in the Journal of Physics: Conference Series (JPCS)

For models with several Higgs doublets we present an alternative method to the one proposed by Branco, Gerard and Grimus, in 1984, to check whether or not CP is spontaneously violated in the Higgs potential. The previous method is powerful and rigorous. It requires the identification of a matrix $U$ corresponding to a symmetry of the Lagrangian and verifying a simple relation involving the vacuum expectation values. The nonexistence of such a matrix signals spontaneous CP violation. However, as the number of Higgs doublets increases, finding such a matrix $U$ may not be straightforward and it may turn out to be easier to analyse the potential by going to the so-called Higgs basis. The transformation to the Higgs basis is straightforward once the vacuum expectation values are known. The method proposed in this work is also powerful and rigorous and can be particularly useful to analyse models with more than two Higgs doublets and with continuous symmetries., Comment: 9 pages, no figures. v2: minor changes, matching JHEP version

This Report summarizes the results of the activities of the LHC Higgs Cross Section Working Group in the period 2014-2016. The main goal of the working group was to present the state-of-the-art of Higgs physics at the LHC, integrating all new results that have appeared in the last few years. The first part compiles the most up-to-date predictions of Higgs boson production cross sections and decay branching ratios, parton distribution functions, and off-shell Higgs boson production and interference effects. The second part discusses the recent progress in Higgs effective field theory predictions, followed by the third part on pseudo-observables, simplified template cross section and fiducial cross section measurements, which give the baseline framework for Higgs boson property measurements. The fourth part deals with the beyond the Standard Model predictions of various benchmark scenarios of Minimal Supersymmetric Standard Model, extended scalar sector, Next-to-Minimal Supersymmetric Standard Model and exotic Higgs boson decays. This report follows three previous working-group reports: Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002), Handbook of LHC Higgs Cross Sections: 2. Differential Distributions (CERN-2012-002), and Handbook of LHC Higgs Cross Sections: 3. Higgs properties (CERN-2013-004). The current report serves as the baseline reference for Higgs physics in LHC Run 2 and beyond., Comment: 869 pages, 295 figures, 248 tables and 1645 citations. Working Group web page: https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWG

We show how a novel fine-tuning problem present in the Standard Model can be solved through the introduction of a single flavour symmetry G, together with three $Q = - 1/3$ quarks, three $Q = 2/3$ quarks, as well as a complex singlet scalar. The symmetry G is extended to the additional fields and it is an exact symmetry of the Lagrangian, only spontaneously broken by the vacuum. Specific examples are given and a phenomenological analysis of the main features of the model is presented. It is shown that even for vector-like quarks with masses accessible at the LHC, one can have realistic quark masses and mixing, while respecting the strict constraints on process arising from flavour changing neutral currents (FCNC). The vector-like quark decay channels are also described., Comment: 25 pages, no figures

Models with an extended scalar sector may in principle provide new sources of CP violation originating in the scalar potential. One of the simplest ways to implement this idea is to have CP violation in a two-Higgs-doublet model. Here, it leads to CP violation in trilinear weak gauge boson couplings. We discuss how these couplings are becoming constrained in the alignment limit. In a model with three Higgs doublets, subject to an $S_3$ symmetry, several complex vacua are possible. Some of these, but not all, may lead to spontaneous CP violation., Comment: 8 pages, Proceedings of the Corfu Summer Institute 2015 "Summer School and Workshop on the Standard Model and Beyond", 1-11 September 2015 Corfu, Greece

We relate the observed pattern of leptonic mixing to the quaidegeneracy of three Majorana neutrinos. We show how lifting the degeneracy may lead to the measured value of $|U_{13}|$ and to sizeable CP violation of Dirac-type. We show some of the correlations obtained among physical observables, starting from some of the most interesting schemes proposed in the literature., Comment: Contribution to the 17th Lomonosov Conference. 7 pages. One figure

We point out that, in the context of the SM, $|V^2_{13}| + | V^2_{23}|$ is expected to be large, of order one. The fact that $|V^2_{13}| + |V^2_{23}| \approx 1.6 \times 10^{-3}$ motivates the introduction of a symmetry S which leads to $V_{CKM} ={1\>\!\!\!\mathrm{I}} $, with only the third generation of quarks acquiring mass. We consider two scenarios for generating the mass of the first two quark generations and full quark mixing. One consists of the introduction of a second Higgs doublet which is neutral under S. The second scenario consists of assuming New Physics at a high energy scale , contributing to the masses of light quark generations, in an effective field theory approach. This last scenario leads to couplings of the Higgs particle to $s\overline s$ and $c \overline c$ which are significantly enhanced with respect to those of the SM. In both schemes, one has scalar-mediated flavour- changing neutral currents which are naturally suppressed. Flavour violating top decays are predicted in the second scenario at the level $ \mbox{Br} (t \rightarrow h c ) \geq 5\times 10^{-5}$., Comment: 11 pages, 1 figure

We present a detailed study of the vacua of the $S_3$-symmetric three-Higgs-doublet potential, specifying the region of parameters where these minimisation solutions occur. We work with a CP conserving scalar potential and analyse the possible real and complex vacua with emphasis on the cases in which the CP symmetry can be spontaneously broken. Results are presented both in the reducible-representation framework of Derman, and in the irreducible-representation framework. Mappings between these are given. Some of these implementations can in principle accommodate dark matter and for that purpose it is important to identify the residual symmetries of the potential after spontaneous symmetry breakdown. We are also concerned with constraints from vacuum stability., Comment: 37 pages. v2: Minor changes in the references, matches published version. v3: Table 6 corrected: two additional cases conserve CP. Related discussion adapted. Version consistent with JHEP Erratum

We analyse various flavour changing processes like $t\to hu,hc$, $h\to \tau e,\tau\mu$ as well as hadronic decays $h\to bs,bd$, in the framework of a class of two Higgs doublet models where there are flavour changing neutral scalar currents at tree level. These models have the remarkable feature of having these flavour-violating couplings entirely determined by the CKM and PMNS matrices as well as $\tan\beta$. The flavour structure of these scalar currents results from a symmetry of the Lagrangian and therefore it is natural and stable under the renormalization group. We show that in some of the models the rates of the above flavour changing processes can reach the discovery level at the LHC at 13 TeV even taking into account the stringent bounds on low energy processes, in particular $\mu\to e\gamma$., Comment: 33 pages, 8 figures; matches version accepted for publication

We analise phenomenological implications of two Higgs doublet models with Higgs flavour changing neutral currents suppressed in the quark sector by small entries of the Cabibbo-Kokayashi-Maskawa matrix. This suppression occurs in a natural way since it is the result of a symmetry applied to the Lagrangian. These type of models were proposed some time ago by Branco Grimus and Lavoura. Our results clearly show that these class of models allow for new physical scalars, with masses which are reachable at the LHC. The imposed symmetry severely reduces the number of free parameters and allows for predictions. Therefore these models can eventually be proved right or eliminated experimentally., Comment: Contribution to 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2014) 02-06 Dec 2014. London, United Kingdom. 8 pages, two figures. Uses jpconf.cls

In the context of two Higgs doublet models, we study the conditions required in order to have stable quasi-alignment in flavour space. We show that stability under the RGE imposes strong constraints on the flavour structure of the Yukawa couplings associated to each one of the Higgs doublets. In particular, we find a novel solution, where all Yukawa couplings are proportional to the so-called democratic matrix. This solution is rather unique, since it is the only stable solution which is a good starting point for reproducing the observed pattern of quark masses and mixing. We also show that this stable solution can be obtained by imposing on the Lagrangian a $Z_3 \times Z^\prime_3$ flavour symmetry. Quark masses of the lighter quark generations are generated through the breaking of this discrete symmetry, and, at this stage, scalar mediated FCNC arise, but are naturally suppressed by the smallness of light quark masses. In this way, we relate Higgs alignment to the hierarchy of quark masses through a discrete family symmetry., Comment: 16 pages, 3 figures

We propose that the observed large leptonic mixing may just reflect a quasidegeneracy of three Majorana neutrinos. The limit of exact degeneracy of Majorana neutrinos is not trivial, as leptonic mixing and even CP violation may occur. We conjecture that the smallness of $|U_{13}|$, when compared to the other elements of $U_{PMNS}$, may just reflect the fact that, in the limit of exact mass degeneracy, the leptonic mixing matrix necessarily has a vanishing element. We show that the lifting of the mass degeneracy can lead to the measured value of $|U_{13}|$ while at the same time accommodating the observed solar and atmospheric mixing angles. In the scenario we consider for the breaking of the mass degeneracy there is only one CP violating phase, already present in the limit of exact degeneracy, which upon the lifting of the degeneracy generates both Majorana and Dirac-type CP violation in the leptonic sector. We analyse some of the correlations among physical observables and point out that in most of the cases considered, the implied strength of leptonic Dirac-type CP violation is large enough to be detected in the next round of experiments., Comment: 16 pages, 4 figures. Matches published version, references added, improved discussion, results unchanged

We analyse the constraints and some of the phenomenological implications of a class of two Higgs doublet models where there are flavour-changing neutral currents (FCNC) at tree level but the potentially dangerous FCNC couplings are suppressed by small entries of the CKM matrix $V$. This class of models have the remarkable feature that, as a result of a discrete symmetry of the Lagrangian, the FCNC couplings are entirely fixed in the quark sector by $V$ and the ratio $v_2 /v_1$ of the vevs of the neutral Higgs. The discrete symmetry is extended to the leptonic sector, so that there are FCNC in the leptonic sector with their flavour structure fixed by the leptonic mixing matrix. We analyse a large number of processes, including decays mediated by charged Higgs at tree level, processes involving FCNC at tree level, as well as loop induced processes. We show that in this class of models one has new physical scalars beyond the standard Higgs boson, with masses reachable at the next round of experiments., Comment: 33 pages, 9 figures, 6 tables; corrected typos, improved results, minor changes in the text. Matches version accepted for publication

Flavour-Changing-Neutral-Currents (FCNC) play an important r\^ ole in testing the Standard Model (SM) while probing the possibility of having New Physics beyond the SM. In the SM, FCNC are forbidden at three level, but arise through calculable one-loop contributions. We review some of the features of FCNC in two examples of minimal extensions of the SM. In the first example, we consider an extension of the SM consisting of the addition of one vector-like quark either of the up-type ($Q=2/3$) or the down type ($Q=- 1/3$). In this extension there are non-vanishing but naturally suppressed Z-mediated FCNC at tree level. In the second example, we discuss extensions of the SM with two Higgs doublets, without the assumption of natural flavour conservation, giving rise to Higgs mediated FCNC. The existence of strict experimental limits on processes sensitive to Higgs FCNC requires a strong suppression of these currents. We present scenarios resulting from discrete symmetries where all new flavour structures in the quark sector are parametrized by elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, together with the ratio of vacuum expectation values of the Higgs doublets in the Higgs basis defined by the symmetry. We extend these scenarios to the leptonic sector with the Pontecorvo-Maki-Nakagawa-Sakata matrix playing a r\^ ole similar to the CKM matrix in the quark sector., Comment: Proceedings of the Corfu Summer Institute 2012 "School and Workshops on Elementary Particle Physics and Gravity" September 8-27, 2012 Corfu, Greece. Write-up of two invited Workshop talks given separately by the two authors with titles: "New Physics in the Flavour Sector in the Presence of Heavy Fermions" (GCB) and "Minimal Flavour Violation with Two Higgs Doublets" (MNR)

We analyze the scalar sector properties of a general class of two-Higgs-doublet models which has a global U(1) symmetry in the quartic terms. We find constraints on the parameters of the potential from the considerations of unitarity of scattering amplitudes, the global stability of the potential and the $\rho$-parameter. We concentrate on the spectrum of the non-standard scalar masses in the decoupling limit which is preferred by the Higgs data at the LHC. We exhibit charged-Higgs induced contributions to the diphoton decay width of the 125\,GeV Higgs boson and its correlation with the corresponding $Z\gamma$ width., Comment: 12 pages, 15 eps figure files; minor modifications made and a few references added