Search

We study the flavor invariants of the SM augmented by one singlet vector-like quark. Aided by the Hilbert series, we construct all the basic invariants with which any flavor invariant can be written as a polynomial. In special, this theory contains one CP odd invariant of degree six which has degree much lower than the usual Jarlskog invariant of the SM. We find the nonlinear polynomial relations (syzygies) of lowest degrees involving these basic invariants, including the expression of the square of the CP odd invariant of lowest degree in terms of CP even invariants. The $SU(3)$ identity underlying this syzygy is uncovered in terms of invariant tensors, which can be applied to rewrite any square of a CP odd invariant of the same form, involving three hermitean matrices of size three. We demonstrate by an example that there is CP violation that is not detected by the CP odd invariants proposed in the literature so far but it can be detected with the full list of CP odd invariants found here., Comment: 24pp, some tables and many figure files. v2: the set of basic invariants can be extended to the case of the full U(4) weak basis transformations including the VLQ; see around eq.(59). Ap.A now includes the graded Hilbert series. Accepted for JHEP

We investigate how the solution to the strong CP problem and the explanation for the observed fermion mass hierarchies can be intrinsically related. Specifically, we explore the Nelson-Barr mechanism and identify its "seesaw limit", where light quark masses are suppressed by large CP-violating terms. Upon adding three (two) vector-like quarks that mix with the down-type (up-type) quark sector of the Standard Model, we demonstrate how the lack of CP violation in the strong sector and the observed quark mass hierarchy can be simultaneously achieved., Comment: As accepted for publication in PLB. This paper is dedicated to the memory of our friend and collaborator, Prof. Alex Gomes Dias (1977-2024). He will be fondly remembered for his remarkable knowledge, tireless dedication to science and generous heart

The seesaw extension of the SM explains the tiny neutrino masses and it is accompanied by many CP violating phases. We study the case where all leptonic CP violation arises from the soft breaking in the heavy Majorana mass matrix. Parameter counting reveals that one less parameter is needed to describe this case. This reduction leads to restrictions on the parameter space of heavy neutrinos. We analyze the minimal seesaw case in detail and find that mass degeneracy of heavy neutrinos is not possible for certain values of the CP phases., Comment: 29pp, 8 figures. To appear in PRD

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

Nelson-Barr models solve the strong CP problem based on spontaneous CP violation and generically requires vector-like quarks (VLQs) mixing with standard quarks to transmit the CP violation. We devise an explicit parametrization for the case of two VLQs of either down-type or up-type and quantitatively study several aspects including the hierarchy of the VLQ Yukawas and their irreducible contribution to $\bar{\theta}$. In particular, with the use of the parametrization, we show that a big portion of the parameter space for two up-type VLQs at the TeV scale is still allowed by the constraint on $\bar{\theta}$, although this case had been previously shown to be very restricted based on estimates.

One simple way to lower the scale of the seesaw mechanism that generates neutrino masses is to attribute part of their smallness to a suppressed vacuum expectation value of a second Higgs doublet as in the neutrinophilic 2HDM or in the type IB seesaw model. On that structure we add one charged singlet scalar to induce a chirally enhanced contribution to $(g-2)_\mu$ with the same righthanded neutrinos of the seesaw. We discuss the interplay of generating the necessary contribution to the latter with lepton flavor violation which is also necessarily brought to low scale. We show that it is possible to explain $(g-2)_\mu$ even for heavy neutrino masses of order of a few TeV., Comment: Complies with the most-up-to-date experimental value for g-2. References added, title slightly changed, sections 1 and 5 improved

Leptonic CP violation is yet to be confirmed as an additional source of CP violation in fundamental interactions. We study the case where leptonic CP violation is spontaneous and is induced by the mixing with a heavy charged vector-like lepton (VLL). We show that the non-decoupling of this VLL is linked with the presence of CP violation and its coupling with the SM leptons are partly fixed from the SM Yukawas. Due to the large leptonic mixing angles, these couplings are typically of the same order and there is no flavor preference. Strong but not definitive constraints come from charged lepton flavor violating processes because the VLL can decouple from one or two leptonic flavors in very special points of parameter space. These special points are very sensitive to the neutrino Majorana phases., Comment: Complies with published version

The Nelson-Barr (NB) mechanism to solve the strong CP problem assumes CP conservation, arranges vanishing $\bar{\theta}$ at tree-level and requires vector-like quarks (VLQs) to transmit the CP breaking to the SM. We analyze the flavor constraints coming from the presence of one such down type VLQ of NB type by performing a global fit on the relevant flavor observables. A comparison is made to the case of one generic VLQ. We find that the allowed parameter space for the VLQ Yukawa couplings and the mixing to the SM are confined to a region much smaller than in the generic case, making the NB case falsifiable in principle., Comment: Appendices added

We formulate three-flavor type-I leptogenesis in the $\mu\tau$ basis which is convenient because in the three-flavor regime, both $\mu$ and $\tau$ charged lepton Yukawa interactions are in thermal equilibrium and the thermal bath is symmetric under the exchange $\mu \leftrightarrow \tau$. We apply this formalism to models with $\mu\tau$-reflection $\mathsf{CP}^{\mu\tau}$ symmetry. We confirm the previous result that leptogenesis fails in the three-flavor regime with exact $\mathsf{CP}^{\mu\tau}$ symmetry. Allowing $\mathsf{CP}^{\mu\tau}$ symmetry to be broken to various degrees, we show that leptogenesis can be successful in the three-flavor regime only in certain tuned parameter space, which could further imply additional symmetry is at play. As a bonus, we derive analytical expressions which could be utilized whenever the branching ratios for the decays to $\mu$ and $\tau$ flavors are equal or approximately so., Comment: 22 pages, 7 figures, 4 appendices

The Nelson-Barr mechanism to solve the strong CP problem requires vector-like quarks (VLQs) to transmit the spontaneous CP breaking to the SM. We study the scenario where only these VLQs are within reach at the TeV scale while the spontaneous CP breaking sector is inaccessible. We investigate how these VLQs of Nelson-Barr type differ from generic VLQs and find from parameter counting that one less parameter is needed. In particular, for one VLQ of Nelson-Barr type, there is only one CP odd quantity that is responsible for all CP violation. In this case, we solve the technical problem of parametrizing only the new physics parameters while keeping the SM parameters as independent inputs. For one down-type VLQ, the model is largely flavor safe because the VLQ couplings to the SM up quarks and the $W$ are hierarchically smaller for lighter quarks., Comment: Slightly updates; references and appendix added. Comply with published version

A very simple model is presented where all CP violation in Nature is spontaneous in origin. The CKM phase is generated unsuppressed and the strong CP problem is solved with only moderately small couplings between the SM and the CP violation sector or mediator sector because corrections to $\bar{\theta}$ arise only at two loops. The latter feature follows from an underlying unconventional CP symmetry of order 4 imposed in the sectors beyond the SM composed of only two vector-like quarks of charge $-1/3$ and one complex scalar singlet. No additional symmetry is necessary to implement the Nelson-Barr mechanism., Comment: Comments added, comply with published version

We present a model based on the $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ gauge symmetry that relates the mass hierarchy of the fermions with the solution to the strong CP problem through the $U(1)_{PQ}$ Peccei-Quinn symmetry. This last symmetry arises accidentally with the imposition of a discrete $Z_9$ symmetry, which also secludes the different scales in the double seesaw mechanism taking place in the neutrino sector. The symmetry breakdown is performed by three scalar triplets plus a scalar singlet hosting an axion field, whose particle excitation can be a component of dark matter. We show a mechanism where a small effective vev is generated for a scalar triplet which is supposed to have a bare mass above the energy scale where the $SU(3)_L\otimes U(1)_X$ symmetry is broken. Combined with the energy scale in which the $U(1)_{PQ}$ is broken, such a mechanism gives rise to a natural hierarchy to the fermions. Beyond the Standard Model particle content, the model predicts an invisible axion, $a$, three GeV neutrinos, $N_{iL}$, plus several new particles at the TeV scale which are: five vector bosons, $U^\pm$, $V^0$, $V^{0\dagger}$, and $Z^\prime$; one up-type $U$, and two down-type $D_a$ quarks; and at least a CP-even, $H_1$, plus non-hermitian neutral, $\phi^0$, $\phi^{0\dagger}$, scalar bosons. The model may be tested by looking for the possible production of such particles at the LHC., Comment: 24 pages

The $\mu\tau$-reflection symmetric neutrino mass matrix can accommodate all known neutrino mixing angles, with maximal atmospheric angle fixed, and predicts all the unknown CP phases of the lepton sector but is unable to predict the absolute neutrino mass scale. Here we present a highly predictive scenario where $\mu\tau$-reflection is combined with a discrete abelian symmetry to enforce a texture-zero in the mass matrix of the heavy right-handed neutrinos that generate the light neutrino masses. Such a restriction reduces the free parameters of the low energy theory to zero and the absolute neutrino mass scale is restricted to few discrete regions, three in the few meV range and one extending up to around 30 meV. The heavy neutrino sector is dependent only on two free parameters which are further restricted to small regions from the requirement of successful leptogenesis. Mass degenerate heavy neutrinos are possible in one case but there is no resonant enhancement of the CP asymmetry., Comment: 22 pages, 8 figures. One figure on neutrinoless double beta decay added. Published version

We review the current status of the data on neutrino masses and lepton mixing and the prospects for measuring the CP-violating phases in the lepton sector. The possible connection between low energy CP violation encoded in the Dirac and Majorana phases of the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix and successful leptogenesis is emphasized in the context of seesaw extensions of the Standard Model with a flavor symmetry Gf (and CP symmetry)., Comment: 36 pages, 4 figures. Chapter 6 of the review volume "Leptogenesis: Current Challenges for Model Building, Phenomenology and Non-Equilibrium Field Theory"

We develop a ${\rm SU}(3)_C\otimes {\rm SU}(3)_L\otimes {\rm U}(1)_X$ model where the number of fermion generations is fixed by cancellation of gauge anomalies, being a type of 3-3-1 model with new charged leptons. Similarly to the economical 3-3-1 models, symmetry breaking is achieved effectively with two scalar triplets so that the spectrum of scalar particles at the TeV scale contains just two CP even scalars, one of which is the recently discovered Higgs boson, plus a charged scalar. Such a scalar sector is simpler than the one in the Two Higgs Doublet Model, hence more attractive for phenomenological studies, and has no FCNC mediated by scalars except for the ones induced by the mixing of SM fermions with heavy fermions. We identify a global residual symmetry of the model which guarantees mass degeneracies and some massless fermions whose masses need to be generated by the introduction of effective operators. The fermion masses so generated require less fine-tuning for most of the SM fermions and FCNC are naturally suppressed by the small mixing between the third family of quarks and the rest. The effective setting is justified by an ultraviolet completion of the model from which the effective operators emerge naturally. A detailed particle mass spectrum is presented, and an analysis of the $Z^\prime$ production at the LHC run II is performed to show that it could be easily detected by considering the invariant mass and transverse momentum distributions in the dimuon channel., Comment: To appear in PRD. 24 pages, 4 figures

The Two-Higgs-Doublet model (2HDM) is a simple and viable extension of the Standard Model (SM) with a scalar potential complex enough that two minima may coexist. In this work we investigate if the procedure to identify our vacuum as the global minimum by tree-level formulas carries over to the one-loop corrected potential. In the CP conserving case, we identify two distinct types of coexisting minima --- the regular ones (moderate $\tan\beta$) and the non-regular ones (small or large $\tan\beta$) --- and conclude that the tree level expectation fails only for the non-regular type of coexisting minima. For the regular type, the sign of $m^2_{12}$ already precisely indicates which minima is the global one, even at one-loop., Comment: to appear in JHEP

The $\mu\tau$-reflection symmetry is a simple symmetry capable of predicting all the unknown CP phases of the lepton sector and the atmospheric angle but too simple to predict the absolute neutrino mass scale or the mass ordering. We show that by combining it with a discrete abelian symmetry in a nontrivial way we can additionally enforce a texture-zero and obtain a highly predictive scenario where the lightest neutrino mass is fixed to be in the few meV range for two normal ordering (NO) solutions or in the tens of meV in one inverted ordering (IO) solution. The rate for neutrinoless double beta decay is predicted to be negligible for NO or have effective mass $m_{\beta\beta}\approx 14\text{ -- }29\,{\rm meV}$ for IO, right in the region to be probed in future experiments., Comment: 8 pp., 1 figure. v2. updates references and few words. To appear in JHEP

The combination of $\nu_\mu$-$\nu_\tau$ exchange together with CP conjugation in the neutrino sector (known as $\mathrm{CP}^{\mu\tau}$ symmetry or $\mu\tau$-reflection) is known to predict the viable pattern: $\theta_{23}=45^\circ$, maximal Dirac CP phase and trivial Majorana phases. We implement such a CP symmetry as a new CP symmetry in theories with $A_4$ flavor. The implementation in a complete renormalizable model leads to a new form for the neutrino mass matrix that leads to further predictions: normal hierarchical spectrum with lightest mass and $m_{\beta\beta}$ ($0\nu\beta\beta$) of only few meV, and either $\nu_1$ or $\nu_2$ has opposite CP parity. An approximate $L_\mu-L_\tau$ symmetry arises naturally and controls the flavor structure of the model. The light neutrino masses are generated by the extended seesaw mechanism with 6 right-handed neutrinos (RHNs). The requirement of negligible one-loop corrections to light neutrino masses, validity of the extended seesaw approximation and not too long-lived BSM states to comply with BBN essentially restricts the parameters of the model to a small region: three relatively light right-handed neutrinos at the GeV scale, heavier neutrinos at the electroweak scale and Yukawa couplings smaller than the electron Yukawa. Such a small Yukawa couplings render these RHNs unobservable in terrestrial experiments., Comment: 23pp, 7 figs; v2: published version with small updates in text

We discuss gauge models incorporating $\mu-\tau$ flavored CP symmetry (called CP$^{\mu\tau}$ in the text) in combination with $L_\mu-L_\tau$ invariance to understand neutrino mixings and discuss their phenomenological implications. We show that viable leptogenesis in this setting requires that the lightest right-handed neutrino mass must be between $10^9-10^{12}$ GeV and for effective two hierarchical right-handed neutrinos, leptogenesis takes place only in a narrower range of $5\times 10^{10}-10^{12}$ GeV. A multi-Higgs realization of this idea implies that there must be a pseudoscalar Higgs boson with mass less than 300 GeV. Generically, the vev alignment problem can be naturally avoided in our setting., Comment: 34pp. v3: matches journal version

Light pseudoscalars known as axion like particles (ALPs) may be behind physical phenomena like the Universe transparency to ultra-energetic photons, the soft $\gamma$-ray excess from the Coma cluster, and the 3.5 keV line. We explore the connection of these particles with the inverse seesaw (ISS) mechanism for neutrino mass generation. We propose a very restrictive setting where the scalar field hosting the ALP is also responsible for generating the ISS mass scales through its vacuum expectation value on gravity induced nonrenormalizable operators. A discrete gauge symmetry protects the theory from the appearance of overly strong gravitational effects and discrete anomaly cancellation imposes strong constraints on the order of the group. The anomalous U$(1)$ symmetry leading to the ALP is an extended lepton number and the protective discrete symmetry can be always chosen as a subgroup of a combination of the lepton number and the baryon number., Comment: 29pp. v4: published version with erratum. Conclusions unchanged

We analyze the compatibility between abelian symmetries acting in two different sectors of a theory using the Smith Normal Form method. We focus on N-Higgs-doublet models (NHDMs) and on the compatibility between symmetries in the Higgs potential and in the Yukawa interactions, which were separately analyzed previous works. It is shown that two equal (isomorphic) symmetry groups that act in two separate sectors are not necessarily compatible in the whole theory and an upper bound is found for the size of the group that can be implemented in the entire NHDM. We also develop useful techniques to analyze compatibility and extend a symmetry from one sector to another. Consequences to the supersymmetric case are briefly discussed., Comment: v2: 40pp; some modifications in text, brief discussion on the supersymmetric case added; to appear in JHEP

An attractive feature of New Physics models with multiple Higgs fields is that they are equipped with discrete symmetry groups in the Higgs and flavour sectors. These symmetry groups are often broken at the global minimum of the Higgs potential, either completely or to a proper subgroup, with certain phenomenological consequences. Here, we systematically explore these symmetry breaking patterns in the scalar sector of the three-Higgs-doublet model (3HDM). We use the full list of discrete symmetry groups allowed in 3HDM, and for each group we find all possible ways it can break by the Higgs vacuum expectation value alignment. We also discuss the interplay between these symmetry groups and various forms of CP-violation in the scalar sector of 3HDM. Not only do our results solve the problem for 3HDM, but they also hint at several general features in multi-scalar sectors., Comment: 24 pages, 5 figures, 2 tables; v2: expanded introduction, matches published version

The recent detection of the cosmic microwave background polarimeter experiment BICEP2 of tensor fluctuations in the B-mode power spectrum basically excludes all plausible axion models where its decay constant is above $10^{13}$ GeV. Moreover, there are strong theoretical, astrophysical, and cosmological motivations for models involving, in addition to the axion, also axion-like particles (ALPs), with decay constants in the intermediate scale range, between $10^9$ GeV and $10^{13}$ GeV. Here, we present a general analysis of models with an axion and further ALPs and derive bounds on the relative size of the axion and ALP photon (and electron) coupling. We discuss what we can learn from measurements of the axion and ALP photon couplings about the fundamental parameters of the underlying ultraviolet completion of the theory. For the latter we consider extensions of the Standard Model in which the axion and the ALP(s) appear as pseudo Nambu-Goldstone bosons from the breaking of global chiral $U(1)$ (Peccei-Quinn (PQ)) symmetries, occuring accidentally as low energy remnants from exact discrete symmetries. In such models, the axion and the further ALP are protected from disastrous explicit symmetry breaking effects due to Planck-scale suppressed operators. The scenarios considered exploit heavy right handed neutrinos getting their mass via PQ symmetry breaking and thus explain the small mass of the active neutrinos via a seesaw relation between the electroweak and an intermediate PQ symmetry breaking scale. We show some models that can accommodate simultaneously an axion dark matter candidate, an ALP explaining the anomalous transparency of the universe for $\gamma$-rays, and an ALP explaining the recently reported 3.55 keV gamma line from galaxies and clusters of galaxies, if the respective decay constants are of intermediate scale., Comment: 43pp, 4 figures. v2: version accepted for publication in JHEP

To study a flavour model with a non-minimal Higgs sector one must first define the symmetries of the fields; then identify what types of vacua exist and how they may break the symmetries; and finally determine whether the remnant symmetries are compatible with the experimental data. Here we address all these issues in the context of flavour models with any number of Higgs doublets. We stress the importance of analysing the Higgs vacuum expectation values that are pseudo-invariant under the generators of all subgroups. It is shown that the only way of obtaining a physical CKM mixing matrix and, simultaneously, non-degenerate and non-zero quark masses is requiring the vacuum expectation values of the Higgs fields to break completely the full flavour group, except possibly for some symmetry belonging to baryon number. The application of this technique to some illustrative examples, such as the flavour groups Delta(27), A4 and S3, is also presented., Comment: 13 pages, 3 figures, title and abstract changed, comments and references added; matches version to appear in The European Physical Journal C

We investigate finite abelian groups which can represent symmetries of the N-Higgs-doublet models with quarks. We build a general formalism based on the powerful method of the Smith normal form and obtain an analytic upper bound on the order of abelian symmetry groups for any N. We investigate in detail the case N=2 and rederive known results in a more compact and intuitive fashion. We also study the NHDM with the maximal finite abelian symmetry for all small N cases up to N=5, and show that in each case all Yukawa textures compatible with such symmetry originate from a unique basic structure. This work opens the way to a systematic exploration of phenomenology of the NHDM with a desired symmetry, and illustrates the power of the Smith normal form technique., Comment: 31 pages, no figures; v2: extra references, matches published version

We classify explicitly all the possible generalized CP (GCP) symmetries that are definable in $\Delta(27)$ flavor models. In total, only 12 transformations are possible. We also show interesting consequences of considering some of them as residual symmetries of the neutrino sector., Comment: 16 pages. Comment on independent consistency condition. To appear in PRD

A generalized CP symmetry for leptons is presented where CP transformations are part of an $S_4$ symmetry that connects different families. We study its implications for lepton mixings in a gauge model realization of the idea using type II seesaw for neutrino masses. The model predicts maximal atmospheric mixing, nonzero $\theta_{13}$ and maximal Dirac phase $\delta_{D}= \pm\pi/2$., Comment: 9pp, 2 figures; v3: matches journal version. To appear in PRD

We propose a simple extension of the electroweak standard model based on the discrete $S_3$ symmetry that is capable of realizing a nearly minimal Fritzsch-type texture for the Dirac mass matrices of both charged leptons and neutrinos. This is achieved with the aid of additional $Z_5$ and $Z_3$ symmetries, one of which can be embedded in $U(1)_{B-L}$. Five complex scalar singlet fields are introduced in addition to the SM with right-handed neutrinos. Although more general, the modified texture of the model retains the successful features of the minimal texture without fine-tuning; namely, it accommodates the masses and mixing of the leptonic sector and relates the emergence of large leptonic mixing angles with the seesaw mechanism. For large deviations of the minimal texture, both quasidegenerate spectrum or inverted hierarchy are allowed for neutrino masses., Comment: 11pp, 2 figures. v2: vev alignment addressed, additional analysis performed; to appear in PRD

We show that in the multi-Higgs extension of minimal supersymmetric standard model, which has N-pairs of Higgs doublets (called NHMSSM), it is impossible to break CP spontaneously, if we do not allow for fine-tuning relations between parameters. The result holds true even in the presence of spontaneous R-parity breaking., Comment: 11pp. REVTeX4. v2: some typos corrected

We study the implementation of global $SO(4)\sim SU(2)_L\otimes SU(2)_R$ symmetry in general potentials with N-Higgs-doublets in order to obtain models with custodial $SO(3)_C$ symmetry. We conclude that any implementation of the custodial SO(4) symmetry is equivalent, by a basis transformation, to a canonical one if $SU(2)_L$ is the gauge factor, $U(1)_Y$ is embedded in $SU(2)_R$ and we require $N$ copies of the doublet representation of $SU(2)_R$. The invariance by SO(4) automatically leads to a CP invariant potential and the basis of the canonical implementation of SO(4) is aligned to a basis where CP-symmetry acts in the standard fashion. We show different but equivalent implementations for the 2HDM, including an implementation not previously considered., Comment: 22pp, REVTeX4. Published version

We show there is a non-null probability to produce neutrinos of the ``wrong'' type in general decays, within the SM augmented by the known three massive neutrinos and nontrivial mixing. Such effect is equivalent to an intrinsic flavor violation (lepton flavor violation) at creation without requiring neutrino propagation. The exact amount of flavor violation depends on the neutrino flavor state to be detected. For realistic conditions, the violation is tiny but much larger than other indirect lepton flavor violation processes not involving neutrinos as final states. For neutrinos produced in a continuous spectrum, we show the effect is larger, in relative terms, for neutrinos produced in the low-energy portion of the spectrum. For muon decay, if the usual neutrino flavor state is assumed a flavor violation as large as 1\% is possible in the channel $\mu^+\to\bnu_\tau e^+ \nu_e$. We also discuss the relation between flavor violation and flavor indefiniteness for neutrino flavor states., Comment: 27pp

We study the scalar sector of the general N-Higgs-doublet model via geometric constructions in the space of gauge orbits. We give a detailed description of the shape of the orbit space both for general N and, in more detail, for N=3. We also comment on remarkable analogies between NHDM and quantum information theory., Comment: 27 pages, 2 figures

It is shown that intrinsic neutrino flavor violation invariably occurs when neutrinos are created within the SM augmented by the known massive neutrinos, with mixing and nondegenerate masses. The effects are very small but much greater than the naive estimate $\Delta m^2/E_\nu^2$ or the branching ratio of indirect flavor violating processes such as $\mu\to e\gamma$ within the SM. We specifically calculate the probability (branching ratio) of pion decay processes with flavor violation, such as $\pi\to \mu\bar{\nu}_e$, showing nonzero results., Comment: v3: published version

The possibility to access the absolute neutrino mass scale through the measurement of the wrong helicity contribution of charged leptons is investigated in pion decay. Through this method, one may have access to the same effective mass $m^2_\beta$ extractable from the tritium beta decay experiments for electron neutrinos as well as the analogous effective mass $(m^2_{\nu_\mu})_{\rm eff}$ for muon neutrinos. In the channel $\pi^-\to e^-\bar{\nu}$, the relative probability of producing an antineutrino with left helicity is enhanced if compared with the naive expectation $(m_\nu/2E_\nu)^2$. The possibility to constrain new interactions in the context of Two-Higgs-Doublet models is also investigated., Comment: v2: References and comments added. v3: reference numbers changed. Accepted for Mod. Phys. Lett. A

An exactly solvable Quantum Field Theory (QFT) model of Lee-type is constructed to study how neutrino flavor eigenstates are created through interactions and how the localization properties of neutrinos follows from the parent particle that decays. The two-particle states formed by the neutrino and the accompanying charged lepton can be calculated exactly as well as their creation probabilities. We can show that the coherent creation of neutrino flavor eigenstates follows from the common negligible contribution of neutrino masses to their creation probabilities. On the other hand, it is shown that it is not possible to associate a well defined "flavor" to mixed states of charged leptons., Comment: v2: 25pp in preprint form, typos corrected and references added, one paragraph around Eq.(90) added in conclusions

A direct connection between physical parameters of general Two-Higgs-Doublet Model (2HDM) potentials after electroweak symmetry breaking (EWSB) and the parameters that define the potentials before EWSB is established. These physical parameters, such as the mass matrix of the neutral Higgs bosons, have well defined transformation properties under basis transformations transposed to the fields after EWSB. The relations are also explicitly written in a basis covariant form. Violation of these relations may indicate models beyond 2HDMs. In certain cases the whole potential can be defined in terms of the physical parameters. The distinction between basis transformations and reparametrizations is pointed out. Some physical implications are discussed., Comment: 11 pages. 1 figure. v2: references and comments added

Conditions for CP violation in the scalar potential sector of general N-Higgs-doublet models (NHDMs) are analyzed from a group theoretical perspective. For the simplest two-Higgs-doublet model (2HDM) potential, a minimum set of conditions for explicit and spontaneous CP violation is presented. The conditions can be given a clear geometrical interpretation in terms of quantities in the adjoint representation of the basis transformation group for the two doublets. Such conditions depend on CP-odd pseudoscalar invariants. When the potential is CP invariant, the explicit procedure to reach the real CP-basis and the explicit CP transformation can also be obtained. The procedure to find the real basis and the conditions for CP violation are then extended to general NHDM potentials. The analysis becomes more involved and only a formal procedure to reach the real basis is found. Necessary conditions for CP invariance can still be formulated in terms of group invariants: the CP-odd generalized pseudoscalars. The problem can be completely solved for three Higgs-doublets., Comment: RevTeX4 used. Minor modifications, in particular, the parameter counting of $Z$. v3: Eqs.(28)-(31) corrected

We consider a model with soft CP violation which accommodate the CP violation in the neutral kaons even if we assume that the Cabibbo-Kobayashi-Maskawa mixing matrix is real and the sources of CP violation are three complex vacuum expectation values and a trilinear coupling in the scalar potential. We show that for some reasonable values of the masses and other parameters the model allows to explain all the observed CP violation processes in the $K^0$-$\bar{K}^0$ system., Comment: 19 pages, RevTeX 4. Minor modifications

Neutrino oscillations are treated from the point of view of relativistic first quantized theories and compared to second quantized treatments. Within first quantized theories, general oscillation probabilities can be found for Dirac fermions and charged spin 0 bosons. A clear modification in the oscillation formulas can be obtained and its origin is elucidated and confirmed to be inevitable from completeness and causality requirements. The left-handed nature of created and detected neutrinos can also be implemented in the first quantized Dirac theory in presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. Concerning second quantized approaches, it is shown in a calculation using virtual neutrino propagation that both neutrinos and antineutrinos may also contribute as intermediate particles. The sign of the contributing neutrino energy may have to be chosen explicitly without being automatic in the formalism. At last, a simple second quantized description of the flavor oscillation phenomenon is devised. In this description there is no interference terms between positive and negative components, but it still gives simple normalized oscillation probabilities. A new effect appearing in this context is an inevitable but tiny violation of the initial flavor of neutrinos. The probability loss due to the conversion of left-handed neutrinos to right-handed neutrinos is also presented., Comment: version accepted for publication

General Fierz-type identities are examined and their well known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral basis for the complex $4\times4$ matrices. Other completeness relations for the fundamental representations of SU(N) algebras can be extracted using the same reasoning., Comment: 9pages. Few sentences modified in introduction and in conclusion. Typos corrected. An example added in introduction. Title modified

Arguments continue to appear in the literature concerning the validity of the standard oscillation formula. We point out some misunderstandings and try to explain in simple terms our viewpoint., Comment: 4 pages [1 colored LaTex-fig], AMS-TeX

We give a detailed analysis of the oscillation formula within the context of the wave packet formalism. Particular attention is made to insure flavor eigenstate creation in the physical cases (Delta p not equal 0). This requirement imposes non instantaneous particle creation in all frames. It is shown that the standard formula is not only exact when the mass wave packets have the same velocity, but it is a good approximation when minimal slippage occurs. For more general situations the oscillation formula contains additional arbitrary parameters, which allows for the unknown form of the wave packet envelope., Comment: 15 pages [8 figs], AMS-TeX