We study the capability of generating correct flavor neutrino mass matrix in a scalar clockwork model. First, we assume that the flavor structure is controlled by the Yukawa couplings as same as the standard model. In this case, the correct flavor neutrino mass matrix could be obtained by appropriate Yukawa couplings $Y_{\ell^\prime\ell}$ where $\ell^\prime, \ell = e, μ, τ$. Next, we assume that the Yukawa couplings are extremely democratic $|Y_{\ell^\prime\ell} |=1$. In this case, the model parameters of the scalar clockwork sector, such as the site number of a clockwork gear in a clockwork chain, should have the flavor indices $\ell^\prime$ and/or $\ell$ to generate correct flavor neutrino mass matrix. We show some examples of the assignments of the flavor indices which can yield the correct flavor neutrino mass matrix.
Clockwork models can explain the flavor hierarchies in the Standard Model quark and lepton spectrum. We construct supersymmetric versions of such flavor clockwork models. The zero modes of the clockwork are identified with the fermions and sfermions of the Minimal Supersymmetric Standard Model. In addition to generating a hierarchical fermion spectrum, the clockwork also predicts a specific flavor structure for the soft SUSY breaking sfermion masses. We find sizeable flavor mixing among first and second generation squarks. Constraints from Kaon oscillations require the masses of either squarks…
The clockwork mechanism provides a natural way to obtain hierarchical masses and couplings in a theory. We propose a clockwork model that has nine clockwork generations. In this model, the candidates of the origin of the neutrino mixings are nine Yukawa mass matrix elements $Y^{aβ}$ that connect neutrinos and clockwork fermions, nine clockwork mass ratios $q_{aβ}$, and nine numbers of clockwork fermions $n_{aβ}$, where $a, β=1,2,3$. Assuming $|Y^{aβ}|=1$, the neutrino mixings originate from the pure clockwork sector. We show that the observed neutrino mixings are exactly obtained from a clockw…
We propose a simple clockwork model of flavor which successfully generates the Standard Model flavor hierarchies from random order-one couplings. With very few parameters we achieve distributions of models in excellent agreement with observation. We explain in some detail the interpretation of our mechanism as random localization of zero modes in theory space. The scale of the vectorlike fermions is mostly constrained by lepton flavor violation with secondary constraints arising from rare meson decays.
We introduce a set of clockwork models of flavor that can naturally explain the large hierarchies of the Standard Model quark masses and mixing angles. Since the clockwork only contains chains of new vector-like fermions without any other dynamical fields, the flavor constraints allow for relatively light new physics scale. For two benchmarks with gear masses just above 1 TeV, allowed by flavor constraints, we discuss the collider searches and the possible ways of reconstructing gear spectra at the LHC. We also examine the similarities and differences with the other common solutions to the SM …
In this paper we present an augmented version of the Abelian scalar clockwork model to generate geometrically suppressed vacuum expectation values (vev) of the pseudo Nambu-Goldstone bosons, that we call the clockworked vevs. We briefly comment on generalization of the setup and possible 5D UV realizations. We demonstrate how tiny neutrino mass can be generated by clockworking a weak scale vev.
The clockwork is an extra-dimensional set-up for generating light particles with exponentially suppressed or hierarchical couplings of light particles with N massive states having comparable masses near the threshold scale of the mechanism in theories which contain no small parameters at the fundamental level. We explore the prospect of charged lepton flavour violation (cLFV) in a clockwork framework which encompasses Dirac mass terms as well as Majorana mass terms for the new clockwork fermions. We deive the masses of the non zero clockwork Majorana masses, and new particles in a clockwork fr…
Clockwork (CW) mechanism can explain the smallness of neutrino masses without introducing unnaturally small input parameters. In this paper we study the simplest CW neutrino model, the "uniform" clockwork, as well as a broader class of "generalized" clockwork models. We derive constraints on such models from lepton-flavor violating processes, as well as precision electroweak fits. These constraints allow excited CW neutrino states with masses of order 100 GeV -- 1 TeV, within reach of the LHC and proposed lepton colliders, as long as the input neutrino Yukawa coupling is of order $10^{-1}-10^{…
We propose new mechanisms for small neutrino masses based on clockwork mechanism. The Standard Model neutrinos and lepton number violating operators communicate through the zero mode of clockwork gears, one of the two couplings of the zero mode is exponentially suppressed by clockwork mechanism. Including all known examples for the clockwork realization of the neutrino masses, different types of models are realized depending on the profile and chirality of the zero mode fermion. Each type of realization would have phenomenologically distinctive features with the accompanying heavy neutrinos.
The clockwork mechanism, which can naturally explain the origin of small numbers, is implemented in $SO(10)$ grand unified theories to address the origin of hierarchies in fermion masses and mixings. We show that a minimal Yukawa sector involving a $10_H$ and $\overline{126}_H$ of Higgs bosons, extended with two clockwork chains consisting of $16+\overline{16}$ vector-like fermions, can explain the hierarchical patterns with all the Yukawa couplings being of order one. Emergence of a realistic mass spectrum does not require any symmetry that distinguishes the three generations. We develop cloc…
We present realistic models of flavor in SU(5) and SO(10) grand unified theories (GUTs). The models are renormalizable and do not require any exotic representations in order to accommodate the necessary GUT breaking effects in the Yukawa couplings. They are based on a simple clockwork Lagrangian whose structure is enforced with just two (one) vectorlike U(1) symmetries in the case of SU(5) and SO(10) respectively. The inter-generational hierarchies arise spontaneously from products of matrices with order one random entries.
Cosmic inflation driven by the vacuum energy associated with the $D$-term of a supersymmetric abelian gauge group and a possible existence of long-range force mediated by an ultra-light gauge boson $Z^\prime$ are two extreme examples of models based on extra $U(1)$ symmetries. Large vacuum energy sets the scale of inflation while the scales of long-range forces induced by anomaly free extra gauged $U(1)$ symmetries are constrained by neutrino oscillations, binary pulsar timings and invisible neutrino decay. There exists a difference of about 40 orders of magnitude between the scales of these t…
We consider various bulk fields with general dilaton couplings in the linear dilaton background in five dimensions as the continuum limit of clockwork models. We show that the localization of the zero modes of bulk fields and the mass gap in the KK spectrum depend not only on the bulk dilaton coupling, but also on the bulk mass parameter in the case of a bulk fermion. The consistency from universality and perturbativity of gauge couplings constrain the dilaton couplings to the brane-localized matter fields as well as the bulk gauge bosons. Constructing the Clockwork Standard Model (SM) in the …
In this paper, we study the effect of active-neutrino-sterile-neutrino mixing in the expected high-energy astrophysical neutrino flavor content. Non-unitarity in the measurement of the three active neutrinos can be due to the existence of sterile neutrino states. We introduce the concept of the four-flavor tetrahedron in order to visualize the lack of unitarity in the astrophysical neutrino three-flavor triangle. We demonstrate that active-sterile neutrino mixings modify the allowed region of the astrophysical flavor ratio from the standard case. However, a projection of the four-flavor tetrah…
The spin flavor precession (SFP) is investigated in the three neutrino generation case assuming that the neutrinos are Majorana type. Approximate analytical formulas including all transition magnetic moments are provided for the electron neutrino survival probability and electron neutrino -> electron anti-neutrino transition probability in the SFP framework. The accuracy of the formulas is checked out for two different magnetic field profiles in the Sun.
We extend the work of Carone, Chaurasia and Vasquez on non-supersymmetric models of flavor based on the double tetrahedral group. Three issues are addressed: (1) the sector of flavor-symmetry-breaking fields is simplified and their potential studied explicitly, (2) a flavorful axion is introduced to solve the strong CP problem and (3) the model is extended to include the neutrino sector. We show how the model can accommodate the strong hierarchies manifest in the charged fermion Yukawa matrices, while predicting a qualitatively different form for the light neutrino mass matrix that is consiste…
In this paper we discuss the ontology of flavor states of oscillating neutrinos. While an heuristic approach to this subject, experimentally successful in the high energy regime, is generally adopted, a logically consistent definition of flavor states describing neutrinos produced and detected in weak processes is still desirable and essential from a theoretical perspective. Here we briefly review basic facts and present some arguments which suggest that the definition of flavor states as eigenstates of flavor charges is the most reasonable one.
The magic texture is one of the successful textures of the flavor neutrino mass matrix for the Majorana type neutrinos. The name "magic" is inspired by the nature of the magic square. We estimate the compatibility of the magic square with the Dirac, instead of the Majorana, flavor neutrino mass matrix. It turned out that some parts of the nature of the magic square are appeared approximately in the Dirac flavor neutrino mass matrix and the magic squares prefer the normal mass ordering rather than the inverted mass ordering for the Dirac neutrinos.
In this paper, we discuss neutrino mass eigenvalues for four flavor neutrino mixing. An extra mass states, in four flavor mixing and possible various combination of CP violating Majorana phases effects the neutrino mass eigenvalues. We have considered the effective Majorana mass m_{e}, related for \,\left(ββ\right)_{0ν\,} decay. In calculation, we consider two different neutrino mass orders, normal and inverted. We find the limits for neutrino mass eigenvalue m_{i} in the different neutrino mass spectrum and the sum of all four neutrino masses is \text{Σ}\text{\ensuremath{\equiv}}m_{1}+m_{2}+m…
Can we observe the solar eclipses in the neutrino light? In principle, this is possible by identifying the lunar matter effects on the flavor conversions of solar neutrinos when they traverse the Moon before reaching the detectors at the Earth. Unfortunately, we show that the lunar matter effects on the survival probability of solar $^8{\rm B}$ neutrinos are suppressed by an additional factor of $1.2\%$, compared to the day-night asymmetry. However, we point out that the matter effects on the flavor conversions of high-energy astrophysical neutrinos, when they propagate through the Sun, can be…
In the context of quantum field theory, we derive flavor energy uncertainty relations for neutrino oscillations. By identifying the non conserved flavor charges with the clock observables, we arrive at the Mandelstam Tamm version of time energy uncertainty relations. In the ultrarelativistic limit these relations yield the well known condition for neutrino oscillations. Ensuing non relativistic corrections to the latter are explicitly evaluated. The analogy among flavor states and unstable particles and a novel interpretation of our uncertainty relations, based on the unitary inequivalence of …
