Ultraviolet Completion of Flavour Models

Effective Flavour Models do not address questions related to the nature of the fundamental renormalisable theory at high energies. We study the ultraviolet completion of Flavour Models, which in general has the advantage of improving the predictivity of the effective models. In order to illustrate the important features we provide minimal completions for two known A4 models. We discuss the phenomenological implications of the explicit completions, such as lepton flavour violating contributions that arise through the exchange of messenger fields.Comment: 18 pages, 8 figure

Reactor mixing angle from hybrid neutrino masses

In terms of its eigenvector decomposition, the neutrino mass matrix (in the basis where the charged lepton mass matrix is diagonal) can be understood as originating from a tribimaximal dominant structure with small deviations, as demanded by data. If neutrino masses originate from at least two different mechanisms, referred to as "hybrid neutrino masses", the experimentally observed structure naturally emerges provided one mechanism accounts for the dominant tribimaximal structure while the other is responsible for the deviations. We demonstrate the feasibility of this picture in a fairly model-independent way by using lepton-number-violating effective operators, whose structure we assume becomes dictated by an underlying $A_4$ flavor symmetry. We show that if a second mechanism is at work, the requirement of generating a reactor angle within its experimental range always fixes the solar and atmospheric angles in agreement with data, in contrast to the case where the deviations are induced by next-to-leading order effective operators. We prove this idea is viable by constructing an $A_4$-based ultraviolet completion, where the dominant tribimaximal structure arises from the type-I seesaw while the subleading contribution is determined by either type-II or type-III seesaw driven by a non-trivial $A_4$ singlet (minimal hybrid model). After finding general criteria, we identify all the $\mathbb{Z}_N$ symmetries capable of producing such $A_4$-based minimal hybrid models.Comment: 18 pages, 5 figures. v3: section including sum rules added, accepted by JHE

Decaying Dark Matter in the Supersymmetric Standard Model with Freeze-in and Seesaw mechanims

Inspired by the decaying dark matter (DM) which can explain cosmic ray anomalies naturally, we consider the supersymmetric Standard Model with three right-handed neutrinos (RHNs) and R-parity, and introduce a TeV-scale DM sector with two fields \phi_{1,2} and a $Z_3$ discrete symmetry. The DM sector only interacts with the RHNs via a very heavy field exchange and then we can explain the cosmic ray anomalies. With the second right-handed neutrino N_2 dominant seesaw mechanism at the low scale around 10^4 GeV, we show that \phi_{1,2} can obtain the vacuum expectation values around the TeV scale, and then the lightest state from \phi_{1,2} is the decay DM with lifetime around \sim 10^{26}s. In particular, the DM very long lifetime is related to the tiny neutrino masses, and the dominant DM decay channels to \mu and \tau are related to the approximate \mu-\tau symmetry. Furthermore, the correct DM relic density can be obtained via the freeze-in mechanism, the small-scale problem for power spectrum can be solved due to the decays of the R-parity odd meta-stable states in the DM sector, and the baryon asymmetry can be generated via the soft leptogensis.Comment: 24 pages,3 figure

An SO(10) Grand Unified Theory of Flavor

We present a supersymmetric SO(10) grand unified theory (GUT) of flavor based on an $S_4$ family symmetry. It makes use of our recent proposal to use SO(10) with type II seesaw mechanism for neutrino masses combined with a simple ansatz that the dominant Yukawa matrix (the {\bf 10}-Higgs coupling to matter) has rank one. In this paper, we show how the rank one model can arise within some plausible assumptions as an effective field theory from vectorlike {\bf 16} dimensional matter fields with masses above the GUT scale. In order to obtain the desired fermion flavor texture we use $S_4$ flavon multiplets which acquire vevs in the ground state of the theory. By supplementing the $S_4$ theory with an additional discrete symmetry, we find that the flavon vacuum field alignments take a discrete set of values provided some of the higher dimensional couplings are small. Choosing a particular set of these vacuum alignments appears to lead to an unified understanding of observed quark-lepton flavor: (i) the lepton mixing matrix that is dominantly tri-bi-maximal with small corrections related to quark mixings; (ii) quark lepton mass relations at GUT scale: $m_b\simeq m_{\tau}$ and $m_\mu\simeq 3 m_s$ and (iii) the solar to atmospheric neutrino mass ratio $m_\odot/m_{\rm atm}\simeq \theta_{\rm Cabibbo}$ in agreement with observations. The model predicts the neutrino mixing parameter, $U_{e3} \simeq \theta_{\rm Cabibbo}/(3\sqrt2) \sim 0.05$, which should be observable in planned long baseline experiments.Comment: Final version of the paper as it will appear in JHEP

Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models

Recent T2K results indicate a sizeable reactor angle theta_13 which would rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector (1,1,1)^T/sqrt{3}, with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable S4 model in which the 1' and 1" flavons of A4 are unified into a doublet of S4 which is spontaneously broken to A4 by a flavon which enters the neutrino sector at higher order. We study the vacuum alignment in the S4 model and show that it predicts accurate trimaximal mixing with approximate tri-bimaximal mixing, leading to a new mixing sum rule testable in future neutrino experiments. Both A4 and S4 models preserve form dominance and hence predict zero leptogenesis, up to renormalisation group corrections.Comment: 24 pages, 2 figures, version to be published in JHE

The Interplay Between GUT and Flavour Symmetries in a Pati-Salam x S4 Model

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry $S_4$ that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between $\lambda^{-2}$ and $\lambda^2$, with $\lambda\simeq0.2$. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.Comment: 62 pages, 4 figures; references added, version accepted for publication in JHE

Generalised CP and Δ(6n2)\Delta (6n^2) Family Symmetry in Semi-Direct Models of Leptons

We perform a detailed analysis of $\Delta (6n^2)$ family symmetry combined with a generalised CP symmetry in the lepton sector, breaking to different remnant symmetries $G_{\nu}$ in the neutrino and $G_{l}$ in the charged lepton sector, together with different remnant CP symmetries in each sector. We discuss the resulting mass and mixing predictions for $G_{\nu}=Z_2$ with $G_{l}=K_4,Z_p,p>2$ and $G_{\nu}=K_4$ with $G_{l}=Z_2$. All cases correspond to the preserved symmetry smaller than the full Klein symmetry, as in the semi-direct approach, leading to predictions which depend on a single undetermined real parameter, which mainly determines the reactor angle. We focus on five phenomenologically allowed cases for which we present the resulting predictions for the PMNS parameters as a function of $n$, as well as the predictions for neutrinoless double beta decay.Comment: 65 pages, 19 figures, and the predictions for neutrinoless double beta decay are update

Effect of controlled and uncontrolled cooling rate on motility parameters of cryopreserved ram spermatozoa

<p>Abstract</p> <p>Background</p> <p>Ram spermatozoa are sensitive to extreme changes in temperature during the freeze-thaw process. The degree of damage depends on a combined effect of various factors including freezing temperature. The aim of this study was to determine the effects of two cooling method (controlled-rate and uncontrolled-rate) on pre-freezing and post-thaw sperm motility parameters.</p> <p>Results</p> <p>Ejaculates were collected using the artificial vagina from four Chal rams and three replicates of the ejaculates were diluted with a Tris-based extender and packed in 0.25 ml straws. Then, sample processed according to the two methods. Method 1: straws cooled from 37 to 5°C, at a liner rate of -0.3°C/min in a controlled-rate cooling machine (custom-built) and equilibrated at 5°C for 80 min, then the straws were frozen at rate of -0.3°C/min from 5°C to -10°C and -25°C/min from -10°C to -150°C and plunged into liquid nitrogen for storage. Method 2: straws were transferred to refrigerator and maintained at 5°C for 3 h, then the straws were frozen in liquid nitrogen vapor, 4 cm above the liquid nitrogen for 15 min and plunged into liquid nitrogen. Computer-assisted sperm motility analysis was used to analyze sperm motion characteristics.</p> <p>Conclusions</p> <p>Controlled rate of freezing (Method 1) significantly improve the pre-freezing and post-thaw total and progressive motility compared to uncontrolled rate (Method 2). In specific kinetic parameters, Method 1 gives significantly higher value for VSL and VCL in comparison with Method 2. There are no significant differences between the two methods for VAP and LIN. In conclusion, controlled rate of cooling conferred better cryopreserving ability to ram spermatozoa compared to uncontrolled rate of cooling prior to programmable freezing.</p

Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian's approach

Non-Abelian discrete family symmetries play a pivotal role in the formulation of models with tri-bimaximal lepton mixing. We discuss how to obtain symmetries such as A4, semidirect product of Z7 and Z3, and Delta(27) from an underlying SU(3) gauge symmetry. Higher irreducible representations are required to achieve the spontaneous breaking of the continuous group. We present methods of identifying the required vacuum alignments and discuss in detail the symmetry breaking potentials.Comment: 21 page