Based on Friedberg and Lee's geometric picture by which the tribimaximal Pontecorvo-Maki-Nakawaga-Sakata leptonic mixing matrix is constructed, namely, corresponding mixing angles correspond to the geometric angles among the sides of a cube. We suggest that the three realistic mixing angles, which slightly deviate from the values determined for the cube, are due to a viable deformation from the perfectly cubic shape. Taking the best-fitted results of $θ_{12}$ and $θ_{23}$ as inputs, we determine the central value of $\sin^22θ_{13}$ should be 0.0238, with a relatively large error tolerance; this value lies in the range of measurement precision of the Daya Bay experiment and is consistent with recent results from the T2K Collaboration.
We propose octahedral group O_h as the family symmetry of neutrino-lepton sector. We find that O_h contains subgroups Z_2(mu-tau) x Z_2(solar) and Z_4^l for realizing the bimaximal (BM) mixings, theta_{23} = theta_{12} = 45^o and theta_{13}=0^o, where Z_2(mu-tau) x Z_2(solar) and Z_4^l serve as the residual symmetries of neutrinos and charged leptons, respectively. We present geometric interpretations of BM mixing in the octahedron, and construct natural geometrical breaking of Z_4^l, leading to nontrivial deviations from the BM mixings. Our theory makes truly simple predictions of a relativel…
We propose the complex group theoretical Clebsch-Gordon coefficients as a novel origin of CP violation. This is manifest in our model based on SUSY SU(5) combined with the double tetrahedral group, T', as a family symmetry. Due to the presence of the doublet representations in T', there exist complex CG coefficients, leading to explicit CP violation in the model, while the Yukawa couplings and the vacuum expectation values of the scalar fields remain real. The tri-bimaximal neutrino mixing matrix arises from the CG coefficients of T'. In addition to the prediction for theta_{13} ~ (1/ (3\sqrt{…
The moderately large measured value of theta13 signals a departure from the approximate two-flavour oscillation framework. As a consequence, the relation between the value of theta23 in nature, and the mixing angle measured in muon neutrino disappearance experiments is non-trivial. In this paper, we calculate this relation analytically. We also derive the correct conversion between degenerate values of theta23 in the two octants. Through simulations of a muon neutrino disappearance experiment, we show that there are observable consequences of not using the correct relation in calculating oscil…
We present the Bayesian method for evaluating the evidence for a non-zero value of the leptonic mixing angle theta_13 and CP-violation in neutrino oscillation experiments. This is an application of the well-established method of Bayesian model selection, of which we give a concise and pedagogical overview. When comparing the hypothesis theta_13 = 0 with hypotheses where theta_13 > 0 using global data but excluding the recent reactor measurements, we obtain only a weak preference for a non-zero theta_13, even though the significance is over 3 sigma. We then add the reactor measurements one by o…
When solar neutrino and KamLAND data are analyzed separately one finds that, even though allowed regions of neutrino parameters overlap, the values of $δm^2$ and the mixing angle $θ_{12}$ at the $χ^2$ minima are different. We show that a non-zero, but small value of the angle $θ_{13}$ can account for this behavior. From the joint analysis of solar neutrino and KamLAND data we find the best fit value of $\sin^2 2 θ_{13} = 0.01 ^{-0.01}_{+0.09}$.
We show that seesaw models based on flavor symmetries (such as A_4 and Z_7 X Z_3) which produce exact tribimaximal neutrino mixing, also imply a vanishing leptogenesis asymmetry. We show that higher order symmetry breaking corrections in these models can give a non-zero leptogenesis asymmetry and generically also give deviations from tribimaximal mixing and a non-zero theta13 >~ 10^(-2)
We provide a short summary of three-flavour neutrino oscillation parameters as determined from a global fit to 2008 data, and we comment on possible hints in favour of a non-zero value of the mixing angle theta_{13} found in arXiv:0806.2649. We do confirm a hint from solar + KamLAND data at about 1.5 sigma, which can be understood from the recent SNO CC/NC measurment. However, we show that a claimed hint from atmospheric data is much less robust. It depends on details of event rate calculations and treatment of theoretical uncertainties. We could identify two data points showing an 'excess' (a…
We discuss the neutrino oscillations, using texture zero mass matrices for the leptons, including radiative correction. The neutrino mixing angle theta_13 is calculated and agrees with the result of the new Daya Bay experiment.
We study the effects of breaking S3 symmetry in the neutrino mass matrix for the masses and mixing matrix of neutrinos. At zeroth order the model gives degenerate neutrino masses and accommodates tribimaximal mixing. We introduce perturbations in terms of a small and complex parameter. The perturbations are introduced in a manner such that the S3 symmetry is broken by its elements in the same representation. Successive perturbations introduce mass splitting, sizable non-zero reactor mixing angle and CP violation. This scheme of breaking S3 symmetry can reproduce a relatively large reactor mixi…
Recent neutrino oscillation data hint that the smallest neutrino mixing angle theta_{13} is possible to lie in the range 5^\circ \lesssim θ_{13} \lesssim 12^\circ. We show that reasonable perturbations to the democratic mixing pattern, which is geometrically related to the tri-bimaximal mixing pattern through an equal shift θ_* \simeq 9.7^\circ of two large mixing angles, can naturally produce a nearly tri-bimaximal neutrino mixing matrix V with sufficiently large theta_{13}. Two especially simple but viable scenarios of V are proposed and their phenomenological consequences are discussed.
We present a new class of models which produce zero theta (QCD} angle at the tree and one-loop level due to hermiticity of sub-blocks in the extended quark mass matrices. The structure can be maintained typically by non-abelian generation symmetry. Two examples are given for this class of solutions.
We study the effects that a non zero strong-CP-violating parameter theta would have on the deuteron and diproton binding energies and on the triple-alpha process. Both these systems exhibit fine tuning, so it is plausible that a small change in the nuclear force would produce catastrophic consequences. Such a nuclear force is here understood in the framework of an effective Lagrangian for pions and nucleons, and the strength of the interaction varies with theta. We find that the effects are not too dramatic.
In view of the latest T2K and MINOS neutrino oscillation data which hint at a relatively large theta_13, we perform a systematic study of the Majorana neutrino mass matrix M_nu with two independent texture zeros. We show that three neutrino masses (m_1, m_2, m_3) and three CP-violating phases (delta, rho, sigma) can fully be determined from two neutrino mass-squared differences (delta m^2, Delta m^2) and three flavor mixing angles (theta_12, theta_23, theta_13). We find that seven patterns of M_nu (i.e., A_{1,2}, B_{1,2,3,4} and C) are compatible with current experimental data at the 3-sigma l…
The recent analyses of the world neutrino data, including the T2K and MINOS results, point toward a statistically significant deviation of theta13 from zero. In this paper we present a SUSY SU(5) model based on the discrete S4 group which predicts a large theta13 of order lambdaC, lambdaC being the Cabibbo angle. The other mixing angles in the neutrino sector are all compatible with current experimental data. In the quark sector, the entries of the CKM mixing matrix as well as the mass hierarchies in both up and down quark sectors are well reproduced and only a small enhancement is needed to r…
We discuss the bounds on the cosmological lepton number from Big Bang Nucleosynthesis (BBN), in light of recent evidences for a large value of the neutrino mixing angle theta13. The largest asymmetries for electron and muon or tau neutrinos compatible with 4He and 2H primordial yields are computed versus the neutrino mass hierarchy and mixing angles. The flavour oscillation dynamics is traced till the beginning of BBN and neutrino distributions after decoupling are numerically computed. The latter contains in general, non thermal distortion due to the onset of flavour oscillations driven by so…
Solar and KamLAND data are in slight tension when interpreted in the standard two-flavor oscillations framework and this may be alleviated allowing for a non-zero value of the mixing angle theta_13. Here we show that, likewise, non-standard flavor-changing interactions (FCI), possibly intervening in the propagation of solar neutrinos, are equally able to alleviate this tension and therefore constitute a potential source of confusion in the determination of theta_13. By performing a full three-flavor analysis of solar and KamLAND data in presence of FCI we provide a quantitative description of …
We present a simple texture that predicts the cotangent of the solar neutrino mixing angle to be equal to the golden ratio. This prediction is 1.4 standard deviations below the present best-fit value and final SNO and KamLAND data could discriminate it from tri-bi-maximal mixing. The neutrino mass matrix is invariant under a Z_2 x Z'_2 symmetry: that geometrically is a reflection along the diagonal of the golden rectangle. Assuming an analogous structure in the quark sector suggests a golden prediction for the Cabibbo angle, theta_C = pi/4- theta_12 = 13.3 degree, up to uncertainties comparabl…
In a previous paper [Phys. Rev. D 83, 113013 (2011)] we have shown that the solar sector data (solar and KamLAND) are sensitive to the parameter theta_14, encoding the admixture of the electron neutrino with a fourth (essentially) sterile mass eigenstate. In that work we evidenced that such data prefer a non-zero value of theta_14 and that such a preference is completely degenerate with that of non-zero theta_13. In this report we show how the evidence of theta_13 > 0, recently emerged from global neutrino data analyses, lifts such a degeneracy and disfavors the case of sterile neutrino mixing…
To realize the condition of sin^2(2theta_{12})>>sin^2(theta_{13}), we find constraints on flavor neutrino masses M_{ij} (ij=e,μ,τ): C1) c_{23}^2 M_{μμ} + s_{23}^2 M_{ττ} \approx 2 s_{23} c_{23}M_{μτ} + M_{ee} and/or C2) |c_{23}M_{eμ} -s_{23}M_{eτ}|>> |s_{23}M_{eμ} +c_{23}M_{eτ}|, where c_{23}=cos(theta_{23}) (s_{23}=sin(theta_{23})) and theta_{12}, theta_{13} and theta_{23} are the mixing angles for three flavor neutrinos. The applicability of C1) and C2) is examined in models with one massless neutrino and two massive neutrinos suggested by \det(M)=0, where M is a mass matrix constructed from…
Measuring flux ratios of ultra-high energy neutrinos is an alternative method to determine the neutrino mixing angles and the CP phase delta. We conduct a systematic analysis of the neutrino mixing probabilities and of various flux ratios measurable at neutrino telescopes. The considered cases are neutrinos from pion, neutron and muon-damped sources. Explicit formulae in case of mu-tau symmetry and its special case tri-bimaximal mixing are obtained, and the leading corrections due to non-zero theta_{13} and non-maximal theta_{23} are given. The first order correction is universal as it appears…
The newly proposed finite symmetry Sigma(81) is applied to the problem of neutrino tribimaximal mixing. The result is more satisfactory than those of previous models based on A_4 in that the use of auxiliary symmetries (or mechanisms) may be avoided. Deviations from the tribimaximal pattern are expected, but because of its basic structure, only tan^2 (theta_12) may differ significantly from 0.5 (say 0.45) with sin^2 (2 theta_23) remaining very close to one, and theta_13 very nearly zero.
We consider QED on a two-dimensional Euclidean torus with $f$ flavors of massless fermions and flavor-dependent chemical potentials. The dependence of the partition function on the chemical potentials is reduced to a $(2f-2)$-dimensional theta function. At zero temperature, the system can exist in an infinite number of phases characterized by certain values of traceless number densities and separated by first-order phase transitions. Furthermore, there exist many points in the $(f-1)$-dimensional space of traceless chemical potentials where two or three phases can coexist for $f=3$ and two, th…
We perform a systematic study of the modifications to the QCD vacuum energy density $ε_{vac}$ in the zero-temperature case ($T=0$) caused by a small, but non-zero, value of the parameter $θ$, using different effective Lagrangian models which include the flavour-singlet meson field and implement the $U(1)$ axial anomaly of the fundamental theory. In particular, we derive the expressions for the topological susceptibility $χ$ and for the second cumulant $c_4$ starting from the $θ$ dependence of $ε_{vac}(θ)$ in the various models that we have considered. Moreover, we evaluate numerically our resu…
A non-vanishing vacuum expectation value for an antisymmetric tensor field leads to the violation of Lorentz invariance, controlled by the dimension (-2) parameter, theta_{mu nu}. We assume that the zeroth order term in theta-expansion represents the Standard Model and study the effects induced by linear terms in theta_{mu nu}. If coupling to theta_{mu nu} is realized in strongly interacting sector of the theory, the clock comparison experiments place the limit on the possible size of this background at the level of 1/\sqrt{theta}>~5X10^{14} GeV. If the interaction with theta_{mu nu} is initia…
The leptonic mixing angle theta_13 is currently a high-priority topic in the field of neutrino physics, with five experiments under way, searching for neutrino oscillations induced by this angle. We review the phenomenology of theta_13 and discuss the information from present global oscillation data. A description of the upcoming reactor and accelerator experiments searching for a non-zero value of theta_13 is given, and we evaluate the sensitivity reach within the next few years.
Recent results from the Daya Bay and RENO reactor experiments have measured the smallest lepton mixing angle and found it to have a value of theta_13 approximately 9 degrees. This result presents a new challenge for the existing paradigms of discrete flavour symmetries which attempt to describe all quark and lepton masses and mixing angles. Here we propose a Supersymmetric Grand Unified Theory of Flavour based on Delta(96) x SU(5), together with a U(1) x Z3 symmetry, including a full discussion of Delta(96) in a convenient basis. The Grand Delta(96) x SU(5) Flavour Model relates the quark mixi…
We consider chiral perturbation theory (ChPT) with a non-zero theta term. Due to the CP violating term, the vacuum of chiral fields is shifted to a non-trivial element on the SU(N_f) group manifold. The CP violation also provides mixing of different CP eigenstates, between scalar and pseudoscalar, or vector and axialvector operators. We investigate upto O(theta^2) effects on the mesonic two point correlators of ChPT to the one-loop order. We also address the effects of fixing topology, by using saddle point integration in the Fourier transform with respect to theta.
Predictions for a light collective $Θ^+$ baryon state (with strangeness +1) based on the collective quantization of chiral soliton models are shown to be inconsistent with large $N_c$ QCD. The lightest strangeness +1 state to emerge from the analysis has an excitation energy which at large $N_c$ scales as $N_c^0$ while collective quantization is legitimate only for excitations which go to zero as $N_c \to \infty$. This inconsistency strongly suggests that predictions for $Θ^+$ properties based on collective quantization of chiral solitons are not valid.
Reductions from odd to even dimensionalities ($5\to 4$ or $3\to 2$), for which the effective low-energy theory contains chiral fermions, present us with a mismatch between ultraviolet and infrared anomalies. This applies to both local (gauge) and global currents; here we consider the latter case. We show that the mismatch can be explained by taking into account a change in the spectral asymmetry of the massive modes--an odd-dimensional analog of the phenomenon described by the Atiyah-Patodi-Singer theorem in even dimensionalities. The result has phenomenological implications: we present a scen…
It was argued recently that, in general, an arbitrary induced theta vacuum state would be created in the heavy ion collisions, similar to the creation of the disoriented chiral condensatewith an arbitrary isospin direction. It should be a large domain with a wrong theta orientation which will mimic the physics of the world when the fundamental theta is non-zero. I suggest a few simple observables which can (hopefully) be measured on an event by event basis at RHIC, and which uniquely determine whether the induced theta vacuum state is created.
We prove the analyticity of the finite volume QCD partition function for complex values of the theta-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits ^ cusp singularities in the vacuum energy density and never v cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at theta=0 and has an important consequence: the absence of a first order phase transition at theta=0. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vector-like gauge th…
In this work, extending a previous study at zero temperature ($T=0$), we perform a systematic study of the modifications to the QCD vacuum energy density $ε_{vac}$ in the finite-temperature case, above the chiral transition at $T_c$, caused by a nonzero value of the parameter $θ$, using two different effective Lagrangian models which implement the $U(1)$ axial anomaly of the fundamental theory and which are both well defined also above $T_c$. In particular, we derive (and critically compare) the expressions for the topological susceptibility $χ$ and for the second cumulant $c_4$ starting from …
