Proton decay in flux compactifications

We study proton decay in a six-dimensional orbifold GUT model with gauge group $SO(10)\times U(1)_A$. Magnetic $U(1)_A$ flux in the compact dimensions determines the multiplicity of quark-lepton generations, and it also breaks supersymmetry by giving universal GUT scale masses to scalar quarks and leptons. The model can successfully account for quark and lepton masses and mixings. Our analysis of proton decay leads to the conclusion that the proton lifetime must be close to the current experimental lower bound. Moreover, we find that the branching ratios for the decay channels $p \rightarrow e^+\pi^0$ and $p\rightarrow \mu^+\pi^0$ are of similar size, in fact the latter one can even be dominant. This is due to flavour non-diagonal couplings of heavy vector bosons together with large off-diagonal Higgs couplings, which appears to be a generic feature of flux compactifications.Comment: 26 pages, 3 figures, 2 table

Discrete symmetries for electroweak natural type-I seesaw mechanism

The naturalness of electroweak scale in the models of type-I seesaw mechanism with ${\cal O}(1)$ Yukawa couplings requires TeV scale masses for the fermion singlets. In this case, the tiny neutrino masses have to arise from the cancellations within the seesaw formula which are arranged by fine-tuned correlations between the Yukawa couplings and the masses of fermion singlets. We motivate such correlations through the framework of discrete symmetries. In the case of three Majorana fermion singlets, it is shown that the exact cancellation arranged by the discrete symmetries in seesaw formula necessarily leads to two mass degenerate fermion singlets. The remaining fermion singlet decouples completely from the standard model. We provide two candidate models based on the groups $A_4$ and $\Sigma(81)$ and discuss the generic perturbations to this approach which can lead to the viable neutrino masses.Comment: 26 pages, 4 figures; references added, matches published versio

Flavour physics without flavour symmetries

We quantitatively analyze a quark-lepton flavour model derived from a six-dimensional supersymmetric theory with $SO(10)\times U(1)$ gauge symmetry, compactified on an orbifold with magnetic flux. Two bulk $\mathbf{16}$-plets charged under the $U(1)$ provide the three quark-lepton generations whereas two uncharged $\mathbf{10}$-plets yield two Higgs doublets. At the orbifold fixed points mass matrices are generated with rank one or two. Moreover, the zero modes mix with heavy vectorlike split multiplets. The model possesses no flavour symmetries. Nevertheless, there exist a number of relations between Yukawa couplings, remnants of the underlying GUT symmetry and the wave function profiles of the zero modes, which lead to a prediction of the light neutrino mass scale, $m_{\nu_1} \sim 10^{-3}$ eV and heavy Majorana neutrino masses in the range from $10^{12}$ GeV to $10^{14}$ GeV. The model successfully includes thermal leptogenesis.Comment: Minor additions; Published versio

Interpreting 750 GeV diphoton excess in SU(5) grand unified theory

The ATLAS and CMS experiments at the LHC have found significant excess in the diphoton invariant mass distribution near 750 GeV. We interpret this excess in a predictive nonsupersymmetric SU(5) grand unified framework with a singlet scalar and light adjoint fermions. The 750 GeV resonance is identified as a gauge singlet scalar. Both its production and decays are induced by 24 dimensional adjoint fermions predicted within SU(5). The adjoint fermions are assumed to be odd under $Z_2$ symmetry which forbids their direct coupling to the standard model fermions. We show that the observed diphoton excess can be explained with sub-TeV adjoint fermions and with perturbative Yukawa coupling. A narrow width scenario is more preferred while a simultaneous explanation of observed cross section and large total decay width requires some of the adjoint fermions lighter than 375 GeV. The model also provides a singlet fermion as a candidate of cold dark matter. The gauge coupling unification is achieved in the framework by introducing color sextet scalars while being consistent with the proton decay constraint.Comment: Discussion added, conclusion unchanged; Matches published version in Physics Letters

Revisiting lepton flavor violation in supersymmetric type II seesaw

In view of the recent measurement of reactor mixing angle $\theta_{13}$ and updated limit on $BR(\mu \to e \gamma)$ by the MEG experiment, we re-examine the charged lepton flavor violations in a framework of supersymmetric type II seesaw mechanism. Supersymmetric type II seesaw predicts strong correlation between $BR(\mu \to e \gamma)$ and $BR(\tau \to \mu \gamma)$ mainly in terms of the neutrino mixing angles. We show that such a correlation can be determined accurately after the measurement of $\theta_{13}$. We compute different factors which can affect this correlation and show that the mSUGRA-like scenarios, in which slepton masses are taken to be universal at the high scale, predicts $3.5 \lesssim BR(\tau \to \mu \gamma)/BR(\mu \to e \gamma) \lesssim 30$ for normal hierarchical neutrino masses. Any experimental indication of deviation from this prediction would rule out the minimal models of supersymmetric type II seesaw. We show that the current MEG limit puts severe constraints on the light sparticle spectrum in mSUGRA model if the seesaw scale lies within $10^{13}$-$10^{15}$ GeV. It is shown that these constraints can be relaxed and relatively light sparticle spectrum can be obtained in a class of models in which the soft mass of triplet scalar is taken to be non-universal at the high scale.Comment: Minor changes in text; accepted for publication in Phys. Rev.

Generalized μ\mu-τ\tau symmetry and discrete subgroups of O(3)

The generalized $\mu$-$\tau$ interchange symmetry in the leptonic mixing matrix $U$ corresponds to the relations: $|U_{\mu i}|=|U_{\tau i}|$ with $i=1,2,3$. It predicts maximal atmospheric mixing and maximal Dirac CP violation given $\theta_{13} \neq 0$. We show that the generalized $\mu$-$\tau$ symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of $O(3)$. The groups $A_4$, $S_4$ and $A_5$ are the only such groups which can entirely fix $U$ at the leading order. The neutrinos can be (a) non-degenerate or (b) partially degenerate depending on the choice of their residual symmetries. One obtains either vanishing or very large $\theta_{13}$ in case of (a) while only $A_5$ can provide $\theta_{13}$ close to its experimental value in the case (b). We provide an explicit model based on $A_5$ and discuss a class of perturbations which can generate fully realistic neutrino masses and mixing maintaining the generalized $\mu$-$\tau$ symmetry in $U$. Our approach provides generalization of some of the ideas proposed earlier in order to obtain the predictions, $\theta_{23}=\pi/4$ and $\delta_{\rm CP} = \pm \pi/2$.Comment: 18 page

Fermion Masses in SO(10) Models

We examine many SO(10) models for their viability or otherwise in explaining all the fermion masses and mixing angles. This study is carried out for both supersymmetric and non-supersymmetric models and with minimal ($10+\bar{126}$) and non-minimal ($10+\bar{126}+120$) Higgs content. Extensive numerical fits to fermion masses and mixing are carried out in each case assuming dominance of type-II or type-I seesaw mechanism. Required scale of the B-L breaking is identified in each case. In supersymmetric case, several sets of data at the GUT scale with or without inclusion of finite supersymmetric corrections are used. All models studied provide quite good fits if the type-I seesaw mechanism dominates while many fail if the type-II seesaw dominates. This can be traced to the absence of the $b$-$\tau$ unification at the GUT scale in these models. The minimal non-supersymmetric model with type-I seesaw dominance gives excellent fits. In the presence of a $45_H$ and an intermediate scale, the model can also account for the gauge coupling unification making it potentially interesting model for the complete unification. Structure of the Yukawa coupling matrices obtained numerically in this specific case is shown to follow from a very simple U(1) symmetry and a Froggatt-Nielsen singlet.Comment: 31 pages, 9 Tables, 4 figure

Pseudo-Dirac neutrinos from flavour dependent CP symmetry

Discrete residual symmetries and flavour dependent CP symmetries consistent with them have been used to constrain neutrino mixing angles and CP violating phases. We discuss here role of such CP symmetries in obtaining a pseudo-Dirac neutrino which can provide a pair of neutrinos responsible for the solar splitting. It is shown that if (a) $3\times 3$ Majorana neutrino matrix $M_\nu$ is invariant under a discrete $Z_2\times Z_2$ symmetry generated by $S_{1,2}$, (b) CP symmetry $X$ transform $M_\nu$ as $X^T M_\nu X=M_\nu^*$, and (c) $X$ and $S_{1,2}$ obey consistency conditions $X S_{1,2}^* X^\dagger=S_{2,1}$, then two of the neutrino masses are degenerate independent of specific forms of $X$, $S_1$ and $S_2$. Explicit examples of this result are discussed in the context of $\Delta(6 n^2)$ groups which can also be used to constrain neutrino mixing matrix $U$. Degeneracy in two of the masses does not allow complete determination of $U$ but it can also be fixed once the perturbations are introduced. We consider explicit perturbations which break $Z_2\times Z_2$ symmetries but respect CP. These are shown to remove the degeneracy and provide a predictive description of neutrino spectrum. In particular, a correlation $\sin 2\theta_{23}\sin\delta_{CP}=\pm {\rm Im}[p]$ is obtained between the atmospheric mixing angle $\theta_{23}$ and the CP violating phase $\delta_{CP}$ in terms of a group theoretically determined phase factor $p$. Experimentally interesting case $\theta_{23}=\frac{\pi}{4}$, $\delta_{CP}=\pm \frac{\pi}{2}$ emerges for groups which predict purely imaginary $p$. We present detailed predictions of the allowed ranges of neutrino mixing angles, phases and the lightest neutrino mass for three of the lowest $\Delta(6 n^2)$ groups with $n=2,4,6$.Comment: 17 pages, 4 figures; Minor modification, published versio