arXiv subjects

K. T. Mahanthappa

Publications and source records attributed to K. T. Mahanthappa.

At least 19 recordsLinked to original sources

arXiv2014

CP Violation from Finite Groups

We discuss the origin of CP violation in settings with a discrete (flavor) symmetry $G$. We show that physical CP transformations always have to be class-inverting automorphisms of $G$. This allows us to categorize finite groups into three types: (i) Groups that do not exhibit such an automorphism and, therefore, in generic settings, explicitly violate CP. In settings based on such groups, CP violation can have pure group-theoretic origin and can be related to the complexity of some Clebsch-Gordan coefficients. (ii) Groups for which one can find a CP basis in which all the Clebsch-Gordan coefficients are real. For such groups, imposing CP invariance restricts the phases of coupling coefficients. (iii) Groups that do not admit real Clebsch-Gordan coefficients but possess a class-inverting automorphism that can be used to define a proper (generalized) CP transformation. For such groups, imposing CP invariance can lead to an additional symmetry that forbids certain couplings. We make use of the so-called twisted Frobenius-Schur indicator to distinguish between the three types of discrete groups. With $Δ(27)$, $T^{\prime}$, and $Σ(72)$ we present one explicit example for each type of group, thereby illustrating the CP properties of models based on them. We also show that certain operations that have been dubbed generalized CP transformations in the recent literature do not lead to physical CP conservation.

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arXiv2013

Large θ_13 in a SUSY SU(5)xT' Model

In the model based on SUSY SU(5) combined with the T' family symmetry, it is shown in Phys. Lett. B 652, 34 (2007) and Phys. Lett. B 681, 444 (2009) that fermion mass hierarchy and mixing angles can be naturally generated in both lepton and quark sectors compatible with various experimental measurements. But the predicted value for the non-zero lepton mixing angle of θ_13 \simeq θ_c/3\sqrt{2} contradicts the recent experimental results from Daya Bay and RENO. We propose to introduce one more singlet flavon field in the neutrino sector, and with its additional contribution, we are able to generate the large mixing angle θ_13 ~ 8^{\circ}-10^{\circ}. The analytical expressions of the mixing angles and neutrino masses with the additional flavon field are derived. Our numerical results show that a large region in the model parameter space is allowed for the normal hierarchy case, while a much smaller region is allowed for the inverted hierarchy case. In addition, the predicted value of the solar mixing angle is not affected by the additional singlet contribution. On the other hand, there exists a correlation between θ_13 value and θ_23 - π/4, as a result of the additional singlet contribution. We also make predictions for various other variables that can be potentially tested in the future neutrino experiments such as the Dirac CP phase, which is predicted to be in the range of δ~ (195^{\circ}-200^{\circ}), and the neutrinoless double beta decay matrix element, . One numerical example with the minimal χ^2 fit is presented, and the model predictions are consistent with all experimental results.

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arXiv2011

Leptogenesis in a SUSY SU(5) x T' Model with Geometrical CP Violation

The complex Clebsch-Gordon coefficients in the double tetrahedral group T' offers the possibility that CP violation can be entirely geometrical in origin, as pointed out by us recently. In this note, we investigate leptogenesis in a SUSY SU(5) x T' model, which gives rise to realistic quark masses and CKM matrix elements, a near tri-bimaximal neutrino mixing pattern, as well as CP violating measures for all quarks and leptons. In terms of 9 independent parameters in the Yukawa sector, the predicted values of the 22 observables agree with current experimental values, including the recent T2K and MINOS results. The correction to the tri-bimaximal mixing pattern is related to the Cabibbo angle, leading to interesting quark-lepton complementarity sum rules. Our predicted value for the leptonic Dirac CP phase is 227 degrees, which gives rise to sufficient amount of lepton number asymmetry, in the presence of the flavor effect. As this is the only non-vanishing CP violating phase in the lepton sector, there is a direct connection between leptogenesis and CP violation in neutrino oscillation in our model.

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arXiv2010

Models and Phenomenology of Neutrino Masses circa 2010

We review recent developments in models of neutrino masses and mixing. Emphases are given to models based on finite group family symmetries from which the tri-bimaximal neutrino mixing can arise. In particular, we describe one recent model based on SUSY SU(5) combined with a family symmetry based on the double tetrahedral group, T'. All 22 observable fermion masses and mixing angles and CP violating measures are fitted with only 9 parameters. In this model, a near tri-bimaximal MNS matrix and a realistic CKM matrix are simultaneously generated; the MNS matrix gets slightly modified by virtue of having the Georgi-Jarlskog relations. Due to the presence of complex Clebsch-Gordan coefficients in T', CP violation in this model is entirely geometrical in origin. The prediction of the model for the leptonic Dirac CP phase is 227 degrees, which turns out to be very close to the current best fit value of 220 degrees from SuperK.

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arXiv2010

Geometrical Origin of CP Violation and CKM and MNS Matrices in SU(5) x T'

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{2}) theta_{c}, the model gives rise to a sum rule, tan^{2} theta_{sol} ~ tan^{2} theta_{sol, TBM}} + (1/2) theta_{c} cos(delta_{lep}), which is a consequence of the Georgi-Jarlskog relations in the charged fermion sector. The predicted leptonic Dirac CP phase, delta_{lep}, gives the correct value of the solar mixing angle, and the predicted CP violation measures in the quark sector are consistent with the current experimental data. Since the Dirac CP phase is the only non-vanishing phase predicted in the lepton sector, there is a connection between leptogenesis and low energy leptonic CP violating processes in our model.

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arXiv2010

A Viable Randall-Sundrum Model for Quarks and Leptons with T' Family Symmetry

We propose a Randall-Sundrum model with a bulk family symmetry based on the double tetrahedral group, T', which generates the tri-bimaximal neutrino mixing pattern and a realistic CKM matrix, including CP violation. Unlike 4D models where the generation of mass hierarchy requires additional symmetry, the warped geometry naturally gives rise to the fermion mass hierarchy through wavefunction localization. The T' symmetry forbids tree-level flavor changing neutral currents in both the quark and lepton sectors, as different generations of fermions are unified into multiplets of T'. This results in a low first KK mass scale and thus the model can be tested at collider experiments.

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arXiv2009

Neutrinos versus Quarks, MNS versus CKM

We review recent developments in models of fermion masses and mixing for both quark and lepton sectors. Emphases are given to models based on finite group family symmetries. In particular, we describe one recent model based on SU(5) combined with a family symmetry based on the double tetrahedral group, T'. In this model, a near tri-bimaximal MNS matrix and a realistic CKM matrix are simultaneously generated; the MNS matrix gets slightly modified by virtue of having the Georgi-Jarlskog relations. Due to the presence of complex Clebsch-Gordon coefficients in T', CP violation in this model is entirely geometrical in origin.

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arXiv2009

Group Theoretical Origin of CP Violation

We propose the complex group theoretical Clebsch-Gordon coefficients as a novel origin of CP violation. This is manifest in our model based on SU(5) combined with the T' group as the family symmetry. The complex CG coefficients in T' lead to explicit CP violation which is thus geometrical in origin. The predicted CP violation measures in the quark sector are consistent with the current experimental data. The corrections due to leptonic Dirac CP violating phase gives the experimental best fit value for the solar mixing angle, and we also gets the right amount of the baryonic asymmetry.

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arXiv2009

A Viable Flavor Model for Quarks and Leptons in RS with T' Family Symmetry

We propose a Randall-Sundrum model with a bulk family symmetry based on the double tetrahedral group, T', which generates the tri-bimaximal neutrino mixing pattern and a realistic CKM matrix. The T' symmetry forbids tree-level flavor-changing-neutral-currents in both the quark and lepton sectors, as different generations of fermions are unified into multiplets of T'. This results in a low first KK mass scale and thus the model can be tested at collider experiments.

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arXiv2009

A Novel Origin of CP Violation

We propose the complex group theoretical Clebsch-Gordon coefficients as a novel origin of CP violation. This is manifest in our model based on SU(5) combined with the double tetrahedral group, T'. Due to the presence of the doublet representations in $T^{\prime}$, there exist complex CG coefficients, leading to explicit CP violation in the model, while the Yukawa couplings and the vacuum expectation of the scalar fields remain real. The tri-bimaximal neutrino mixing matrix arises from the CG coefficients of the T'. In addition to the prediction for theta_{13} ~ theta_{c}/(3 sqrt{2}), the model gives rise to a sum rule, tan^2 theta_{sol} ~ \tan^2 theta_{sol,TBM} + (1/2) theta_{c} cos(delta), which is a consequence of the Georgi-Jarlskog relations in the charged fermion sector. The leptonic Dirac CP violating phase, delta_{ell}, is predicted to be ~227^{o}, which turns out to be the value needed to account for the difference between the experimental best fit value for the solar mixing angle and the TBM prediction. The predicted CP violation measures in the quark sector are also consistent with the current experimental data.

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arXiv2008

Neutrino Mass Models: circa 2008

We review recent developments in theoretical models for neutrino masses and mixing. Emphases are given to models based on finite group family symmetries. In particular, we describe one recent model based on SU(5), in which both the tri-bimaximal neutrino mixing and realistic CKM matrix are generated. We also discuss two models based on a non-anomalous U(1)_F family symmetry in which the gauge anomalies are cancelled due to the presence of the right-handed neutrinos. In one of these models, the seesaw scale can be as low as a TeV; in the other model, which is based on SUSY SU(5), the U(1)_F symmetry forbids Higgs-mediated proton decays.

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arXiv2007

Tri-bimaximal Neutrino Mixing and CKM Matrix in a SU(5)x(d)T Model

In this talk, we present a model based on SU(5)x(d)T which successfully gives rise to near tri-bimaximal leptonic mixing as well as realistic CKM matrix elements for the quarks. The Georgi-Jarlskog relations for three generations are also obtained. Due to the (d)T transformation property of the matter fields, the b-quark mass can be generated only when the (d)T symmetry is broken, giving a dynamical origin for the hierarchy between m_b and m_t. There are only nine operators allowed in the Yukawa sector up to at least mass dimension seven due to an additional Z12 x Z12' symmetry, which also forbids, up to some high orders, operators that lead to proton decay. The resulting model has a total of nine parameters in the charged fermion and neutrino sectors, and hence is very predictive. In addition to the prediction for theta13 ~ theta_c/3sqrt{2}, the model gives rise to a sum rule, tan^2(theta_{solar}) ~ tan^2(theta_{solar,TBM}) - 1/2*theta_c*cos(beta), which is a consequence of the Georgi-Jarlskog relations in the quark sector. This deviation could account for the difference between the experimental best fit value for the solar mixing angle and the value predicted by the tri-bimaximal mixing matrix.

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arXiv2007

CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model

We propose a model based on SU(5) x {}^{(d)}T which successfully gives rise to near tri-bimaximal leptonic mixing as well as realistic CKM matrix elements for the quarks. The Georgi-Jarlskog relations for three generations are also obtained. Due to the {}^{(d)}T transformation property of the matter fields, the b-quark mass can be generated only when the {}^{(d)}T symmetry is broken, giving a dynamical origin for the hierarchy between m_{b} and m_{t}. There are only nine operators allowed in the Yukawa sector up to at least mass dimension seven due to an additional Z_{12} x Z'_{12} symmetry, which also forbids, up to some high orders, operators that lead to proton decay. The resulting model has a total of nine parameters in the charged fermion and neutrino sectors, and hence is very predictive. In addition to the prediction for θ_{13} \simeq θ_{c}/3 \sqrt{2}, the model gives rise to a sum rule, \tan^{2}θ_{\odot} \simeq \tan^{2} θ_{\odot, \mathrm{TBM}} - {1/2} θ_{c} \cosβ, which is a consequence of the Georgi-Jarlskog relations in the quark sector. This deviation could account for the difference between the experimental best fit value for the solar mixing angle and the value predicted by the tri-bimaximal mixing matrix.

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arXiv2006

Low Scale Seesaw, Electron EDM and Leptogenesis in a Model with Spontaneous CP Violation

Strong correlations between leptogenesis and low energy CP violating leptonic processes have been shown by us to exist in the minimal left-right symmetric model with spontaneous CP violation. In this note, we investigate the implications of this model for the electric dipole moment of the electron. With an additional broken U(1)_H symmetry, the seesaw scale can be lowered to close to the electroweak scale. This additional symmetry also makes the connection between CP violation in quark sector to that in the lepton sector possible.

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arXiv2006

Relating Leptogenesis to Low Energy CP Violation

In the minimal left-right symmetric model with spontaneous CP violation, there are only two intrinsic CP violating phases to account for all CP violation in both the quark and lepton sectors. In addition, the left-and right-handed Majorana mass terms for the neutrinos are proportional to each other due to the parity in the model. This is thus a very constrained framework, making the existence of correlations among the CP violation in leptogenesis, neutrino oscillation and neutrinoless double beta decay possible.

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arXiv2005

Fermion Mixing and Soft Leptogenesis in a SUSY SO(10) x SU(2)_F Model

We have constructed a SUSY SO(10) x SU(2)_F model in which a set of symmetric mass matrices with five texture zeros (having 11 parameters) leads to 22 measurable fermion masses, mixing angles and CP phases, all in agreement with available experimental data within one sigma. The LMA solution for solar neutrinos is obtained as well as neutrino mixing angles and absolute values of neutrino masses. We have investigated the possibility of baryogenesis resulting from soft leptogenesis. We find that, with soft SUSY masses assuming their natural values of the order of a TeV, the observed baryon asymmetry in the Universe can be accommodated in our model. Unlike models with lop-sided textures which give rise to a dangerously large decay rate for mu -> e + gamma, the decay rate we get is much suppressed and yet it is large enough to be accessible to the next generation of experiments.

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arXiv2005

Relating Leptogenesis to Low Energy Flavor Violating Observables in Models with Spontaneous CP Violation

In the minimal left-right symmetric model, there are only two intrinsic CP violating phases to account for all CP violation in both the quark and lepton sectors, if CP is broken spontaneously by the complex phases in the VEV's of the scalar fields. In addition, the left- and right-handed Majorana mass terms for the neutrinos are proportional to each other due to the parity in the model. This is thus a very constrained framework, making the existence of correlations among the CP violation in leptogenesis, neutrino oscillation and neutrinoless double beta decay possible. In these models, CP violation in the leptonic sector and CP violation in the quark sector are also related. We find, however, that such connection is rather weak due to the large hierarchy in the bi-doublet VEV required by a realistic quark sector.

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arXiv2004

Lepton Flavor Violating Decays, Soft Leptogenesis and SUSY SO(10)

We investigate lepton flavor violating decays in a SUSY SO(10) model with symmetric textures recently constructed by us. Unlike the models with lop-sided textures which give rise to a large decay rate for mu -> e gamma, the decay rate we get is much suppressed and yet it is large enough to be accessible to the next generation of experiments. We have also investigated the possibility of baryogenesis resulting from soft leptogenesis. We find that with the soft SUSY masses assuming their natural values, B^\prime \equiv \sqrt{BM_{1}} ~ 1.4 TeV and Im(A) ~ 1 TeV, the observed baryon asymmetry in the Universe can be accommodated in our model. We have also updated the predictions of our model for the masses, mixing angles and CP violating measures in both charged fermion and neutrino sectors, using the most up-to-date experimental data as input.

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