S3 x Z2 model for neutrino mass matrices

We propose a model for lepton mass matrices based on the seesaw mechanism, a complex scalar gauge singlet and a horizontal symmetry S_3 \times \mathbbm{Z}_2. In a suitable weak basis, the charged-lepton mass matrix and the neutrino Dirac mass matrix are diagonal, but the vacuum expectation value of the scalar gauge singlet renders the Majorana mass matrix of the right-handed neutrinos non-diagonal, thereby generating lepton mixing. When the symmetry $S_3$ is not broken in the scalar potential, the effective light-neutrino Majorana mass matrix enjoys $\mu$--$\tau$ interchange symmetry, thus predicting maximal atmospheric neutrino mixing together with $U_{e3} = 0$. A partial and less predictive form of $\mu$--$\tau$ interchange symmetry is obtained when the symmetry $S_3$ is softly broken in the scalar potential. Enlarging the symmetry group S_3 \times \mathbbm{Z}_2 by an additional discrete electron-number symmetry \mathbbm{Z}_2^{(e)}, a more predicitive model is obtained, which is in practice indistinguishable from a previous one based on the group $D_4$.Comment: 13 pages, 3 figures, final version for publication in JHE

Derivative corrections to the Born-Infeld action through beta-function calculations in N=2 boundary superspace

We calculate the beta-functions for an open string sigma-model in the presence of a U(1) background. Passing to N=2 boundary superspace, in which the background is fully characterized by a scalar potential, significantly facilitates the calculation. Performing the calculation through three loops yields the equations of motion up to five derivatives on the fieldstrengths, which upon integration gives the bosonic sector of the effective action for a single D-brane in trivial bulk background fields through four derivatives and to all orders in alpha'. Finally, the present calculation shows that demanding ultra-violet finiteness of the non-linear sigma-model can be reformulated as the requirement that the background is a deformed stable holomorphic U(1) bundle.Comment: 25 pages, numerous figure

A model realizing the Harrison-Perkins-Scott lepton mixing matrix

We present a supersymmetric model in which the lepton mixing matrix $U$ obeys, at the seesaw scale, the Harrison--Perkins--Scott \textit{Ansatz}--vanishing $U_{e3}$, maximal atmospheric neutrino mixing, and $\sin^2{\theta_\odot} = 1/3$ ($\theta_\odot$ is the solar mixing angle). The model features a permutation symmetry $S_3$ among the three lepton multiplets of each type--left-handed doublets, right-handed charged leptons, and right-handed neutrinos--and among three Higgs doublets and three zero-hypercharge scalar singlets; a fourth right-handed neutrino, a fourth Higgs doublet, and a fourth scalar singlet are invariant under $S_3$. In addition, the model has seven \mathbbm{Z}_2 symmetries, out of which six do not commute with $S_3$. Supersymmetry is needed in order to eliminate some quartic terms from the scalar potential, quartic terms which would make impossible to obtain the required vacuum expectation values of the three Higgs doublets and three scalar singlets. The Yukawa couplings to the charged leptons are flavour diagonal, so that flavour-changing neutral Yukawa interactions only arise at loop level.Comment: 16 pages, plain LaTeX, no figures; some clarifying remarks in the conclusions and references added, version accepted for publication in JHE

Dissidents and God-Talk in the Johannine Epistles

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