Why Is The Neutrino Oscillation Formula Expanded In Δm212/Δm312\Delta m_{21}^{2}/\Delta m_{31}^{2} Still Accurate Near The Solar Resonance In Matter?

The conventional approximate formula for neutrino oscillation in matter which is obtained from the expansion in terms of the ratio of mass square differences $\alpha=\Delta m_{21}^{2}/\Delta m_{31}^{2}\approx0.03$, first proposed by Cervera, et al and Freund, turns out to be an accurate formula for accelerator neutrino experiments. Originally it required the neutrino energy to be well above the solar resonance to validate the expansion but it is found to be still very accurate when the formula is extrapolated to the resonance, which is practically important for the T2K experiment. This paper shows that the accuracy is guaranteed by cancellations of branch cut singularities and also, for the first time, analytically computes the actual error of the formula. The actual error implies that the original requirement can be safely removed in current experiments.Comment: 22 pages,7 figures. Some materials are removed for simplicity. Accepted by JHE

Tensor and scalar interactions of neutrinos may lead to observable neutrino magnetic moments

Recently more generalized four-fermion interactions of neutrinos such as tensor and scalar interactions (TSIs) have been extensively studied in response to forthcoming precision measurements of neutrino interactions. In this letter, we show that due to the chirality-flipping nature, at the 1-loop level TSIs typically generate much larger ($10^{7}\sim10^{10}$) neutrino magnetic moments ($\nu$MMs) than the vector case. For some cases, the large $\nu$MMs generated by TSIs may reach or exceed the known bounds, which implies potentially important interplay between probing TSIs and searching for $\nu$MMs in current and future neutrino experiments.Comment: Comments on effective magnetic moment add; matches the journal versio

Tree-level vacuum stability of two-Higgs-doublet models and new constraints on the scalar potential

The scalar potential of the two-Higgs-doublet model (2HDM) may have more than one local minimum and the usually considered vacuum could be located at one of them that could decay to another. This paper studies the condition that the usually considered vacuum is the global minimum which, combined with the bounded-from-below condition, will stabilize the vacuum at tree-level. We further apply these conditions to a specific 2HDM and obtain new constraints which could be important in phenomenological studies.Comment: 12 pages, references adde

Trimaximal μ\mu-τ\tau reflection symmetry

The $\mu$-$\tau$ reflection symmetry $(\nu_{e},\thinspace\nu_{\mu},\thinspace\nu_{\tau})\rightarrow(\overline{\nu}_{e},\thinspace\overline{\nu}_{\tau},\thinspace\overline{\nu}_{\mu})$ and the TM1 mixing (a PMNS matrix with the first column fixed to the TBM form) are both well compatible with experiments. If both approaches are simultaneously assumed, all lepton mixing parameters except for $\theta_{13}$ are predicted. In particular, one expects maximal CP violation ($|\delta|=90^{\circ}$), maximal atmospheric mixing ($\theta_{23}=45^{\circ}$), a slightly less-than-TBM solar mixing angle ($\theta_{12}\approx34^{\circ}$), as well as values of $0$ or $\pi$ for the two Majorana phases. We study the renormalization stability of this highly predictive framework when neutrino mass is described by an effective Weinberg operator and by the type I seesaw mechanism, both in the Standard Model and with supersymmetry.Comment: 12 pages, comments added, version to appear in PR

A left-right symmetric flavor symmetry model

We discuss flavor symmetries in left-right symmetric theories. We show that such frameworks are a different environment for flavor symmetry model building compared to the usually considered cases. This does not only concern the need to obey the enlarged gauge structure, but also more subtle issues with respect to residual symmetries. Furthermore, if the discrete left-right symmetry is charge conjugation, potential inconsistencies between the flavor and charge conjugation symmetries should be taken care of. In our predictive model based on $A_4$ we analyze the correlations between the smallest neutrino mass, the atmospheric mixing angle and the Dirac CP phase, the latter prefers to lie around maximal values. There is no lepton flavor violation from the Higgs bi-doublet.Comment: 10 pages, 5 figure

Origin of Symmetric PMNS and CKM Matrices

The PMNS and CKM matrices are phenomenologically close to symmetric, and a symmetric form could be used as zeroth-order approximation for both matrices. We study the possible theoretical origin of this feature in flavor symmetry models. We identify necessary geometric properties of discrete flavor symmetry groups that can lead to symmetric mixing matrices. Those properties are actually very common in discrete groups such as $A_{4}$, $S_{4}$ or $\Delta(96)$. As an application of our theorem, we generate a symmetric lepton mixing scheme with $\theta_{12}=\theta_{23}=36.21^{\circ};\theta_{13}=12.20^{\circ}$ and $\delta=0$, realized with the group $\Delta(96)$.Comment: 8 pages. 4 figures. minor corrections to appear in PR

Robustness of Neutrino Mass Matrix Predictions

We investigate the stability of neutrino mass matrix predictions on important and currently unknown observables. Those are the octant of $\theta_{23}$, the sign of $\sin\delta$ and the neutrino mass ordering. Determining those unknowns is expected to be useful in order to distinguish neutrino mass models. Therefore it may be interesting to know how robust the predictions of a mass matrix for the octant of $\theta_{23}$ or the neutrino mass ordering are. By applying general multiplicative perturbations we explicitly quantify how probable it is that a perturbed mass matrix predicts an octant of $\theta_{23}$ different from the original mass matrix, or even a neutrino mass ordering different from the original one. Both the general case and an explicit flavor symmetry model are studied. We give the probabilities as a function of the smallest neutrino mass, showing that for values exceeding 0.1 eV the chance to switch the prediction quickly approaches $50\,\%$.Comment: 8 pages,10 figures, published by NP