The low energy $S$-matrix which describes non-relativistic scattering arising from finite-range forces has UV/IR symmetries that are hidden in the corresponding effective field theory (EFT) action. It is shown that the $S$-matrix symmetries are manifest as geometric symmetries of the RG flow of coupling constants in the EFT action in both three and two spatial dimensions. An example is given demonstrating that UV/IR symmetry breaking in the $S$-matrix implies strong constraints on the RG flow of the coefficients of the corresponding symmetry-breaking operators in the EFT.
Lam suggested that the PMNS matrix (or at least some of its elements) can be predicted by embedding the residual symmetry of the leptonic mass terms into a bigger symmetry. We analyze the possibility that the residual symmetries consist of involution generators only and explore how Lam's idea can be implemented.
We explore a flavor structure of quarks in the standard model under the assumption that flavor symmetries exist in a theory beyond the standard model, and chase after their properties, using a bottom-up approach. We reacknowledge that a flavor-symmetric part of Yukawa coupling matrix can be realized by a rank-one matrix and a democratic-type one occupies a special position, based on Dirac's naturalness.
The s-wave nucleon-nucleon (NN) scattering matrix ($S$-matrix) exhibits UV/IR symmetries which are hidden in the effective field theory (EFT) action and scattering amplitudes, and which explain some generic features of the phase shifts. These symmetries offer clarifying interpretations of existing pionless EFT expansions, and suggest starting points for novel expansions. The leading-order (LO) $S$-matrix obtained in the pionless EFT with scattering lengths treated exactly is shown to have a UV/IR symmetry which leaves the sum of s-wave phase shifts invariant. A new scheme, which treats effecti…
The Standard Model does not explain the hierarchy problem. Before the discovery of nonzero lepton mixing angle θ13 high hopes in explanation of the shape of the lepton mixing matrix were combined with non abelian symmetries. Nowadays, assuming one Higgs doublet, it is unlikely that this is still valid. Texture zeroes, that are combined with abelian symmetries, are intensively studied. The neutrino mass matrix is a natural way to study such symmetries.
The flavour neutrino puzzle is often addressed by considering neutrino mass matrices $m$ with a certain number of vanishing entries ($m_{ij}=0$ for some values of the indices), since a reduction in the number of free parameters increases the predictive power. Symmetries that can enforce textures zero can also enforce a more general type of conditions $f(m_{ij})=0$ with $f$ some function of the matrix elements $m_{ij}$. In this case $m$ can have all entries non-vanishing with no reduction in its predictive power. We classify all generation-dependent $U(1)$ symmetries which, in the presence of t…
我们考虑轻子质量矩阵的剩余对称性的两个新的方案。首先，我们假设带电轻子质量矩阵具有Z2 × Z2对称性G_ell，轻中微子质量矩阵具有Z2对称性G_nu。通过这种设置，轻子混合矩阵的一列元素的模被固定到重新排序。在这种情况下，可以互换G_ell和G_nu的角色，从而约束混合矩阵的行而不是列。其次，我们假设一个剩余对称群G_ell \cong Zm（m>2）是由一个具有双退化特征值的矩阵生成的。然后，用G_nu \cong Z 2 x Z 2，轻子混合矩阵的一行元素的模得到固定。使用小群组的库，我们已经执行了对可能在这两个场景中的每一个中嵌入G_ell和G_nu的群组的搜索。我们只发现了两种现象学上可行的可能性，其中一种约束混合矩阵的一列，另一种约束混合矩阵的一行。
We analyze the possible generalized CP symmetries admitted by the Tri-Bi-Maximal (TBM) neutrino mixing. Taking advantage of these symmetries we construct in a systematic way other variants of the standard TBM ansatz. Depending on the type and number of generalized CP symmetries imposed, we get new mixing matrices, all of which related to the original TBM matrix. One of such "revamped" TBM variants is the recently discussed mixing matrix of arXiv:1806.03367. We also briefly discuss the phenomenological implications following from these mixing patterns.
Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which was not yet discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, that the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but that they are simply the result of a reduction of free parameters du…
In this paper, we impose a magic symmetry on the neutrino mass matrix $m_ν$ with universal four-zero texture and diagonal reflection symmetries. Due to the magic symmetry, the MNS matrix has trimaximal mixing inevitably. Since the lepton sector has only six free parameters, physical observables of leptons are all determined from the charged leptons masses $m_{ei}$, the neutrino mass differences $Δm_{i1}^{2}$, and the mixing angle $θ_{23}$. This scheme predicts $\sin θ_{13} = 0.149$, that is almost equal to the latest best fit, as a function of the lepton masses $m_{e, μ}$ and the mass differen…
In this follow up of arXiv:1812.04663 we analyze the generalized CP symmetries of the charged lepton mass matrix compatible with the complex version of the Tri-Bi-Maximal (TBM) lepton mixing pattern. These symmetries are used to `revamp' the simplest TBM \textit{Ansatz} in a systematic way. Our generalized patterns share some of the attractive features of the original TBM matrix and are consistent with current oscillation experiments. We also discuss their phenomenological implications both for upcoming neutrino oscillation and neutrinoless double beta decay experiments.
