{
  "id": "1801.02843",
  "version": "v1",
  "published": "2018-01-09T09:05:52.000Z",
  "updated": "2018-01-09T09:05:52.000Z",
  "title": "Perturbed flavour symmetries and predictions of CP violating phase $δ$",
  "authors": [
    "Anjan S. Joshipura"
  ],
  "comment": "21 pages, two figures",
  "categories": [
    "hep-ph"
  ],
  "abstract": "It is known that the imposition of a class of residual $Z_2\\times Z_2$ symmetries on the neutrino mass matrix $M_\\nu$ and a residual symmetry $Z_n$ ($n\\geq 3$) on the Hermitian combination $M_lM_l^\\dagger$ of the charged lepton mass matrix leads to a universal prediction of vanishing Dirac CP phase $\\delta$ if these symmetries are embedded in $\\Delta(6 n^2)$ groups and if the leptonic doublets transform as a 3 dimensional irreducible representation of the group. The Majorana phases remain arbitrary but they can also be determined in $\\Delta(6 n^2)$ by imposing generalized CP symmetry (GenCP) consistent with the $\\Delta(6 n^2)$ group. We investigate the effects of adding general perturbations on these predictions assuming that perturbations break the $Z_2\\times Z_2$ symmetry completely but preserve GenCP. It is found that if the residual symmetries predict the tri-bimaximal mixing (TBM) among leptons and specific CP conserving values for the Majorana phases then addition of the above perturbations always lead to a neutrino mass matrix invariant under the $\\mu$-$\\tau$ reflection symmetry in the flavour basis with the result that perturbations turn the vanishing $\\delta$ into maximal value $\\pm \\frac{\\pi}{2}.$ One gets non-vanishing but generally large $\\delta$ if the predicted zeroeth order mixing deviates from TBM and/or the predicted Majorana phases are non-trivial. We systematically investigate effects of perturbations in such situations and work out the predicted $\\delta$ for four of the lowest $\\Delta(6 n^2)$ groups with $n=2,4,6,8.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-09T09:05:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cp violating phase",
      "perturbed flavour symmetries",
      "zeroeth order mixing deviates",
      "prediction",
      "perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}