{
  "id": "1610.03038",
  "version": "v1",
  "published": "2016-10-10T19:26:12.000Z",
  "updated": "2016-10-10T19:26:12.000Z",
  "title": "A closer look at the $R_D$ and $R_{D^*}$ anomalies",
  "authors": [
    "Debjyoti Bardhan",
    "Pritibhajan Byakti",
    "Diptimoy Ghosh"
  ],
  "comment": "37 pages",
  "categories": [
    "hep-ph",
    "hep-ex"
  ],
  "abstract": "The measurement of $R_D$ ($R_{D^*}$), the ratio of the branching fraction of $\\overline{B} \\to D \\tau \\bar{\\nu}_\\tau (\\overline{B} \\to D^* \\tau \\bar{\\nu}_\\tau)$ to that of $\\overline{B} \\to D l \\bar{\\nu}_l (\\overline{B} \\to D^* l \\bar{\\nu}_l)$, shows $1.9 \\sigma$ $(3.3 \\sigma)$ deviation from its Standard Model (SM) prediction. The combined deviation is at the level of $4 \\sigma$ according to the Heavy Flavour Averaging Group (HFAG). In this paper, we perform an effective field theory analysis (at the dimension-6 level) of these potential New Physics (NP) signals assuming $\\rm SU(3)_{C} \\times SU(2)_{L} \\times U(1)_{Y}$ gauge invariance. We first show that, in general, $R_D$ and $R_{D^*}$ are theoretically independent observables and hence, their theoretical predictions are not correlated. We identify the operators that can explain the experimental measurements of $R_D$ and $R_{D^*}$ individually and also together. Motivated by the recent measurement of the $\\tau$ polarisation in $\\overline{B} \\to D^* \\tau \\bar{\\nu}_\\tau$ decay, $P_\\tau (D^*)$ by the Belle collaboration, we study the impact of a more precise measurement of $P_\\tau (D^*)$ (and a measurement of $P_\\tau (D)$) on the various possible NP explanations. Furthermore, we show that the measurement of $R_{D^*}$ in bins of $q^2$, the square of the invariant mass of the lepton neutrino system, along with the information on $\\tau$ polarisation, can completely distinguish the various operator structures. We also provide the full expressions of the double differential decay widths for the individual $\\tau$ helicities in the presence of all the 10 dimension-6 operators that can contribute to these decays.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-10T19:26:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closer look",
      "measurement",
      "double differential decay widths",
      "heavy flavour averaging group",
      "lepton neutrino system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}