https://doi.org/10.1140/epjc/s10052-020-8059-7
Letter
at a rate of one out of 
tau decays?
1
Department of Physics, Indiana University, Bloomington, IN, 47408, USA
2
Center for Exploration of Energy and Matter, Indiana University, Bloomington, IN, 47408, USA
3
Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany
4
Theoretische Physik I, Universität Siegen, 57068, Siegen, Germany
5
Theory Center, Thomas Jefferson National Accelerator Facility, Newport News, VA, 23606, USA
* e-mail: matteo.fael@kit.edu
Received:
29
January
2020
Accepted:
19
May
2020
Published online:
5
June
2020
We present in a full analytic form the partial widths for the lepton flavour violating decays 
and 
, with 
, mediated by neutrino oscillations in the one-loop diagrams. Compared to the first result by Petcov (Sov J Nucl Phys 25:340, 1977), obtained in the zero momentum limit 
, we retain full dependence on 
, the momenta and masses of external particles, and we determine the branching ratios in the physical limit 
. We show that the claim presented in Pham (Eur Phys J C8:513, 1999) that the 
branching ratios could be as large as 
, as a consequence of keeping the dependence, is flawed. We find rates of order 
, even smaller than those obtained in the zero momentum limit, as the latter prediction contains an unphysical logarithmic enhancement.
© The Author(s), 2020
