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Journal Article
τ→μμμ at a rate of one out of 1014 tau decays?
2020
Overview
We present in a full analytic form the partial widths for the lepton flavour violating decays
μ
±
→
e
±
e
+
e
-
and
τ
±
→
ℓ
±
ℓ
′
+
ℓ
′
-
, with
ℓ
,
ℓ
′
=
μ
,
e
, 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
P
≪
m
ν
≪
M
W
, we retain full dependence on
P
, the momenta and masses of external particles, and we determine the branching ratios in the physical limit
m
ν
≪
P
≪
M
W
. We show that the claim presented in Pham (Eur Phys J C8:513, 1999) that the
τ
→
ℓ
ℓ
′
ℓ
′
branching ratios could be as large as
10
-
14
, as a consequence of keeping the
P
dependence, is flawed. We find rates of order
10
-
55
, even smaller than those obtained in the zero momentum limit, as the latter prediction contains an unphysical logarithmic enhancement.
