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4 Tests of lepton universality
The lepton universality tests probe the Standard Model prediction that the
charged weak current interaction has the same coupling for all leptons.
The precision of such tests has been significantly improved by the
addition of the recent Belle τ lifetime
measurement [2], while improvements from the τ branching fraction fit are negligible.
We compute the universality tests like in the previous report by using
proper ratios of the partial widths of a heavier lepton L decaying to a
lighter lepton ℓ [74],
| Γ(L → νL ℓ | | ℓ (γ)) =
| | =
| | f | ⎛
⎜
⎜
⎝ | | ⎞
⎟
⎟
⎠ |
rWL rγL ,
|
| | | | | | | | | | |
|
where
| Gℓ | | | |
f(x) | = 1 −8x +8x3 −x4 −12x2 lnx , | |
rWL | | | |
rγL | | |
|
We use rγτ=1−43.2· 10−4 and
rγµ=1−42.4· 10−4 [74] and MW
from PDG 2013 [17].
We use HFAG 2014 averages and PDG 2013 for the other quantities.
Using pure leptonic processes we obtain
| | ⎛
⎜
⎜
⎝ | | | ⎞
⎟
⎟
⎠ | = 1.0011 ± 0.0015 , |
| | | ⎛
⎜
⎜
⎝ | | | ⎞
⎟
⎟
⎠ | = 1.0029 ± 0.0015 , |
| | | ⎛
⎜
⎜
⎝ | | | ⎞
⎟
⎟
⎠ | = 1.0018 ± 0.0014 .
|
| | | | | | |
|
Using semi-hadronic processes
| | ⎛
⎜
⎜
⎝ | | | ⎞
⎟
⎟
⎠ | | =
| |
| |
| ⎛
⎜
⎜
⎝ | | | ⎞
⎟
⎟
⎠ | | ,
|
| | | | | | | | | | |
|
where h = π or K and the radiative corrections are
δπ = (0.16 ± 0.14)% and
δK = (0.90 ± 0.22)% [75],
we measure:
| | = 0.9963 ± 0.0027 , | | ⎛
⎜
⎜
⎝ | | | ⎞
⎟
⎟
⎠ | | = 0.9858 ± 0.0071 .
|
| | | | | | | | |
|
Similar tests could be performed with decays to electrons, however they are
less precise because the hadron two body decays to electrons are
helicity-suppressed.
Averaging the three gτ/gµ ratios we obtain
accounting for statistical correlations.
Table 12 reports the statistical correlation coefficients for the fitted coupling ratios:
Table 12: Universality coupling ratios correlation coefficients (%). |
|
( gτ/ge ) | 53 |
( gµ/ge ) | -49 | 48 |
( gτ/gµ )π | 24 | 26 | 2 |
( gτ/gµ )K | 12 | 10 | -2 | 5 |
| ( gτ/gµ ) | ( gτ/ge ) | ( gµ/ge ) | ( gτ/gµ )π
|
|
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