In conclusion, we have made a measurement of the branching fractions of the radiative leptonic τ decays τ → eγνν¯ and τ → µγνν¯, for a minimum photon energy of 10 MeV in the τ rest frame, using the full dataset of e +e − collisions collected by BABAR at the center-of-mass energy of the Υ(4S) resonance. We find B(τ → µγνν¯) = (3.69 ± 0.03 ± 0.10) × 10−3 , and B(τ → eγνν¯) = (1.847 ± 0.015 ± 0.052) × 10−2 , where the first error is statistical and the second is systematic. These results are more precise by a factor of three compared to previous experimental measurements. Our results are in agreement with the Standard Model values at tree level, B(τ → µγνν¯) = 3.67 × 10−3 , and B(τ → eγνν¯) = 1.84 × 10−2 , and with current experimental bounds.From here.
The pertinent language in the cited source for the Standard Model prediction published October 23, 2013 states:
For radiative τ− decays, with the same threshold Emin γ = 10 MeV, we obtain 1.84 × 10−2 (l = e) and 3.67 × 10−3 (l = µ), to be compared with the values measured by the CLEO Collaboration, (1.75 ± 0.06 ± 0.17) × 10−2 and (3.61 ± 0.16 ± 0.35) × 10−3, respectively, where the first error is statistical and the second one is systematic .
The experimental results from CLEO cited at  in the October 23, 2013 paper were published in the year 2000. The BABAR result was obviously much more accurate and much closer to the theoretical prediction as well. Indeed, the BABAR result is consistent with a true systemic error of zero, rather than the conservative estimate given, with all error seen actually being simply a function of statistical sample size. I noted similar instances of extremely accurate approximations of theoretical predictions in another post as year ago.