13 and systematic uncertainties on A × ϵ ( ∼ 2%) and the statistical uncertainty on the π $^{±}$γ background fit ( ∼ 5%). ergy (due to bremsstrahlung) and improves overall elec- tron identification efficiency. This selection results in a sample with ≤ 5% background, the dominant sources of which are W ± → τ $^{±}$ν , Z 0 → e $^{+}$e − decays and multijet events with one of the jets misidentified as an electron. The backgrounds are subtracted using MC simulation and the resulting σ × BR ( W ± → e $^{±}$ν ) is found to be consistent with previous measurements [10]. The dom- inant source of uncertainty on the cross section is the uncertainty on the luminosity [16], which cancels in the ratio Γ( W ± → π $^{±}$γ ) / Γ( W ± → e $^{±}$ν ). The 95% C.L. upper limit on the ratio of partial widths Γ( W ± → π $^{±}$γ ) / Γ( W ± → e $^{±}$ν ), calculated using a Bayesian approach that takes into account the effect of systematic uncertainties [18], is 6 . 4 × 10 − $^{5}$. This improves the previous world’s best limit [5] by more than a factor of 10. The corresponding 95% C.L. upper limit on the branching ratio BR ( W ± → π $^{±}$γ ), calculated using the world average BR ( W ± → e $^{±}$ν ) = 0 . 1075 ± 0 . 0013 [14], is 7 . 0 × 10 − $^{6}$. While no W ± → π $^{±}$γ signal was observed, the sensitivity of the CDF experiment to this decay chan- nel has reached a level comparable to theoretical predic- tions. With increases in the dataset size, we expect the $_{sensitivity to improve as 1/}$√$_{L}$$_{, where L is the integrated}$ luminosity. Other sources of the systematic uncertainties that cancel almost entirely in the measurement of Γ( W ± → π $^{±}$γ ) / Γ( W ± → e $^{±}$ν ) include the uncertainties on the trigger efficiency as well as the uncertainties on parton distribution functions [17] and on the W transverse momentum, which affect the experimental acceptance. The uncertainties on the electron and photon identification efficiences cancel partially but result in a negligible uncertainty on the measurement of Γ( W ± → π $^{±}$γ ) / Γ( W ± → e $^{±}$ν ). The dominant remaining sources of uncertainties are the statistical We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contribu- tions. This work was supported by the U.S. Depart- ment of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Min-