9 close to the kinematics properties of the W ± → e $^{±}$ν de- cay, which has been extensively studied at the Tevatron [10]. Consequently, many common systematic uncertain- ties cancel in the ratio Γ( W ± → π $^{±}$γ ) / Γ( W ± → e $^{±}$ν ), and we use sample of W ± → e $^{±}$ν events collected with the same trigger to normalize the results of the search. by a factor of ≈ 50. The CDF II detector is a general purpose particle de- tector and is described in detail elsewhere [6]. The z - axis of the detector coordinate system points along the direction of the proton beam. The event geometry and kinematics are described using the azimuthal angle φ and the pseudorapidity η = − ln(tan θ/ 2), where θ is the po- lar angle with respect to the beam axis. The transverse energy and momentum of the reconstructed particles are defined as E$_{T}$ = E sin θ , p$_{T}$ = p sin θ , where E is the energy and p is the momentum. The three level calorimeter-based trigger selects events with at least one central calorimeter cluster with E$_{T}$ > 25 GeV and a large fraction of energy deposited in the CEM: E$_{CHA}$/E$_{CEM}$ < 0 . 0055 + 0 . 00045 × E . A cluster is required to be isolated such that the additional en- ergy in a cone of Δ R = √ Δ φ 2 + Δ η 2 = 0 . 4 is less than 10% of the cluster energy. To reduce background from the multi-photon decays of neutral mesons, most impor- tantly π 0 mesons, the lateral profile of the CES shower is required to be consistent with that produced by a single photon. Offline π $^{±}$γ selection requires each event pass- ing the trigger to have a photon candidate with E$_{T}$ > 25 GeV and a charged pion candidate with p$_{T}$ > 25 GeV / c and with significant azimuthal separation (Δ φ > 2 radi- ans) between them. The analysis presented below uses electron ( e $^{±}$), pho- ton ( γ ), and charged pion ( π $^{±}$) candidates, reconstructed and identified using information from the central outer tracker (COT) [7], central electromagnetic (CEM) and hadronic calorimeters (CHA), and the central shower maximum detector (CES) [8, 9]. Candidate π $^{±}$γ events are collected using an inclusive photon trigger that has no tracking requirements. As a result, the trigger has similar efficiencies for selecting high- p$_{T}$ electrons and photons. The kinematic proper- ties of the W ± → π $^{±}$γ decay are also in many respects Photon candidates are reconstructed from CEM en-