ergy clusters with | η | ≤ 1 . 1 and within the CES fiducial. A cluster may be pointed to by at most one track; this track must have p$_{T}$ less than 1 GeV / c + 0 . 005 × E γ $_{T}$/c . To reject background from neutral mesons decaying into photons, we veto candidates which have additional CES clusters with energy above 2 . 4 GeV + 0 . 01 × E γ T in the same CES chamber. As photons from W ± → π $^{±}$γ de- cays are expected to be isolated, we require the total additional energy deposited in the calorimeter within a cone of Δ R = 0 . 4 around the photon candidate to be less than 1 . 6 GeV + 0 . 02 × E γ T and the sum of transverse momenta of the COT tracks within the same cone to be less than 2 . 0 GeV / c + 0 . 005 × E γ $_{T}$/c . 

Charged pion candidates are reconstructed as COT tracks with impact parameter ≤ 0 . 2 cm with respect to the beam axis. The track must be consistent with origi- nating from the primary event vertex, which is required to be within 60 cm of the center of the detector along the beam line. The track must point to a narrow calorimeter cluster and extrapolate to a fiducial region of the CES de- tector. As with photons, pions from W ± → π $^{±}$γ decays are expected to be isolated, and the pion candidates are 

required to satisfy a number of tracking and calorimeter isolation criteria. A pion candidate is rejected if there is another track originating from the same vertex having p$_{T}$ > 1 GeV / c within a cone of 10 ◦ around the pion track. The total additional calorimeter energy within the cone of Δ R = 0 . 4 around the cluster is required to be less than 10% of the track p$_{T}$ and the sum of transverse momenta of all tracks within Δ R = 0 . 4 of the pion track is required to be less than 5% of its p$_{T}$ . To reject background from QCD jets, which often contain neutral particles, no CES clusters with energy greater than 500 MeV may be found within 30 ◦ of the track. Finally, pion candidates passing electron identification criteria are excluded from the anal- ysis. This selection yields a total of 1398 π $^{±}$γ candidate events. 

The acceptance for the W ± → π $^{±}$γ decay is deter- mined using a sample of Monte Carlo (MC) events gen- erated with the pythia event generator [11] and the CTEQ5L parton distribution functions [12]. The angu- lar distribution of pions in the W boson rest frame is described by the formula dN/d cos θ = 1 + cos $^{2}$θ , where θ is the angle of the pion with respect to the W boson line 

