Search for Lepton Flavor Violation in the Decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>τ</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mi>γ</mml:mi></mml:math>

A search for the nonconservation of lepton flavor in the decay ${\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{e}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\gamma}$ has been performed with $2.07\ifmmode\times\else\texttimes\fi{}{10}^{8}$ ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ events collected by the BABAR detector at the SLAC PEP II storage ring at a center-of-mass energy near 10.58 GeV. We find no evidence for a signal and set an upper limit on the branching ratio of $\mathcal{B}({\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{e}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\gamma})&lt;1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ at 90% confidence level.

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