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Improved Limits on the Lepton-Flavor Violating Decays<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>l</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>l</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>l</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

Improved Limits on the Lepton-Flavor Violating Decays<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>l</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>l</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>l</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

A search for the neutrinoless, lepton-flavor violating decay of the tau lepton into three charged leptons has been performed using 376 fb−1 of data collected at an e+e− center-of-mass energy around 10.58 GeV with the BABAR detector at the SLAC PEP-II storage rings. In all six decay modes considered, the …