Measurement of the absolute branching fractions for Ds- -> l- nu-bar and extraction of the decay constant f(Ds)

The absolute branching fractions for the decays D-s(-) -> l(-) (nu) over bar (l) (l = e, mu, or tau) are measured using a data sample corresponding to an integrated luminosity of 521 fb(-1) collected at center-of-mass energies near 10.58 GeV with the BABAR detector at the PEP-II e(+)e(-) collider at SLAC. The number of D-s(-) mesons is determined by reconstructing the recoiling system DKX gamma in events of the type e(+)e(-) -> DKXDs*(-), where D-s*(-) -> D-s(-) gamma and X represents additional pions from fragmentation. The D-s(-) -> l(-) nu(l) events are detected by full or partial reconstruction of the recoiling system DKX gamma l. The branching fraction measurements are combined to determine the D-s(-) decay constant f(Ds) (258.6 +/- 6.4 +/- 7:5) MeV, where the first uncertainty is statistical and the second is systematic.