Exclusive branching-fraction measurements of semileptonic τ decays into three charged hadrons, into φπ-ντ, and into φk-ντ

Using a data sample corresponding to an integrated luminosity of 342 fb{sup -1} collected with the BABAR detector at the SLAC PEP-II electron-positron storage ring operating at a center-of-mass energy near 10.58 GeV, we measure B({tau}{sup -}{yields}{pi}{sup -}{pi}{sup -}{pi}{sup +}{nu}{sub {tau}}(ex.K{sub S}{sup 0}))=(8.83{+-}0.01{+-}0.13)%, B({tau}{sup -}{yields}K{sup -}{pi}{sup -}{pi}{sup +}{nu}{sub {tau}}(ex.K{sub S}{sup 0}))=(0.273{+-}0.002{+-}0.009)%, B({tau}{sup -}{yields}K{sup -}{pi}{sup -}K{sup +}{nu}{sub {tau}})=(0.1346{+-}0.0010{+-}0.0036)%, and B({tau}{sup -}{yields}K{sup -}K{sup -}K{sup +}{nu}{sub {tau}})=(1.58{+-}0.13{+-}0.12)x10{sup -5}, where the uncertainties are statistical and systematic, respectively. These include significant improvements over previous measurements and a first measurement of B({tau}{sup -}{yields}K{sup -}K{sup -}K{sup +}{nu}{sub {tau}}) in which no resonance structure is assumed. We also report a first measurement of B({tau}{sup -}{yields}{phi}{pi}{sup -}{nu}{sub {tau}})=(3.42{+-}0.55{+-}0.25)x10{sup -5}, a new measurement of B({tau}{sup -}{yields}{phi}K{sup -}{nu}{sub {tau}})=(3.39{+-}0.20{+-}0.28)x10{sup -5} and a first upper limit on B({tau}{sup -}{yields}K{sup -}K{sup -}K{sup +}{nu}{sub {tau}}(ex.{phi}))