Study of the decay D(s)(+)-> K(+)K(-)e(+)v(e)

Using 214 fb(-1) of data recorded by the BABAR detector at the PEPII electron-positron collider, we study the decay D(s)(+) -> K(+) K(-) e(+) v(e). Except for a small S-wave contribution, the events with K(+)K(-) masses in the range 1.01-1.03 GeV/c(2) correspond to phi mesons. For D(s)(+) ->phi e(+) v(e) decays, we measure the relative normalization of the Lorentz invariant form factors at q(2) = 0, r(V) V(0)/A1(0) = 1.849 +/- 0.060 +/- 0.095, r(2) = A(2)(0)/A(1)(0) = 0.763 +/- 0.071 +/- 0.065 and the pole mass of the axial-vector form factors m(A) =(2.28(-0.18)(+0.230) +/- 0.18) GeV/c(2). Within the same K(+)K(-) mass range, we also measure the relative branching fraction B(D(s)(+) -> K(+) K(-) e(+) v(e))/B(D(s)(+) -> K(+) K (-)pi(+)) = 0.558 +/- 0.007 +/- 0.016, from which we obtain the total branching fraction B(D(s)(+) -> phi e(+) v(e)) = 2.61 +/- 0.03 +/- 0.08 +/- 0.15) x 10(-2). By comparing this value with the predicted decay rate, we extract A(1)(0) = 0.607 +/- 0.011 +/- 0.019 +/- 0.018. The stated uncertainties are statistical, systematic, and from external inputs.