Study of the decay <i>D</i><SUP>0</SUP> → ρ(770)<SUP>-</SUP> <i>e</i><SUP>+</SUP>ν<i>_e</i>

We present a study of the semileptonic decay D-0 -> pi(-)pi(0)e(+)nu(e) using an e(+)e(-) annihilation data sample of 7.93 fb(-1) collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The branching fraction of D-0 -> rho(770)(-) e(+)nu(e) is measured to be (1.439 +/- 0.033(stat) +/- 0.027(syst)) x 10(-3), which is a factor 1.6 more precise than previous measurements. By performing an amplitude analysis, we measure the hadronic form-factor ratios of (D-0 -> rho(770)(-) e(+)nu(e) at q(2) = 0 assuming the single-pole-dominance parametrization: r(V) = V(0)/A(1)(0) = 1.548 +/- 0.079(stat) +/- 0.041(syst) and r(2) = A(2)(0)/A(1)(0) = 0.823 +/- 0.056(stat) +/- 0.026(syst).