Observation of <i>D</i><SUP>+</SUP> → <i>f</i>₀(500)μ<SUP>+</SUP>ν_μ and study of <i>D</i><SUP>+</SUP> → π<SUP>+</SUP>π<SUP>-</SUP> <i>l</i><SUP>+</SUP>ν<i>_l</i> decay dynamics

Using 2.93 fb(-1) of e(+)e(-) collision data collected with the BESIII detector at the center-of-mass energy of 3.773 GeV, we investigate the semileptonic decays D+ -> pi(+)pi(-)l(+)nu(l) (l = e and mu). The D+ -> f(0)(500)mu(+)nu(mu) decay is observed for the first time. By analyzing simultaneously the differential decay rates of D+ -> f(0)(500)mu(+)nu(mu) and D+ -> f(0)(500)e(+)nu(e) in different l(+)nu(l) four-momentum transfer intervals, the product of the relevant hadronic form factor f(+)(f0)(0) and the magnitude of the c -> d Cabibbo-Kobayashi-Maskawa matrix element vertical bar V-cd vertical bar is determined to be f(+)(f0)(0)vertical bar V-cd vertical bar = 0.143 +/- 0.014(stat) +/- 0.011(syst) for the first time. With the input of vertical bar V-cd vertical bar from the global fit in the standard model, we determine f(+)(f0)(0) = 0.63 +/- 0.06(stat) +/- 0.05(syst). The absolute branching fractions of D+ -> f(0)(500)((pi+)pi-)mu(+)nu(mu) and D+ -> rho(0)((pi+pi-))mu(+)nu(mu) are determined as (0.72 +/- 0.13(stat) +/- 0.08(syst)) x 10(-3) and (1.64 +/- 0.13(stat) +/- 0.10(syst)) x 10(-3). Combining these results with those of previous BESIII measurements on their semi-electronic counterparts from the same data sample, we test lepton flavor universality by measuring the branching fraction ratios BD+->rho 0 mu+nu mu/BD+rho 0e+nu e = 0.88 +/- 0.10 and BD+-> f0(500)mu+nu mu/BD+-> f0(500)e+nu e = 1.14 +/- 0.26, which are compatible with the standard model expectation.