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+→π+π−ℓ+νℓ (ℓ=e and μ). The D+→f0(500)μ+νμ decay is observed for the first time. By analyzing simultaneously the differential decay rates of D+→f0(500)μ+νμ and D+→f0(500)e+νe in different ℓ+νℓ 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 |Vcd| is determined to be f+f0(0)|Vcd|=0.143±0.014stat±0.011syst for the first time. With the input of |Vcd| from the global fit in the standard model, we determine f+f0(0)=0.63±0.06stat±0.05syst. The absolute branching fractions of D+→f0(500)(π+π−)μ+νμ and D+→ρ(π+π−)0μ+νμ are determined as (0.72±0.13stat±0.08syst)×10−3 and (1.64±0.13stat±0.10syst)×10−3. Combining these results with those of previous BESIII measurements on their semielectronic counterparts from the same data sample, we test lepton flavor universality by measuring the branching fraction ratios BD+→ρ0μ+νμ/BD+→ρ0e+νe=0.88±0.10 and BD+→f0(500)μ+νμ/BD+→f0(500)e+νe=1.14±0.26, which are compatible with the standard model expectation. Published by the American Physical Society 2024
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