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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 ff0+(0) and the magnitude of the c→d Cabibbo-Kobayashi-Maskawa matrix element |Vcd| is determined to be ff0+(0)|Vcd|=0.0787±0.0060stat±0.0033syst for the first time. With the input of |Vcd| from the global fit in the standard model, we determine ff0+(0)=0.350±0.027stat±0.015syst. The absolute branching fractions of D+→f0(500)(π+π−)μ+νμ and D+→ρ0(π+π−)μ+νμ are determined as (0.72±0.13stat±0.10syst)×10−3 and (1.64±0.13stat±0.11syst)×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±0.28, which are compatible with the standard model expectation.
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 ff0+(0) and the magnitude of the c→d Cabibbo-Kobayashi-Maskawa matrix element |Vcd| is determined to be ff0+(0)|Vcd|=0.0787±0.0060stat±0.0033syst for the first time. With the input of |Vcd| from the global fit in the standard model, we determine ff0+(0)=0.350±0.027stat±0.015syst. The absolute branching fractions of D+→f0(500)(π+π−)μ+νμ and D+→ρ0(π+π−)μ+νμ are determined as (0.72±0.13stat±0.10syst)×10−3 and (1.64±0.13stat±0.11syst)×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±0.28, which are compatible with the standard model expectation.