Semileptonic decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>ρ</mml:mi><mml:msup><mml:mi>l</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mi>ν</mml:mi></mml:m

We investigate the semileptonic decays of charmed mesons to light vector mesons within the framework of light-cone sum rules. Our calculation is performed at leading order in quantum chromodynamics (QCD) coupling, incorporating contributions up to twist-five accuracy from both two-particle and three-particle light-cone distribution amplitudes. Transition form factors are predicted twist by twist to assess the convergence property of the operator product expansion. It is verified that the twist-four and twist-five contributions are indeed negligible for all the decays under consideration. Twist-three dominance is observed for some of the form factors, subject to heavy quark effective field theory interpretation. Branching ratios for the decays <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>D</a:mi><a:mo>+</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:msup><a:mi>ρ</a:mi><a:mn>0</a:mn></a:msup><a:msup><a:mo>ℓ</a:mo><a:mo>+</a:mo></a:msup><a:msub><a:mi>ν</a:mi><a:mo>ℓ</a:mo></a:msub></a:math>, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msubsup><d:mi>D</d:mi><d:mi>s</d:mi><d:mo>+</d:mo></d:msubsup><d:mo stretchy="false">→</d:mo><d:msup><d:mi>K</d:mi><d:mrow><d:mo>*</d:mo><d:mn>0</d:mn></d:mrow></d:msup><d:msup><d:mo>ℓ</d:mo><d:mo>+</d:mo></d:msup><d:msub><d:mi>ν</d:mi><d:mo>ℓ</d:mo></d:msub></d:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>D</g:mi><g:mn>0</g:mn></g:msup><g:mo stretchy="false">→</g:mo><g:msup><g:mi>K</g:mi><g:mrow><g:mo>*</g:mo><g:mo>−</g:mo></g:mrow></g:msup><g:msup><g:mo>ℓ</g:mo><g:mo>+</g:mo></g:msup><g:msub><g:mi>ν</g:mi><g:mo>ℓ</g:mo></g:msub></g:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi>D</j:mi><j:mo>+</j:mo></j:msup><j:mo stretchy="false">→</j:mo><j:msup><j:mover accent="true"><j:mi>K</j:mi><j:mo stretchy="false">¯</j:mo></j:mover><j:mrow><j:mo>*</j:mo><j:mn>0</j:mn></j:mrow></j:msup><j:msup><j:mo>ℓ</j:mo><j:mo>+</j:mo></j:msup><j:msub><j:mi>ν</j:mi><j:mo>ℓ</j:mo></j:msub></j:math> are obtained, and a 10%–20% discrepancy from experimental measurements is found. Our finding indicates that the resonant-width and nonresonant QCD backgrounds effects should be potentially significant, implying the necessity to further implement their contributions in future precision studies of the semileptonic charm decays.