Model-independent description of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>D</mml:mi><mml:mi>π</mml:mi><mml:mo>ℓ</mml:mo><mml:mi>ν</mml:mi></mml:mr

We introduce a new parametrization of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>B</a:mi><a:mo stretchy="false">→</a:mo><a:mi>D</a:mi><a:mi>π</a:mi><a:mo>ℓ</a:mo><a:mi>ν</a:mi></a:mrow></a:math> form factors using a partial-wave expansion and derive bounds on the series coefficients using analyticity and unitarity. This is the first generalization of the model-independent formalism developed by Boyd, Grinstein, and Lebed for <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>B</d:mi><d:mo stretchy="false">→</d:mo><d:mi>D</d:mi><d:mo>ℓ</d:mo><d:mi>ν</d:mi></d:math> to semileptonic decays with multihadron final states, and enables data-driven form-factor determinations with robust, systematically improvable uncertainties. Using this formalism, we extract the form-factor parameters for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>B</g:mi><g:mo stretchy="false">→</g:mo><g:msubsup><g:mrow><g:mi>D</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow><g:mrow><g:mo>*</g:mo></g:mrow></g:msubsup><g:mo stretchy="false">(</g:mo><g:mo stretchy="false">→</g:mo><g:mi>D</g:mi><g:mi>π</g:mi><g:mo stretchy="false">)</g:mo><g:mo>ℓ</g:mo><g:mi>ν</g:mi></g:mrow></g:math> decays in a model-independent way from fits of data from the Belle Experiment. We find that the semileptonic data are compatible with the presence of two poles in the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>D</m:mi><m:mi>π</m:mi></m:math> S-wave channel, which is the scenario preferred by nonleptonic decays and unitarized chiral perturbation theory. Published by the American Physical Society 2024