We present $I=1/2$ $D^{*}\pi$ scattering amplitudes from lattice QCD and determine two low-lying $J^P=1^{+}$ axial-vector $D_1$ states and a $J^P=2^{+}$ tensor $D_2^{*}$. Computing finite-volume spectra at a light-quark mass corresponding to $m_{\pi }\approx 391\mathrm{MeV}$, for the first time, we are able to constrain coupled $J^P=1^{+}$ $D^{*}\pi$ amplitudes with ${}^{2S+1}{\ell }_J={}^3{S}_1$ and ${}^3{D}_1$ as well as coupled $J^P=2^{+}D\pi ({}^1{D}_2\}$ and $D^{*}\pi ({}^3{D}_2\}$ amplitudes via Lüscher’s quantization condition. Analyzing the scattering amplitudes for poles we find a near-threshold bound state, producing a broad feature in $D^{*}\pi \{{}^3{S}_1\}$. A narrow bump occurs in $D^{*}\pi \{{}^3{D}_1\}$ due to a $D_1$ resonance. A single resonance is found in $J^P=2^{+}$ coupled to $D\pi$ and $D^{*}\pi$. A relatively low mass and large coupling are found for the lightest $D_1$, suggestive of a state that will evolve into a broad resonance as the light-quark mass is reduced. An earlier calculation of the scalar $D_0^{*}$ using the same light-quark mass enables comparisons to the heavy-quark limit.

• Received 24 May 2022
• Accepted 20 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.252001

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Published by the American Physical Society