Axial-vector $D_1$ hadrons in $D^{\ast }\pi$ scattering from QCD

Abstract

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

Comments: 7+6 pages, 3+3 figures