Observation of a new excited $D_s^+$ meson in $B^0\to D^+D^-K^+\pi^-$ decays

Using $pp$ collision data corresponding to an integrated luminosity of $5.4\,{\rm fb}^{-1}$ collected with the LHCb detector at a centre-of-mass energy of $13\,{\rm TeV}$, the $B^0\to D^+D^-K^+\pi^-$ decay is studied. A new excited $D_s^+$ meson is observed decaying into the $D^+K^+\pi^-$ final state with large statistical significance. The pole mass and width, and the spin-parity of the new state are measured with an amplitude analysis to be $m_R=2591\pm6\pm7\,{\rm MeV}$, $\Gamma_R=89\pm16\pm12\,{\rm MeV}$ and $J^P=0^-$, where the first uncertainty is statistical and the second systematic. Fit fractions for all components in the amplitude analysis are also reported. The new resonance, denoted as $D_{s0}(2590)^+$, is a strong candidate to be the $D_s(2^1{\rm S}_0)^+$ state, the radial excitation of the pseudoscalar ground-state $D_s^+$ meson.