Precise determination of the properties of X(3872) and of its isovector partner Wc1

We perform a simultaneous fit to BESIII data on e + e - → γ ( D 0 D ‾ 0 π 0 / J / ψ π + π - ) and LHCb data on B + → K + ( J / ψ π + π - ) to precisely determine the properties of the X ( 3872 ) , with full consideration of three-body effects from D ∗ → D π decay, respecting both analyticity and unitarity. The X ( 3872 ) is determined to be a quasi-bound state with a significance of 2.7 σ , representing the most precise determination to date. Its pole is located at - 160 - 74 + 57 - 125 - 38 + 23 i keV , relative to the nominal D 0 D ‾ * 0 threshold. Moreover, we confirm the presence of an isovector partner state, W c 1 . It is found as a virtual state at 3.1 ± 0.7 + 1.3 - 0.6 + 1.9 i MeV relative to the D + D * - threshold on an unphysical Riemann sheet, strongly supporting a molecular nature of both X ( 3872 ) and W c 1 . As a highly nontrivial prediction we show that the W c 1 leads to nontrivial lineshapes around 3.88 GeV in B 0 → K 0 X ( 3872 ) → K 0 D 0 D ¯ 0 π 0 and K 0 J / ψ π + π - —thus the scheme presented here can be tested further by improved measurements.