An X(3872)-Like Peak in B→(J/ψπ⁺π⁻)Kπ Due to Triangle Singularity

Triangle mechanisms for B⁰→(J/ψπ⁺π⁻)K⁺π⁻ are studied. Experimentally, an X(3872) peak has been observed in this process. When the final (J/ψπ⁺π⁻)π invariant mass is around the D^∗D¯^∗ threshold, one of the triangle mechanisms causes a triangle singularity and generates a sharp X(3872)-like peak in the J/ψπ⁺π⁻ invariant mass distribution. The Breit–Wigner mass and width fitted to the spectrum are 3871.68 MeV (a few keV above the D^∗0D¯⁰ threshold) and ∼ 0.4 MeV, respectively. These Breit-Wigner parameters hardly depend on a choice of the model parameters. Comparing with the precisely measured X(3872) mass and width, 3871.69±0.17 MeV and <1.2 MeV, the agreement is remarkable. When studying the X(3872) signal from this process, this non-resonant contribution has to be understood in advance. We also study a charge analogous process B⁰→(J/ψπ⁰π⁻)K⁺π⁰. A similar triangle singularity exists and generates an X⁻(3876)-like peak. (author)