If the X(3872) is a weakly bound charm-meson molecule, it can be produced in e + e − annihilation by the creation of D * 0D * 0 from a virtual photon followed by the rescattering of the charm-meson pair into X and a photon. A triangle singularity produces a narrow peak in the cross section for e + e − → Xγ about 2.2 MeV above the D * 0D * 0 threshold. We predict the normalized cross section in the region near the peak. The peak from the triangle singularity may be observable by the BESIII detector.

If the X(3872) is a weakly bound charm-meson molecule, it can be produced in e + e − annihilation by the creation of D * 0D * 0 from a virtual photon followed by the rescattering of the P-wave charmmeson pair into the X and a photon. A triangle singularity produces a narrow peak in the cross section for e + e − → Xγ 2.2 MeV above the D * 0D * 0 threshold. We predict the normalized cross section in the region of the peak. We show that the absorptive contribution to the cross section for e + e − → D * 0D * 0 → Xγ, which was calculated previously by Dubynskiy and Voloshin, does not give a good approximation to the peak from the triangle singularity.

If the X(3872) is a weakly bound charm-meson molecule, it can be produced by the creation of D * 0D0 or D 0D * 0 at short distances followed by the formation of the bound state from the charm-meson pairs. It can also be produced by the creation of D * D * at short distances followed by the rescattering of the charm mesons into Xπ. We use results of a previous isospin analysis of B meson decays into KD ( * )D( * ) to estimate the short-distance amplitudes for creating D * D * . We use an effective field theory for charm mesons and pions called XEFT to calculate the amplitudes for rescattering of D * D * into Xπ with small relative momentum. The Xπ invariant mass distribution is predicted to have a narrow peak near the D * D * threshold from a charm-meson triangle singularity. We estimate the branching fractions into the peak from the triangle singularity for the decays B 0 → K + Xπ − and B + → K 0 Xπ + .

If the X(3872) is a weakly bound charm-meson molecule, it can be produced by the creation of D * 0D0 or D 0D * 0 at short distances followed by the formation of the bound state from the charmmeson pair. The X can also be produced by the creation of D * D * at short distances followed by the rescattering of the charm-meson pair into Xπ. At a high-energy hadron collider, the prompt cross section from this mechanism has a narrow peak in the Xπ invariant mass distribution near the D * D * threshold from a charm-meson triangle singularity. An order-of-magnitude estimate of the ratio of the cross section for producing the peak in the Xπ ± distribution to the cross section for producing X without an accompanying pion suggests that the peak may be observable at the LHC.

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