Production of X(3872) accompanied by a pion in B meson decay

Abstract

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 + .

Triangle singularity in the B−→K−π0X(3872) reaction and sensitivity to the Sakai1, Oset2, Guo3 2020Phys. Rev. D

“…[32,66], this gives Br(B + → K 0 π + X(3872)) of the order of 2 × 10 −4 . In addition, in the low πX region, the TS contribution is more important for the B − → K − π 0 X(3872) than for the B + → K 0 π + X(3872) [30]. Future updates of the present facilities should make the rates of O(4 × 10 −8 ) attainable.…”

“…In order to get a simple analytic expression for the amplitude, the approximation in Ref. [30] amounts to the approximation of the scalar triangle loop integral by an expression,…”

“…Therefore, the approximation in Ref. [30] may be used for an estimate of the reaction rate, but is not applicable for a precise description of π 0 X line shape in the vicinity of the TS. In fact, the same approximation has been used to establish the power counting in a nonrelativistic effective field theory [41], and it has been pointed out in Ref.…”

“…A variant of this reaction is also proposed in Ref. [30] with the B 0 → K + Xπ − and B + → K 0 Xπ + processes, where the Xπ system develops a TS. The mechanism for the production is given by B → KD * D * 0 (B → KD * D * 0 ) followed by D * → πD 0 (D * → πD 0 ) andD * 0 D 0 (D * 0D0 ) fusing into the X(3872).…”

“…Since we aim at high precision in the determination of the TS energy, we must improve on approximations done in Ref. [30]. The methods used and input are also different, and we also discuss the need to convolve the results with the mass distribution of the X(3872) to compare with experiment.…”