Feynman diagrams for X b production in Υ(5S) → γX b under the B ¯ B * meson loop effects.

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... in Sec. III the numerical results are presented, and a brief summary is given in Sec. IV. Under the assumption that X b is a B ¯ B * molecule, its production can be described by the triangle diagrams in Fig. 1. With the quantum numbers of 1 −− , the initial bottomonium can couple to either two S-wave bottomed mesons in a P -wave, or one P -wave and one S-wave bottomed mesons in an S-or D-wave. The X b couples to the B ¯ B * pair in an S-wave. Because the states considered here are close to the open bottomed mesons thresholds, the ...

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... the diagrams (a), (b), and (c) in Fig. 1, the vertices involving the initial bottomonium are in a P -wave. The momentum in these vertices is contracted with the final photon momentum q and thus should be counted as q. The vertices involving the photon are also in a P -wave, which should be counted as q. The decay amplitude scales ...

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... E γ is the external photon energy, N A contains all the constant factors, and v A is the average of the two velocities corresponding to the two cuts in the triangle diagram. While for the diagrams (d) and (e) in Fig. 1, all the vertices are in S-wave. Then the amplitude for the Figs. 1(d) and (e) scales ...

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... E γ is the external photon energy, N A contains all the constant factors, and v A is the average of the two velocities corresponding to the two cuts in the triangle diagram. While for the diagrams (d) and (e) in Fig. 1, all the vertices are in S-wave. Then the amplitude for the Figs. 1(d) and (e) scales ...

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... calculate the diagrams in Fig. 1, we employ the effective Lagrangians constructed in the heavy quark limit. In this limit, the S-wave heavy-light mesons form a spin multiplet H = (P, V ) with s P l = 1/2 − , where P and V denote the pseudoscalar and vector heavy mesons, respectively, i.e., P (V ) = (B ( * )+ , B ( * )0 , B ( * )0 s ). The s P l = 1/2 + states are ...

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... decay amplitudes of the triangle diagrams in Fig. 1 can be obtained and the explicit transition amplitudes for Υ(5S, 6S) → γX b are presented in Appendix A. The partial decay widths of Υ(5S, 6S) → γX b are given ...