X structures in B+ ? J/? f K+ as one-loop and double-triangle threshold cusps

The LHCb data on B+ -> J/psi phi K+ show four peaks and three dips in the J/psi phi invariant mass distribution, and the peaks are interpreted as X(4140), X(4274), X(4500) and X(4685)/X(4700) resonance contributions. Interestingly, all the peaks and dips are located at (or close to) D-s(*)(D)overbar(s)((*)) , D-s(0)*(2317) (D)overbar(s)((*)), D-s1(2536)(D)overbar(s)((*)) , and psi ' phi thresholds. These coincidences suggest a close connection between the structures and the thresholds, which however has not been seriously considered in previous theoretical studies on the X structures. In fact, if we utilize this connection and interpret the X structures as common s-wave threshold cusps, we face a difficulty: X(4274) and X(4500) have spin-parity that conflict with the experimentally determined ones. In this work, we introduce double triangle mechanisms that cause threshold cusps significantly sharper than the ordinary one-loop ones of the same spin-parity. We demonstrate that all the X and dip structures are well described by a combination of one-loop and double-triangle threshold cusps, thereby proposing a novel interpretation of the X and dip structures.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

The LHCb data reveals four peaks and three dips in the J/psi phi invariant mass distribution of B+ -> J/psi phi K+. These structures are interpreted as resonance contributions and are closely related to specific thresholds, suggesting a novel interpretation of the X and dip structures.