X structures in B+ → J/ψ ϕ K+ as one-loop and double-triangle threshold cusps

Abstract

The LHCb data on B+→J/ψϕK+ show four peaks and three dips in the J/ψϕ 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) Ds⁎D¯s(⁎), Ds0⁎(2317)D¯s(⁎), Ds1(2536)D¯s(⁎), and ψ′ϕ 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.