Triangle singularity appearing as an $X(3872)$-like peak in $B\to (J/ψπ^+π^-) Kπ$

Abstract

X(3872) has been an outstanding candidate of exotic hadrons beyond the conventional quarkantiquark picture, and invited extensive studies. Yet, we still have not seen a clearcut explanation, which does not resort to fine-tuning uncertain hadron dynamics, of the well-established properties of X(3872) such as its mass and width. In this work, we consider a triangle diagram for B → (J/ψπ + π − )Kπ where a X(3872) peak has been observed experimentally. We demonstrate that a triangle singularity inherent in the triangle diagram creates a sharp peak in the J/ψπ + π − invariant mass distribution. The position and width of the peak is 3871.71 MeV (∼30 keV above the D * 0 D0 threshold) and ∼0.5 MeV, respectively, in perfect agreement with the precisely measured X(3872) mass and width: 3871.69 ± 0.17 MeV and < 1.2 MeV. This result is virtually parameter-free because the triangle singularity is a kinematical effect and does not depend on details of hadron dynamics. Although this work is limited to one of several processes where X(3872) has been observed, X(3872) as manifestations of triangle singularities is now a promising option.

Heating triangle singularities in heavy ion collisions

“…We are not currently aware of a detailed computation of the K * width, so we use a crude rounded-off estimate of order Γ K * (T = 0) × (1 + nπ(T ) + n K (T )). Our last and most important example is the singularity recently reported [9] in lieu of the X(3872) in the reaction…”

“…In fact, we do find very acute sensitivity to the kinematic variables. The peak of the singularity is sharpest at T = 0: as temperature increases, the peak diminishes in height and shifts to smaller J/ψπ + π − invariant mass m C , accom- 6) against m C for (B 0 − K + )(A) → (J/ψπ + π − )(C)π − (B) [9]. Top: the temperature affects only the loop variable, but M i , Γ i are fixed at their vacuum values [19].…”

“…Figure 4: Squared triangle graph (|I⊳| 2 ) in Eq. (6) against m C for (B 0 − K + )(A) → (J/ψπ + π − )(C)π − (B)[9]. Top: the temperature affects only the loop variable, but M i , Γ i are fixed at their vacuum values[19].…”

“…Serve as example the recent claim [4] that the a 1 (1420) is no axial-vector meson resonance but such triangle singularity instead. There are several works that explain the mechanism [5,6,7,8,9,10,11]: in brief, the triangle singularity, that receives its name from the Feynman diagram in Fig. 1 happens when the three intermediate particles become on shell and two have parallel momenta, if such kinematics is allowed.…”

X(3872) Production in Relativistic Heavy-Ion Collisions

“…A superposition of two configurations has also been proposed [11,12]. Whether X(3872) is a loosely bound molecule, a compact tetraquark or just a kinematic effect such as triangle singularity is still under debate [13][14][15]. In proton-proton (pp) collisions, the multiplicity dependence of the yield ratio X(3872)/ψ(2S) at LHCb [16] has been measured, and it seems to disfavor the molecular interpretation of X(3872) [17,18].…”