Threshold cusp effects to measure masses of radiatively decaying hadrons: The $B_{s0}^{\ast }$ mass from the ${\rm Y}\varphi$ spectrum

Abstract

Hadrons that decay predominantly into final states containing photons are notoriously difficult to detect at hadron colliders. Prominent examples are the yet-unobserved $B_{s0}^{\ast }$ and $B_{s1}$, the bottom partners of the $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$, which are expected to exhibit exotic properties deviating from the conventional quark-model predictions of $\bar{b}s$ mesons. We propose a general, model-independent method to overcome this problem: when the target hadron has an attractive $S$-wave interaction with a companion hadron of precisely known mass, the line shape of a suitable final state develops a cusp at the pair threshold, or a peak just below it if the attraction binds, so that subtracting the companion mass returns the target mass, up to the binding energy in the latter case. As a proof of concept, a leading-order particle-dimer calculation of the $D{\bar{D}}_{s}K$ three-body system reproduces the $X(4274)$ structure in the LHCb $J/\psi \varphi$ distribution extracted from $B\to KJ/\psi \varphi$, as a $D_{s0}^{\ast }{\bar{D}}_s$ threshold cusp driven by a nearby virtual-state pole, yielding $m_{D_{s0}^{\ast }}=(2322\pm 6)$ MeV in agreement with its measured value and favoring $J^{PC}=0^{-+}$ for the $X(4274)$. Transferring the elastic three-body interaction to the bottom sector, we predict an analogous structure at the $B_{s0}^{\ast }{\bar{B}}_s$ threshold near $11.09$ GeV, making the ${\rm Y}\varphi$ invariant-mass distribution at the LHC a clean probe of the $B_{s0}^{\ast }$ mass.

Comments: 12 pages, 6 figures