Threshold cusp effects to measure masses of radiatively decaying hadrons: The $B_{s0}^*$ mass from the $\Upsilon\phi$ 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 $B_{s0}^*$ and $B_{s1}$, the bottom partners of the $D_{s0}^*(2317)$ 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 $J/\psi\phi$ distribution extracted from $B\to K J/\psi \phi$, as a $D_{s0}^*\bar D_s$ threshold cusp driven by a nearby virtual-state pole, yielding $m_{D_{s0}^*}=(2322\pm6)$ 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 $B_{s0}^*\bar B_s$ threshold near $11.09$ GeV, making the $\Upsilon\phi$ invariant-mass distribution at the LHC a clean probe of the $B_{s0}^*$ mass.