Probing the Color-Octet Mechanism via Dihadron Fragmentation in $χ_b$ Decays

Abstract

The color-octet (CO) mechanism is a cornerstone of non-relativistic QCD, yet its long-distance matrix elements remain limited, preventing stringent tests of the theory. We demonstrate that the Artru-Collins asymmetry in hadronic decays of the $P$-wave bottomonium state $χ_{b2}$ provides a direct probe of CO dynamics. The asymmetry arises exclusively from the CO decay channel, whereas the color-singlet (CS) contribution affects only the unpolarized rate, so that a nonzero signal constitutes unambiguous evidence of the CO mechanism. This observable provides a novel way to extract the ratio $ρ_8$ between CO and CS matrix elements. Focusing on $e^+e^-\toΥ(2S)\toγ\,χ_{b2}$ at Belle, we show that the asymmetric beam configuration preserves the asymmetry in the laboratory frame and avoids the strong suppression present in the center-of-mass frame. With the Belle II dataset, $ρ_8$ could be determined with sufficient precision to address the long-standing discrepancy between the lattice calculations and phenomenological determinations.

Figures (3)

• Figure 1: Leading order kinematic configuration for the production of $\pi^+\pi^-$-dihadron pairs in $\chi_{b2}$ decay at lepton colliders. The $\chi_{b2}$ production is defined in the c.m. frame, while the partonic subprocess is described in the $\chi_{b2}$ rest frame.
• Figure 2: The Artru-Collins asymmetry $A_{12}$ in $\chi_{b2}$ decay with the $\chi_{b2}$ produced in the laboratory frame at an integrated luminosity $\mathcal{L}=1~{\rm ab}^{-1}$, shown as a function of $z_1$ (a) and $M_1$ (b) for two bins in $\cos\theta_p$, with all other kinematical valuables integrated over.
• Figure 3: Expected precision on $\rho_8(m_b)$ extracted from the Artru-Collins asymmetry in $\chi_{b2}$ decay at Belle II as a function of the integrated luminosity, for $\chi_{b2}$ produced in the laboratory frame (blue band) and in the c.m. frame(orange band).