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

TL;DR

This paper proposes using the Artru-Collins asymmetry in $ ext{chi}_b$ decays as a direct probe of the color-octet mechanism in non-relativistic QCD, enabling new tests of the theory and extraction of matrix element ratios.

Contribution

It introduces a novel observable, the Artru-Collins asymmetry in $ ext{chi}_b$ decays, as a direct and unambiguous probe of the color-octet mechanism in bottomonium decays.

Findings

The asymmetry arises solely from the CO decay channel.

The observable can extract the ratio of CO to CS matrix elements.

Potential to resolve discrepancies between lattice and phenomenological values.

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 $\chi_{b2}$ 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 $\rho_8$ between CO and CS matrix elements. Focusing on $e^+e^-\to\Upsilon(2S)\to\gamma\,\chi_{b2}$ 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, $\rho_8$ could be determined with sufficient precision to address the long-standing discrepancy between the lattice calculations and phenomenological determinations.