Probing the Color-Octet Mechanism via Dihadron Fragmentation in ${\chi }_b$ Decays

Abstract

The color-octet (CO) mechanism is a cornerstone of nonrelativistic QCD, yet knowledge of its long-distance matrix elements remains 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. At leading order, 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 $e^{+}{e}^{-}\to {\rm Y}(2S)\to \gamma {\chi }_{b2}$ 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.

6 pages, 3 figures, published version in PRL