Probing Gluon Linear Polarization with Dihadron Fragmentation in $χ_b$ Decays

Abstract

The dihadron fragmentation function (DiFF) of a linearly polarized gluon has not yet been accessed experimentally, leaving an important aspect of spin-dependent gluon hadronization unexplored. We show that, at leading order, the color-singlet decay channel of the $P$-wave bottomonium state $χ_{b0}$ produces two energetic gluons with correlated linear polarizations. Within collinear factorization, their fragmentation into separate dihadron pairs generates an Artru--Collins-type angular correlation that provides the first direct probe of the linearly polarized gluon DiFF, while the corresponding semi-inclusive decay rate constrains the unpolarized gluon DiFF. A spectator-model benchmark indicates percent-level asymmetries, potentially within reach of existing Belle data. A dedicated Belle~II data set would substantially improve the statistical precision, enabling more stringent constraints on the kinematic dependence of the linearly polarized gluon DiFF.