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In the framework of Color Glass Condensate (CGC) effective field theory(EFT), we calculate two-gluon rapidity correlations in the leading andsub-leading orders of $p_\perp/Q_s$. In the leading order, both short- andlong-range rapidity correlations are enhanced. In contrast, the contribution ofsub-leading order is mainly short range quantum correlations. It is muchsmaller than that of the leading one, but is not negligible. Transversemomentum dependence of rapidity correlation shows that the leading order issensitive to the saturation momentum of two incident particles, but thesub-leading one is not.

Sub-leading correction of two-gluon rapidity correlations of strong colour field