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In this paper we study the OPE between two positive helicity outgoing gluonsin the celestial CFT for the Yang-Mills theory chirally coupled to a massivescalar background. This theory breaks the translation as well as scaleinvariance. We compute the subleading terms in the OPE expansion and show thatthey are same as the subleading terms of the OPE expansions in the MHV sector.As a result the amplitudes of this theory also satisfy the set of differentialequations obtained previously for MHV amplitudes in pure YM theory. This is notsurprising because the symmetries coming from the leading and subleading softgluon theorems do not change in the presence of a massive scalar background.

MHV Gluon Scattering in the Massive Scalar Background and Celestial OPE