A Subleading Operator Basis and Matching for $gg \to H$

The Soft Collinear Effective Theory (SCET) is a powerful framework for studying factorization of amplitudes and cross sections in QCD. While factorization at leading power has been well studied, much less is known at subleading powers in the $\lambda\ll 1$ expansion. In SCET subleading soft and collinear corrections to a hard scattering process are described by power suppressed operators, which must be fixed case by case, and by well established power suppressed Lagrangians, which correct the leading power dynamics of soft and collinear radiation. Here we present a complete basis of power suppressed operators for $gg \to H$, classifying all operators which contribute to the cross section at $\mathcal{O}(\lambda^2)$, and showing how helicity selection rules significantly simplify the construction of the operator basis. We perform matching calculations to determine the tree level Wilson coefficients of our operators. These results are useful for studies of power corrections in both resummed and fixed order perturbation theory, and for understanding the factorization properties of gauge theory amplitudes and cross sections at subleading power. As one example, our basis of operators can be used to analytically compute power corrections for $N$-jettiness subtractions for $gg$ induced color singlet production at the LHC.