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The off-diagonal parton-scattering channels $g+\gamma^*$ and $q+\phi^*$ indeep-inelastic scattering are power-suppressed near threshold $x\to 1$. Weaddress the next-to-leading power (NLP) resummation of large double logarithmsof $1-x$ to all orders in the strong coupling, which are present even in theoff-diagonal DGLAP splitting kernels. The appearance of divergent convolutionsprevents the application of factorization methods known from leading powerresummation. Employing $d$-dimensional consistency relations from requiring$1/\epsilon$ pole cancellations in dimensional regularization between momentumregions, we show that the resummation of the off-diagonal parton-scatteringchannels at the leading logarithmic order can be bootstrapped from the recentlyconjectured exponentiation of NLP soft-quark Sudakov logarithms. In particular,we derive a result for the DGLAP kernel in terms of the series of Bernoullinumbers found previously by Vogt directly from algebraic all-order expressions.We identify the off-diagonal DGLAP splitting functions and soft-quark Sudakovlogarithms as inherent two-scale quantities in the large-$x$ limit. We use arefactorization of these scales and renormalization group methods inspired bysoft-collinear effective theory to derive the conjectured soft-quark Sudakovexponentiation formula.

Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization