Abstract
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 λ ≪ 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 → H, classifying all operators which contribute to the cross section at mathcal{O}left({lambda}^2right) , 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.
Highlights
Factorization theorems play an important role in understanding the all orders behavior of observables in Quantum Chromodynamics (QCD)
We present a complete basis of power suppressed operators for gg → H, classifying all operators which contribute to the cross section at O(λ2), and showing how helicity selection rules significantly simplify the construction of the operator basis
We present a complete operator basis to O(λ2) in the Soft Collinear Effective Theory (SCET) power expansion using operators of definite helicity [17,18,19], and discuss how helicity selection rules simplify the structure of the basis
Summary
Factorization theorems play an important role in understanding the all orders behavior of observables in Quantum Chromodynamics (QCD). We let ⊗ include nontrivial color contractions The derivation of such a formula would enable for the resummation of subleading power logarithms using the renormalization group evolution of the different functions appearing in eq (1.5), allowing for an all orders understanding of power corrections to the soft and collinear limits. If L(G0) is proven to be irrelevant, the Hilbert spaces for the soft and collinear dynamics are factorized, and a series of algebraic manipulations can be used to write the cross section as a product of squared matrix elements, each involving only collinear or soft fields This provides a field theoretic definition of each of the functions appearing in eq (1.5) in terms of hard scattering operators and Lagrangian insertions in SCET.
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