Abstract
The factorization of multi-leg gauge theory amplitudes in the soft and collinear limits provides strong constraints on the structure of amplitudes, and enables efficient calculations of multi-jet observables at the LHC. There is significant interest in extending this understanding to include subleading powers in the soft and collinear limits. While this has been achieved for low point amplitudes, for higher point functions there is a proliferation of variables and more complicated phase space, making the analysis more challenging. By combining the subleading power expansion of spinor-helicity variables in collinear limits with consistency relations derived from the soft collinear effective theory, we show how to efficiently extract the subleading power leading logarithms of N-jet event shape observables directly from known spinor-helicity amplitudes. At subleading power, we observe the presence of power law singularities arising solely from the expansion of the amplitudes, which for hadron collider event shapes lead to the presence of derivatives of parton distributions. The techniques introduced here can be used to efficiently compute the power corrections for N-jettiness subtractions for processes involving jets at the LHC.
Highlights
The factorization of multi-leg gauge theory amplitudes in the soft and collinear limits provides strong constraints on the structure of amplitudes, and enables efficient calculations of multi-jet observables at the LHC
By combining the subleading power expansion of spinor-helicity variables in collinear limits with consistency relations derived from the soft collinear effective theory, we show how to efficiently extract the subleading power leading logarithms of N -jet event shape observables directly from known spinor-helicity amplitudes
We exploit consistency relations derived in soft collinear effective theory (SCET) [56,57,58,59,60] to show that the leading logarithms at subleading power for a broad class of multi-jet event shape observables can be computed using only the twoparticle collinear limit, to any order in αs
Summary
We describe in detail the subleading power expansion of spinor helicity variables, focusing on the behavior and parametrization of the two particle collinear limit at subleading powers. While soft limits have been studied extensively [61] for a recent review), subleading power collinear limits are much less well studied, and parametrizations of spinors in these limits are less widely known in the literature. A convenient parametrization of the two particle collinear limit at subleading powers was given in [62, 63]. We generalize this parametrization, and make it explicit in terms of the standard momenta that are useful for calculations of observables in the collinear limit.
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