Factorization theorems underly our ability to make predictions for many processes involving the strong interaction. Although typically formulated at leading power, the study of factorization at subleading power is of interest both for improving the precision of calculations, as well as for understanding the all orders structure of QCD. We use the SCET helicity operator formalism to construct a complete power suppressed basis of hard scattering operators for e + e − → dijets, e − p → e − jet, and constrained Drell-Yan, including the first two subleading orders in the amplitude level power expansion. We analyze the field content of the jet and soft function contributions to the power suppressed cross section for e + e − → dijet event shapes, and give results for the lowest order matching to the contributing operators. These results will be useful for studies of power corrections both in fixed order and resummed perturbation theory.

We compute the e + e − C-parameter distribution using the Soft-Collinear Effective Theory with a resummation to N 3 LL accuracy of the most singular partonic terms. This includes the known fixed-order QCD results up to O(α 3 s ), a numerical determination of the two loop non-logarithmic term of the soft function, and all logarithmic terms in the jet and soft functions up to three loops. Our result holds for C in the peak, tail, and far tail regions. Additionally, we treat hadronization effects using a field theoretic nonperturbative soft function, with moments Ωn. In order to eliminate an O(ΛQCD) renormalon ambiguity in the soft function, we switch from the MS to a short distance "Rgap" scheme to define the leading power correction parameter Ω1. We show how to simultaneously account for running effects in Ω1 due to renormalon subtractions and hadron mass effects, enabling power correction universality between C-parameter and thrust to be tested in our setup. We discuss in detail the impact of resummation and renormalon subtractions on the convergence. In the relevant fit region for αs(mZ ) and Ω1, the perturbative uncertainty in our cross section is 3% at Q = mZ .

We present a global fit for αs(mZ ), analyzing the available C-parameter data measured at center-of-mass energies between Q = 35 and 207 GeV. The experimental data is compared to a N 3 LL + O(α 3 s ) + Ω1 theoretical prediction (up to the missing 4-loop cusp anomalous dimension), which includes power corrections coming from a field theoretical nonperturbative soft function. The dominant hadronic parameter is its first moment Ω1, which is defined in a scheme which eliminates the O(ΛQCD) renormalon ambiguity. The resummation region plays a dominant role in the C-parameter spectrum, and in this region a fit for αs(mZ ) and Ω1 is sufficient. We find αs(mZ ) = 0.1123 ± 0.0015 and Ω1 = 0.421 ± 0.063 GeV with χ 2 /dof = 0.988 for 404 bins of data. These results agree with the prediction of universality for Ω1 between thrust and C-parameter within 1-σ.

On-shell helicity methods provide powerful tools for determining scattering amplitudes, which have a one-to-one correspondence with leading power helicity operators in the Soft-Collinear Effective Theory (SCET) away from singular regions of phase space. We show that helicity based operators are also useful for enumerating power suppressed SCET operators, which encode subleading amplitude information about singular limits. In particular, we present a complete set of scalar helicity building blocks that are valid for constructing operators at any order in the SCET power expansion. We also describe an interesting angular momentum selection rule that restricts how these building blocks can be assembled.

To predict the jet mass spectrum at a hadron collider it is crucial to account for the resummation of logarithms between the transverse momentum of the jet and its invariant mass m J . For small jet areas there are additional large logarithms of the jet radius R, which affect the convergence of the perturbative series. We present an analytic framework for exclusive jet production at the LHC which gives a complete description of the jet mass spectrum including realistic jet algorithms and jet vetoes. It factorizes the scales associated with m J , R, and the jet veto, enabling in addition the systematic resummation of jet radius logarithms in the jet mass spectrum beyond leading logarithmic order. We discuss the factorization formulae for the peak and tail region of the jet mass spectrum and for small and large R, and the relations between the different regimes and how to combine them. Regions of experimental interest are classified which do not involve large nonglobal logarithms. We also present universal results for nonperturbative effects and discuss various jet vetoes.