Subleading Power Corrections for N-Jettiness Subtractions

TL;DR

The paper develops a rigorous SCET-based framework to compute leading subleading-power corrections in N-jettiness subtractions, providing analytic α_s τ ln τ and α_s^2 τ ln^3 τ terms for thrust and beam thrust. By deriving consistency relations and performing explicit thrust and beam-thrust calculations, it demonstrates significant reductions in missing power corrections and improved numerical stability for NNLO subtractions. The work also shows that using a boost-aware (leptonic) definition of N-jettiness dramatically reduces power corrections across phase space, while the hadronic-framed definition can incur rapidity-enhanced corrections. Overall, incorporating these power corrections into subtractions yields an order-of-magnitude improvement in accuracy and efficiency for fixed-order QCD calculations relevant to LHC phenomenology.

Abstract

The $N$-jettiness observable $\mathcal{T}_N$ provides a way of describing the leading singular behavior of the $N$-jet cross section in the $τ=\mathcal{T}_N/Q \to 0$ limit, where $Q$ is a hard interaction scale. We consider subleading power corrections in the $τ\ll 1$ expansion, and employ soft-collinear effective theory to obtain analytic results for the dominant $α_s τ\lnτ$ and $α_s^2 τ\ln^3τ$ subleading terms for thrust in $e^+e^-$ collisions and $0$-jettiness for $q\bar q$-initiated Drell-Yan-like processes at hadron colliders. These results can be used to significantly improve the numerical accuracy and stability of the $N$-jettiness subtraction technique for performing fixed-order calculations at NLO and NNLO. They reduce the size of missing power corrections in the subtractions by an order of magnitude. We also point out that the precise definition of $N$-jettiness has an important impact on the size of the power corrections and thus the numerical accuracy of the subtractions. The sometimes employed definition of $N$-jettiness in the hadronic center-of-mass frame suffers from power corrections that grow exponentially with rapidity, causing the power expansion to deteriorate away from central rapidity. This degradation does not occur for the original $N$-jettiness definition, which explicitly accounts for the boost of the Born process relative to the frame of the hadronic collision, and has a well-behaved power expansion throughout the entire phase space. Integrated over rapidity, using this $N$-jettiness definition in the subtractions yields another order of magnitude improvement compared to employing the hadronic-frame definition.

Figures (11)

• Figure 1: Estimate of the missing power corrections $\Delta\sigma(\tau_{\mathrm{cut}})$ below $\tau_{\mathrm{cut}}$ for the NLO (green), NNLO (blue), and N$^3$LO (orange) contributions without including (solid) and including (dashed) the leading power correction in the subtractions. On the left, the estimate is relative to the full N$^n$LO contribution itself, on the right relative to the LO cross section. The bands show a factor of three variation in the estimate around the solid lines. A similar variation should be considered to apply to the dashed lines, but for simplicity is not shown.
• Figure 2: Representative NLO diagrams where a gluon becomes either soft (a) or collinear (b) with a quark. Collinear particles are shown in light blue, soft particles in orange. The cross represents a Lagrangian correction to the propagator, and the power suppression of the hard scattering operators and Lagrangian insertions is explicitly indicated.
• Figure 3: Representative NLO diagrams when a quark becomes either soft (a) or two quarks becomes collinear (b). The power suppression of the hard scattering operators and Lagrangian insertions is explicitly indicated.
• Figure 4: Representative diagrams of the two-loop hard collinear contributions which contribute at subleading power. Here the grey circle represents a one-loop hard virtual correction. There are contributions when either a gluon becomes collinear with a quark (a) or two quarks become collinear (b). The power suppression of the contributing operators is indicated.
• Figure 5: Diagrams contributing to $\sigma_{qg}$, where either a soft quark crosses the cut (a), or a collinear quark crosses the cut (b). The one-loop corrections to these diagrams give rise to the $T_F(C_F+C_A) \ln^3(\tau)$ correction to beam thrust.