Anomalous dimension of subleading-power N-jet operators

TL;DR

The paper develops a systematic framework to determine the anomalous dimension of subleading-power NLP N-jet operators in SCET, enabling potential resummation of NLP logarithms. It constructs a complete operator basis up to O(λ^2) for N-jet processes and computes the one-loop collinear and soft contributions for the fermion-number two case, showing a universal soft structure and a detailed collinear mixing pattern that includes momentum-fraction dependence. The main result is a general expression for the anomalous dimension Γ that combines soft and collinear parts, reduces to the leading-power form in the appropriate limit, and demonstrates consistent operator mixing at NLP. This work provides a principled path toward NLP resummation in multi-jet processes and sets the stage for higher-order NLP analyses across arbitrary N-jet configurations.

Abstract

We begin a systematic investigation of the anomalous dimension of subleading power N-jet operators in view of resummation of logarithmically enhanced terms in partonic cross sections beyond leading power. We provide an explicit result at the one-loop order for fermion-number two N-jet operators at the second order in the power expansion parameter of soft-collinear effective theory.

Figures (5)

• Figure 1: Collinear loops contributing to the anomalous dimension for two fermionic building blocks in direction $n_{i+}$. Arrows show the fermion flow for two outgoing antiquarks.
• Figure 2: Examples for the four possibilities of adding an extra collinear emission (indicated by the blue line) to a diagram with two fermion lines (chosen to be diagram $(b,i)$ from Fig. \ref{['fig:Jxixi']}. for illustration).
• Figure 3: Collinear loops contributing to the anomalous dimension $Z^{c,i}_{\chi\partial\chi,{\cal A}\chi\chi}$, that describes mixing of B- into C-type operators. Arrows show the fermion flow for two outgoing antiquarks.
• Figure 4: The leading power diagrams with a soft-gluon exchange. The $j$-direction parton is either a (anti)quark or a gluon created by either A0 or A1 current. In the two-fermion sector, the current can be either B1 or B2.
• Figure 5: Sample diagrams contributing to mixing of time-ordered product into power-suppressed local operators. The circle denotes the $\mathcal{O}\left(\lambda\right)$ SCET Lagrangian insertion. Diagram (a) contributes to mixing into $N$-jet operator with B2-type currents; the diagram (b) can induce mixing into C2-type currents and the diagram (c) can generate mixing into an $N$-jet operator containing two different B1-type operators.