On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons

TL;DR

This paper shows that, unlike Weinberg's leading soft-graviton theorem, the subleading soft-graviton behavior receives loop-induced corrections under the standard dimensional-regularization soft limit. The authors connect these corrections to infrared singularities and factorization properties, derive explicit one-loop corrections for both soft-gluon and soft-graviton cases, and establish all-loop constraints that forbid further corrections beyond one loop for the first subleading term and beyond two loops for the second. They also demonstrate the all-loop leading infrared structure via exponentiation and discuss infrared-finite contributions in specific amplitudes. The work clarifies how quantum corrections interact with soft theorems in gauge and gravity theories and highlights the role of regularization prescriptions in shaping these corrections.

Abstract

Cachazo and Strominger recently proposed an extension of the soft-graviton theorem found by Weinberg. In addition, they proved the validity of their extension at tree level. This was motivated by a Virasoro symmetry of the gravity S-matrix related to BMS symmetry. As shown long ago by Weinberg, the leading behavior is not corrected by loops. In contrast, we show that with the standard definition of soft limits in dimensional regularization, the subleading behavior is anomalous and modified by loop effects. We argue that there are no new types of corrections to the first subleading behavior beyond one loop and to the second subleading behavior beyond two loops. To facilitate our investigation, we introduce a new momentum-conservation prescription for defining the subleading terms of the soft limit. We discuss the loop-level subleading soft behavior of gauge-theory amplitudes before turning to gravity amplitudes.

Figures (5)

• Figure 1: The diagrams where leading and subleading contributions to the tree soft factor arise. Leg $n$ is the soft leg.
• Figure 2: At one loop, the simple tree-level soft behavior (a) is corrected by factorizing (b) and nonfactorizing (c) contributions OneLoopSoftBern. In gravity, the corrections are suppressed by factors of the soft momentum $k_n$, but they affect the subleading behavior.
• Figure 3: An example of an integral that has a "nonfactorizing" kinematic pole that contributes to the soft behavior.
• Figure 4: Sample factorizing (a) one- and (b) two-loop contributions to the soft behavior.
• Figure 5: Sample nonfactorizing (a) one- and (b) two-loop contributions to the soft behavior.