Soft Theorems from Effective Field Theory
arXiv:1412.3108
Abstract
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
Plenty of pages, 9 figures; v2: updated discussion of fusion terms in the one-loop soft theorem, added appendix with several explicit, worked examples of the application of the one-loop soft theorem
References in corpus (34)
- New Relations for Gauge-Theory Amplitudes
- Gluon scattering amplitudes at strong coupling
- Conformal properties of four-gluon planar amplitudes and Wilson loops
- MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
- Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
- Evidence for a New Soft Graviton Theorem
- Jets from Massive Unstable Particles: Top-Mass Determination
- Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
- Treating the b quark distribution function with reliable uncertainties
- A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
- Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
- On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
- Loop Corrections to Soft Theorems in Gauge Theories and Gravity
- Factorization of e+e- Event Shape Distributions with Hadronic Final States in Soft Collinear Effective Theory
- Soft sub-leading divergences in Yang-Mills amplitudes
- Subleading soft theorem in arbitrary dimension from scattering equations
- Resummation and NLO Matching of Event Shapes with Effective Field Theory
- The method of regions and next-to-soft corrections in Drell-Yan production
- Constraining subleading soft gluon and graviton theorems
- Threshold resummation for pair production of coloured heavy (s)particles at hadron colliders
- Hard-Soft-Collinear Factorization to All Orders
- Extending Soft-Collinear-Effective-Theory to describe hard jets in dense QCD media
- Diagrammatic insights into next-to-soft corrections
- Tree Level Recursion Relations In General Relativity
- Subleading Soft Factor for String Disk Amplitudes
- Soft Graviton Theorem in Arbitrary Dimensions
- Reparameterization Invariant Collinear Operators
- Are Soft Theorems Renormalized?
- Conformal Invariance of the Subleading Soft Theorem in Gauge Theory
- On the Subleading-Soft Behaviour of QCD Amplitudes
- Jet Vetoes Interfering with H->WW
- Factorized soft graviton theorems at loop level
- A Note on Soft Factors for Closed String Scattering
- Systematic Improvement of Parton Showers with Effective Theory