SnowMass2021

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====== TF04: Scattering amplitudes ======
Co-Conveners: Zvi Bern (UCLA), Jaroslav Trnka (UCD)

===== Description=====
Scattering amplitudes are a key arena where quantum field theory directly confronts experiment and where a precise understanding can be crucial for identifying Beyond Standard Model signals at particle colliders such as the LHC. At the same time, scattering amplitudes have revealed beautiful and intriguing mathematical structures and patterns that suggest that our fundamental understanding of quantum field theory is far from complete. The study of scattering amplitudes has been a growing area of research over the past decade, with applications ranging from precision calculations for the LHC, new approaches to gauge and gravity theories, LIGO physics, to Amplituhedron and exciting connections to geometry and combinatorics.

Subtopics to be explored:

  * Analytic properties of perturbative scattering amplitudes, IR and UV divergences, loop integration techniques, differential equations, application to QCD.
  * Efficient methods to construct scattering amplitudes in general quantum field theories, generalized unitarity, recursion relations.
  * Geometric picture for amplitudes: hidden symmetries, on-shell diagrams, positive Grassmannian, Amplituhedron, cluster algebras, hexagon bootstrap, symbols and co-products.
  * Connections to string theory, CHY constructions.
  * Color-kinematics duality, construction of gravity multi-loop integrands, including those for classical gravitational wave problems.
  * New applications of amplitude methods to problems of direct importance to LIGO physics and to Standard Model Effective field theory.

=====  LOI and white papers in progress =====

This is a partial list of LOIs and white papers in progress lead by leading experts in the field. Contact TF coordinators Zvi Bern or Jaroslav Trnka if you want to propose a new LOI or white paper, or to join the existing one.

1. **Bootstrapping N=4 sYM**.   Coordinator: Lance Dixon (SLAC)

2. **Positive geometry of scattering amplitudes**. Coordinator: Nima Arkani-Hamed (IAS)

3. **Effective field theories and amplitudes**.  Coordinator:  Henriette Elvang (Michigan)

4. **Amplitudes and Gravitational waves**.  Coordinator: Radu Roiban (Penn State)

5. **The double copy and its applications**.  Coordinator: John Joseph Carrasco (Northwestern)

6. **Amplitudes and SMEFT**.  Coordinator  Julio Parra-Martinez (UCLA)

7. **Functions Beyond Polylogarithms in Scattering Amplitudes**. Coordinator: Andrew McLeod (NBI)

8. **Precision collider Physics**.  Coordinator: Fernando Febres Cordero (FSU)

9. **Amplitudes beyond GR**. Coordinator: Mark Trodden (U Penn), Kurt Hinterbichler (Case Western)

===== Submitted LOI =====
Here is the list of submitted LOIs to this  topic. 
 First index before "/"  corresponds to the primary frontier used for the submission.
 {{url>https://www.snowmass21.org/docs/files/list.php?frontier=TF4  noborder 95%,600px}}