Convex Geometry Perspective on the (Standard Model) Effective Field Theory Space

Area of Science:

• High Energy Physics
• Theoretical Physics
• Mathematical Physics

Background:

• Effective Field Theories (EFTs) are crucial for describing physics at different energy scales.
• Understanding the structure of the EFT parameter space is key to constraining theories and probing new physics.
• Existing methods for bounding EFT parameters, like positivity bounds, have limitations.

Purpose of the Study:

• To introduce a novel convex geometry perspective to the EFT parameter space.
• To establish a connection between the geometry of the EFT space and ultraviolet (UV) completions.
• To derive new, potentially stronger theoretical bounds on EFT parameters.

Main Methods:

• Analyzing the second s derivatives of forward EFT amplitudes.
• Utilizing convex geometry to characterize the EFT parameter space as a convex cone.
• Employing group theoretical methods to identify extremal rays of the cone.
• Investigating tree-level UV completions and their relation to extremal rays.

Main Results:

• The second s derivatives of forward EFT amplitudes form a convex cone.
• Extremal rays of this cone are directly linked to states in the UV theory.
• For tree-level UV completions, extremal rays correspond to theories with UV particles in at most one irreducible representation.
• Dim-8 operators are identified as crucial for reverse engineering UV physics from the Standard Model EFT.

Conclusions:

• The geometric structure of the EFT parameter space offers a powerful tool for UV completion reconstruction.
• New theoretical bounds on Wilson coefficients, derived from the cone's boundaries, are generally stronger than current positivity bounds.
• These new bounds arise from scattering amplitudes involving entangled states, highlighting a deep connection between geometry and quantum information in EFTs.