Program Results

Introduction to the event

Effective Field Theories (EFTs) parametrize low-energy physics by higher-dimension operators. Positivity bounds (derived from unitarity, analyticity, Lorentz invariance) constrain Wilson coefficients at tree-level EFT level, but loop corrections and renormalization can in principle spoil or modify those constraints. We ask: can one predict the sign of RG running of certain EFT operators (one-loop) in a way that is similarly constrained by IR principles, i .e. without full UV details? The inspiration is drawn from the a-theorem in conformal field theory, which gives a monotonicity property for RG flows.

With master student 廖有朋 and postdoc Dr. Jasper Nepveu, we prove that for a broad class of effective field theory (EFT), when you insert two 血eracti on of the same mass dimension, the one-loop beta-function of the coupling must have a definite sign.

More precisely, combining unitarity, analyticity, and Lorentz invariance enforce that the coefficient of the log running in this class is positive (or zero). This work establishes the connection between basic physical principles and the direction of renormalization running for certain classes of interaction. This phenomenon in effective field theory has the flavor of a-theorem in conformal field theory.

Implications & Applications:

Preserving positivity bounds: The result yields a criterion whether positivity bounds (derived at tree level) survive RG flow or could seem violated after loop corrections. If the running has the constrained sign, the positivity bounds are stable under renormalization; otherwise, one must check carefully.

Chiral Perturbation Theory: We apply their theorem to ChPT, showing that certain dimension-eight operators' coefficients obey the sign constraints.

SMEFT (Standard Model EFT): Particularly for dimension-eight operators, the constraints are strong; we also discuss some extensions to dimension six. The result gives new insights into which operator mixings / running effects are allowed without violating basic consistency.

The main feature of the theorem is that the UV completions are arbitrary; the theorem relies only on IR consistency principles, so it is broadly applicable. Some positivity bounds may still get violated if loop contributions from lower dimension operators or non-forward kinematics become relevant.