Constraints on anomalous dimensions from the positivity of the S-matrix

Abstract

We show that the analyticity and crossing symmetry of the S-matrix, together with the optical theorem, impose restrictions on the renormalisation group evolution of dimension-eight operators in the Standard Model Effective Field Theory. Moreover, in the appropriate basis of operators, the latter manifest as zeros in the anomalous dimension matrix that, to the best of our knowledge, have not been anticipated anywhere else in the literature. Our results can be trivially extended to other effective field theories.

Revisiting renormalization group equations of the SMEFT dimension-seven operators

“…For the SMEFT itself, RGEs also play a crucial role in the global analysis of experimental data obtained at different energy scales. Therefore, as a powerful tool for resummation and an essential bridge to link physics at different energy scales, the SMEFT RGEs have been extensively studied for the dim-5 [28][29][30], dim-6 [31][32][33][34][35][36], dim-7 [15][16][17]37], and dim-8 [21,[38][39][40][41][42] operators. Some attempts to understand the structure of the anomalous dimension matrix (i.e., zero entries and the perturbative power order) have been successfully made [43][44][45][46][47][48][49][50], which turn out to be very helpful.…”