The effective electroweak Hamiltonian in the gradient-flow formalism

Abstract

The effective electroweak Hamiltonian in the gradient-flow formalism is constructed for the current-current operators through next-to-next-to-leading order QCD. The results are presented for two common choices of the operator basis. This paves the way for a consistent matching of perturbatively evaluated Wilson coefficients and non-perturbative matrix elements evaluated by lattice simulations.

Gradient-flowed order parameter for spontaneous gauge symmetry breaking

“…The same argument holds for the quark fields except for the requirement for an extra field (wave function) renormalization [14]. (Various other aspects have been explored in the context of the gradient flow, such as the non-perturbative renormalization group [15][16][17][18][19][20][21][22][23][24][25][26], holographic theories [27][28][29][30][31][32][33], the O(N ) nonlinear sigma model and its large-N expansion [34][35][36][37], supersymmetric gradient flow [38][39][40][41][42][43][44][45][46][47][48][49], phenomenological applications [50][51][52][53][54][55][56][57][58], and formal issues in quantum field theory [59][60][...…”

Gradient-flowed order parameter for spontaneous gauge symmetry breaking

“…The same argument holds for the quark fields except for the requirement for an extra field (wave-function) renormalization [14]. (Various other aspects have been explored in the context of the gradient flow, such as non-perturbative renormalization group [15][16][17][18][19][20][21][22][23][24][25][26], holographic theories [27][28][29][30][31][32][33], O(N ) nonlinear sigma model and its large-N expansion [34][35][36][37], supersymmetric gradient flow [38][39][40][41][42][43][44][45][46][47][48][49], phenomenological applications [50][51][52][53][54][55][56][57][58], and formal issues in the quantum field theory [59][60][6...…”