8 research outputs found
Two Loop Renormalization of Scalar Theories using a Geometric Approach
We derive a general formula for two-loop counterterms in Effective Field
Theories (EFTs) using a geometric approach. This formula allows the two-loop
results of our previous paper to be applied to a wide range of theories. The
two-loop results hold for loop graphs in EFTs where the interaction vertices
contain operators of arbitrarily high dimension, but at most two derivatives.
We also extend our previous one-loop result to include operators with an
arbitrary number of derivatives, as long as there is at most one derivative
acting on each field. The final result for the two-loop counterterms is written
in terms of geometric quantities such as the Riemann curvature tensor of the
scalar manifold and its covariant derivatives. As applications of our results,
we give the two-loop counterterms and renormalization group equations for the
O(n) EFT to dimension six, the scalar sector of the Standard Model Effective
Field Theory (SMEFT) to dimension six, and chiral perturbation theory to order
.Comment: ChPT results to O() now agree with Bijnens, Colangelo, and
Ecker, hep-ph/990733
An Algebraic Formula for Two Loop Renormalization of Scalar Quantum Field Theory
We give a general formula for the two-loop renormalization counterterms of a
scalar quantum field theory with interactions containing up to two derivatives,
which extends 't Hooft's one-loop result. We show that factorizable topologies
do not contribute to the renormalization group equations. The results will be
combined with the geometric method in a subsequent paper to obtain the
renormalization group equations for the scalar sector of effective field
theories (EFT) to two-loop order.Comment: 25 pages, 8 figure
Comparative Performance of Private and Public Healthcare Systems in Low- and Middle-Income Countries: A Systematic Review
A systematic review conducted by Sanjay Basu and colleagues reevaluates the evidence relating to comparative performance of public versus private sector healthcare delivery in low- and middle-income countries
An algebraic formula for two loop renormalization of scalar quantum field theory
We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending ’t Hooft’s one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order
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An algebraic formula for two loop renormalization of scalar quantum field theory
Abstract
:
We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending ’t Hooft’s one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order
An algebraic formula for two loop renormalization of scalar quantum field theory
Abstract We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending ’t Hooft’s one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order