Related papers: On-shell recursion relations for generic integrand…
We study the one loop renormalization in the most general metric-dilaton theory with the second derivative terms only. The general theory can be divided into two classes, models of one are equivalent to conformally coupled with gravity…
Scattering amplitudes for colored theories have recently been formulated in a new way, in terms of curves on surfaces. In this note we describe a canonical set of functions we call surface functions, associated to all orders in the…
Quantum corrections to three-point functions of scalar single trace operators in planar N=4 Super-Yang-Mills theory are studied using integrability. At one loop, we find new algebraic structures that not only govern all two loop corrections…
The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the…
Effective field theories are useful tools to search for physics beyond the Standard Model (SM). However, effective theories can lead to non-unitary behavior with fastly growing amplitudes. This unphysical behavior may lead to large…
This article studies methods to obtain relations for scattering amplitudes at the loop level, with concrete examples at one loop. These methods originate in the analysis of large so-called Britto-Cachazo-Feng-Witten shifts of tree level…
Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured $\mathbb{CP}^{k-1}$, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster…
We present a set of one-loop integral coefficient relations in QCD. The unitarity method is useful for exposing one-loop amplitudes in terms of tree amplitudes. The coefficient relations are induced by tree-level BCJ amplitude relations. We…
We extend the generalized D-dimensional unitarity method for numerical evaluation of one-loop amplitudes by incorporating massive particles. The issues related to extending the spinor algebra to higher dimensions, treatment of external…
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of…
Using the Schr\"odinger functional we have computed a variety of renormalized on-shell correlation functions to one-loop order of perturbation theory. By studying their approach to the continuum limit we have determined the O($a$)…
Starting from two-loops, there are Feynman integrals with higher powers of the propagators. They arise from self-energy insertions on internal lines. Within the loop-tree duality approach or within methods based on numerical unitarity one…
We describe the origins of recurrence relations between field theory amplitudes in terms of the construction of Feynman diagrams. In application we derive recurrence relations for the amplitudes of QED which hold to all loop orders and for…
It has been a long-standing challenge to define a canonical loop integrand for non-supersymmetric gluon scattering amplitudes in the planar limit. Naive integrands are inflicted with $1/0$ ambiguities associated with tadpoles and massless…
In this paper we study on-shell diagrams in ${\cal N}{<}4$ supersymmetric Yang-Mills (SYM) theory. These are on-shell gauge invariant objects which appear as cuts of loop integrands in the context of generalized unitarity and serve as…
We present a complete one-loop renormalization of the Special Galileon $S-$matrix. Especially we give a complete list of the higher derivative operators which are necessary for one-loop on-shell renormalization and prove the invariance of…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
On-shell amplitude methods allow to derive one-loop renormalization effects from just tree-level amplitudes, with no need of loop calculations. We derive a simple formula to obtain the anomalous dimensions of higher-dimensional operators…
Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and…