Related papers: Off-Shell CHY Amplitudes and Feynman Graphs
We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in an unspecified covariant gauge. The complete Mellin representation of such amplitudes is…
In this work, we prove the new factorization pattern for tree-level Yang-Mills (YM) amplitudes proposed in a companion paper. This pattern reveals a decomposition of amplitudes into a sum of gluings of lower-point amplitudes under specific…
Tree-level scattering amplitudes in planar N=4 super Yang-Mills are known to be Yangian-invariant. It has been shown that integrability allows to obtain a general, explicit method to find such invariants. The uplifting of this result to the…
We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as…
In \cite{Chen:2016fgi} we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles.In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan…
We calculate on-shell scattering amplitudes involving fermions at the tree level in open superstring field theory. We confirm that four-point and five-point amplitudes in the world-sheet path integral with the standard prescription using…
On-shell diagrams are gauge invariant quantities which play an important role in the description of scattering amplitudes. Based on the principles of generalized unitarity, they are given by products of elementary three-point amplitudes…
We apply on-shell and integrability methods that have been developed in the context of scattering amplitudes in N=4 SYM theory to tree-level form factors of this theory. Focussing on the colour-ordered super form factors of the chiral part…
We formulate N=2 twisted super Yang-Mills theory with a gauged central charge by superconnection formalism in two dimensions. We obtain off-shell invariant supermultiplets and actions with and without constraints, which is in contrast with…
This work explores the spectra of quantum graphs where the Schr\"odinger operator on the edges is equipped with a potential. The scattering approach, which was originally introduced for the potential free case, is extended to this case and…
Computing the renormalized masses and S-matrix elements in string theory, involving states whose masses are not protected from quantum corrections, requires defining off-shell amplitude with certain factorization properties. While in the…
We study the dependence of solutions of equations of the form $a_0 + a_1 z^{\ell_1} + ... + a_m z^{\ell_m} = 0$, on the exponents $\ell_1, ..., \ell_m$. We apply our results to equations that appear in graph theory, the theory of…
We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of $n$ massless particles are given…
Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals outside a strip. We deduce lower bounds on the number of resonances (in bounded regions of the complex plane),that are…
One-loop scattering amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed in the paradigm of maximal helicity violating Feynman diagrams. There are very limited number of loop integrals to be evaluated. For a process with n…
We present a novel framework for deriving on-shell recursion relations, with a specific focus on biadjoint and pure Yang-Mills theories. Starting from the double-cover CHY factorization formulae, we identify a suitable set of independent…
We introduce a natural generalization of the scattering equations, which connect the space of Mandelstam invariants to that of points on ${\mathbb{CP}^1}$, to higher-dimensional projective spaces $\mathbb{CP}^{k-1}$. The standard, $k=2$…
To the Yang-Baxter equation an additional relation can be added. This is the reflection equation which appears in various places, with or without spectral parameter. For example, in factorizable scattering on a half-line, integrable lattice…
We study off-shell n-particle form factors of half-BPS operators built from n complex scalar fields at the two-loop order in the planar maximally supersymmetric Yang-Mills theory (sYM). These are known as minimal form factors. We construct…
The consistent construction of scattering amplitudes for processes with off-shell initial partons and involving electro-weak interactions is addressed.