相关论文: Analytic expressions of amplitudes by the cross-ra…

An elegant unified web for amplitudes of various theories was given by Cachazo, He and Yuan in the CHY framework a few years ago. Recently, similar web has also been constructed by Cheung, Shen and Wen, which relies on a set of differential…

In order to generalize the integration rules to general CHY integrands which include higher order poles, algorithms are proposed in two directions. One is to conjecture new rules, and the other is to use the cross-ratio identity method. In…

The factorization form of the integrands in the Cachazo-He-Yuan (CHY) formalism makes the generalized Kawai-Lewellen-Tye (KLT) relations manifest, thus amplitudes of one theory can be expanded in terms of the amplitudes of another theory.…

Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the…

The various formulations of scattering amplitudes presented in recent years have underlined a hidden unity among very different theories. The KLT and BCJ relations, together with the CHY formulation, connect the S-matrices of a wide range…

Symmetries of Einstein-Yang-Mills (EYM) amplitudes, together with the recursive expansions, induce nontrivial identities for pure Yang-Mills amplitudes. In the previous work \cite{Hou:2018bwm}, we have already proven that the identities…

The CHY formalism for massless scattering provides a cohesive framework for the computation of scattering amplitudes in a variety of theories. It is especially compelling because it elucidates existing relations among theories which are…

The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to BCFW recursion…

We show that a recently discovered relation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with one graviton and $(n-1)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons,…

We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as…

It is by now well established that, by means of the integration by part identities, all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is…

We generalize the unifying relations for tree amplitudes to the $1$-loop Feynman integrands. By employing the $1$-loop CHY formula, we construct differential operators which transmute the $1$-loop gravitational Feynman integrand to Feynman…

We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color…

In this paper, we demonstrate that using differential operators one can construct the complete unified web for expansions of amplitudes for a wide range of theories. We first re-derive the expansion of multi-trace Einstein-Yang-Mills…

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the…

This article reviews on-shell methods for analytic computation of loop amplitudes, emphasizing techniques based on unitarity cuts. Unitarity techniques are formulated generally but have been especially useful for calculating one-loop…

New collective coordinates, related to the field at the `center' of the monopoles, are proposed. A systematic computation of the infrared properties of 2+1- and 3+1- dimensional Yang-Mills theory is now possible and is related to solutions…

We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent expansion about epsilon = 0 including the finite terms. The amplitude was constructed…

Up until now, the BCFW technique has been a widely used method in getting the amplitudes in various theories. Usually, the vanishing of the boundary term is necessary for the efficiency of the method. However, there are also many kinds of…

We characterise possible identities among the two-loop partial amplitudes of gluon scattering in Yang-Mills theory. We use known amplitudes in an exhaustive search to identify potential new relations. We find two candidate relations which…