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Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators

Abstract In this work we have studied the Kleiss-Kuijf relations for the recently introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce quadratic Feynman propagators. By doing this, we were able to identify the non-planar one-loop Parke-Taylor factors. In order to check that, in fact, these new factors can describe non-planar amplitudes, we applied them...

One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations

In this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so called scattering amplitudes at one-loop, in order to obtain quadratic propagators. In theories with colour ordering the key ingredient is the redefinition of the Parke-Taylor factors. After classifying all the possible one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless Bi...

Λ scattering equations

The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix...

CHY-graphs on a torus

Recently, we proposed a new approach using a punctured Elliptic curve in the CHY framework in order to compute one-loop scattering amplitudes. In this note, we further develop this approach by introducing a set of connectors, which become the main ingredient to build integrands on \( {\mathfrak{M}}_{1,n} \), the moduli space of n-punctured Elliptic curves. As a particular...

CHY loop integrands from holomorphic forms

Recently, the Cachazo-He-Yuan (CHY) approach for calculating scattering amplitudes has been extended beyond tree level. In this paper, we introduce a way of constructing CHY integrands for Φ3 theory up to two loops from holomorphic forms on Riemann surfaces. We give simple rules for translating Feynman diagrams into the corresponding CHY integrands. As a complementary result, we...

Elliptic scattering equations

Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a \( \mathbb{C}{P}^2 \) space. We show that for the...

Computation of contour integrals on \( {\mathrm{\mathcal{M}}}_{0,\mathrm{n}} \)

Contour integrals of rational functions over \( {\mathrm{\mathcal{M}}}_{0,n} \), the moduli space of n-punctured spheres, have recently appeared at the core of the tree-level S-matrix of massless particles in arbitrary dimensions. The contour is determined by the critical points of a certain Morse function on \( {\mathrm{\mathcal{M}}}_{0,n} \). The integrand is a general rational...

Cross-ratio identities and higher-order poles of CHY-integrand

The evaluation of generic Cachazo-He-Yuan(CHY)-integrands is a big challenge and efficient computational methods are in demand for practical evaluation. In this paper, we propose a systematic decomposition algorithm by using cross-ratio identities, which provides an analytic and easy to implement method for the evaluation of any CHY-integrand. This algorithm aims to decompose a...

N-point tree-level scattering amplitude in the new Berkovits’ string

We give a proof that the pure spinor superstring theory in a novel infinite tension limit, as was discussed recently by Berkovits, reproduces the tree-level scattering amplitudes of the ten-dimensional \( \mathcal{N} \) = 1 super Yang-Mills in its heterotic version and type II supergravity in its type II version. The Yang-Mills case agrees with the result obtained by Mafra...

The overall coefficient of the two-loop superstring amplitude using pure spinors

Humberto Gomez 1 Carlos R. Mafra 0 0 Max-Planck-Institut fur Gravitationsphysik, Albert-Einstein-Institut , Am Muhlenberg 1, 14476 Potsdam, Germany 1 Instituto de Fsica Teorica, UNESP - Universidade

Hepatitis B Virus (HBV)/Hepatitis D Virus (HDV) Coinfection in Outbreaks of Acute Hepatitis in the Peruvian Amazon Basin: The Roles of HDV Genotype III and HBV Genotype F

Recurring outbreaks of acute hepatitis have been a significant cause of morbidity and mortality among Peruvian military personnel stationed in the Amazon Basin region of Peru. The role of hepatitis B virus (HBV) and hepatitis D virus (HDV) infection was investigated as the possible cause of acute hepatitis among 88 military patients stationed at four different jungle outposts...