# A String Deformation of the Parke-Taylor Factor

## TL;DR

This paper introduces a new string Parke-Taylor factor that extends the CHY formalism to open string amplitudes, providing a covariant definition and connecting string theory corrections with field theory results.

## Contribution

It presents a fully covariant definition of the string Parke-Taylor factor and demonstrates its application to formulating open string tree-level amplitudes within the CHY framework.

## Key findings

- Defines a covariant string Parke-Taylor factor
- Establishes its connection to open string amplitudes
- Provides an $ ext{SL}(2, ext{C})$-covariant formulation

## Abstract

Scattering amplitudes in a range of quantum field theories can be computed using the Cachazo-He-Yuan (CHY) formalism. In theories with colour ordering, the key ingredient is the so-called Parke-Taylor factor. In this note we give a fully $\text{SL}(2,\mathbb{C})$-covariant definition and study the properties of a new integrand called the string Parke-Taylor factor. It has an $\alpha'$ expansion whose leading coefficient is the field-theoretic Parke-Taylor factor. Its main application is that it leads to a CHY formulation of open string tree-level amplitudes. In fact, the definition of the string Parke-Taylor factor was motivated by trying to extend the compact formula for the first $\alpha'$ correction found by He and Zhang, while the main ingredient in its definition is a determinant of a matrix introduced in the context of string theory by Stieberger and Taylor.