The Q $$ \mathcal{Q} $$ -cut representation of one-loop integrands and unitarity cut method

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 oneloop amplitude for the massless Bi-adjoint Φ 3 theory. The prescription directly reproduces the quadratic propagators of the traditional Feynman approach.

Section: Bi-adjoint φ 3 At One-loopsupporting

confidence: 63%

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

Gomez

Lopez-Arcos

Talavera

2017

“…string [52,53] and its generalization to the scattering equation formalism [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68]; to Qcuts [69][70][71], and so on. For a broad overview of some of these developments, see e.g.…”

Section: Jhep06(2017)059mentioning

confidence: 99%

Prescriptive unitarity

Bourjaily

Herrmann

Trnka

2017

116

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N k MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions.

“…The details of the one-loop Q-cut construction was further clarified in [2], and generalizations to two loops or more was also illustrated in [1]. The Qcut representation circumvented two difficulties in the attempt for recursive construction of loop integrand: canonical definition of loop momentum and the singularities in the forward limit (which will be referred to as forward singularities).…”

Section: Introductionmentioning

confidence: 99%

“…Recall that the integrand of one-loop four-point amplitude in scalar φ 3 theory, after partial fraction identity, is given by [2] …”

mentioning

confidence: 99%

Note on recursion relations for the Q $$ \mathcal{Q} $$ -cut representation

Feng¹,

He²,

Huang³

et al. 2017

Self Cite

Abstract:In this note, we study the Q-cut representation by combining it with BCFW deformation. As a consequence, the one-loop integrand is expressed in terms of a recursion relation, i.e., n-point one-loop integrand is constructed using tree-level amplitudes and mpoint one-loop integrands with m ≤ n − 1. By giving explicit examples, we show that the integrand from the recursion relation is equivalent to that from Feynman diagrams or the original Q-cut construction, up to scale free terms.