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

Abstract

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.

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

“…As it has been shown in [39,42,43], the CHY-integral in (4.5) reproduces the linear propagators in the internal loop momentum µ , i.e. in the Q-cut representation [53][54][55]. Therefore, as it is very well known, these results match with the traditional Feynman propagators just after using the partial fraction identity and performing a shift in the loop momentum.…”

Integrating anaerobic digestion and slow pyrolysis improves the product portfolio of a cocoa waste biorefinery

“…In contrast, little organic phase was obtained for co-digestate pyrolysis at both temperatures (ca., 5 wt.%, Fig. 7), compared to pyrolysis of mono-digestate (ca., [11][12][13][14][15][16][17][18] wt.%, Fig. 5) and raw cocoa pod husks (ca., 7-16 wt.%, Fig.…”

Quadratic Feynman loop integrands from massless scattering equations

“…and after shifting (S) the internal loop momentum. This is not a trivial process and its real matching is still analized [53][54][55]. For example, let us consider the symmetrized Φ 3 Feynman diagram in figure 1.…”