Momentum shift and on-shell constructible massive amplitudes

Journal Article · 06 November 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.105003 · OSTI ID:2476556

Ema, Yohei; Gao, Ting ; Ke, Wenqi; Liu, Zhen ; Lyu, Kun-Feng; Mahbub, Ishmam

We construct tree-level amplitude for massive particles using on-shell recursion relations based on two classes of momentum shifts: an all-line transverse shift that deforms momentum by its transverse polarization vector, and a massive Britto-Cachazo-Feng-Witten-type shift. We illustrate that these shifts allow us to correctly calculate four-point and five-point amplitudes in massive QED, without an ambiguity associated with the contact terms that may arise from a simple “gluing” of lower-point on-shell amplitudes. We discuss various aspects and applicability of the two shifts, including the large- $z$ behavior and complexity scaling. We show that there exists a “good” all-line transverse shift for all possible little group configurations of the external particles, which can be extended to a broader class of theories with massive particles such as massive QCD and theories with massive spin-1 particles. The massive Britto-Cachazo-Feng-Witten-type shift enjoys more simplicity, but a “good” shift does not exist for all the spin states due to the specific choice of spin axis. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0011842
• OSTI ID: 2476556
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 10 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English