Soft Matters, or the Recursions with Massive Spinors

Abstract

We discuss recursion relations for scattering amplitudes with massive particles of any spin. They are derived via a two-parameter shift of momenta, combining a BCFW-type spinor shift with the soft limit of a massless particle involved in the process. The technical innovation is that spinors corresponding to massive momenta are also shifted. Our recursions lead to a reformulation of the soft theorems. The well-known Weinberg's soft factors are recovered and, in addition, the subleading factors appear reshaped such that they are directly applicable to massive amplitudes in the modern on-shell language. Moreover, we obtain new results in the context of non-minimal interactions of massive matter with photons and gravitons. These soft theorems are employed for practical calculations of Compton and higher-point scattering. As a by-product, we introduce a convenient representation of the Compton scattering amplitude for any mass and spin.

arXiv comment35 pages; v2: typos corrected, references added, more about gravitational Compton scattering

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Cited by in corpus (14)

• Compton Black-Hole Scattering for $s\le 5/2$
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• Classical Limit of Higher-Spin String Amplitudes
• Gravitational Faraday effect from on-shell amplitudes
• Chiral approach to massive higher spins
• Amplitude bases in generic EFTs
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Recursion relations for scattering amplitudes with massive particles
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• Massive On-shell Recursion Relations for n-point Amplitudes
• Recursion relations for scattering amplitudes with massive particles II: massive vector bosons