Continuous-Spin Particles, On Shell
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arXiv
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| Format: | Preprint |
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2024
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| author | Bellazzini, Brando De Angelis, Stefano Romano, Marcello |
| author_facet | Bellazzini, Brando De Angelis, Stefano Romano, Marcello |
| contents | We study on-shell scattering amplitudes for continuous-spin particles (CSPs). Poincaré invariance, little-group $ISO(2)$ covariance, analyticity, and on-shell factorisation (unitarity) impose stringent conditions on these amplitudes. We solve them by realizing a non-trivial representation for all little-group generators on the space of functions of bi-spinors. The three-point amplitudes are uniquely determined by matching their high-energy limit to that of definite-helicity (ordinary) massless particles. Four-point amplitudes are then bootstrapped using consistency conditions, allowing us to analyze the theory in a very transparent way, without relying on any off-shell Lagrangian formulation. We present several examples that highlight the main features of the resulting scattering amplitudes. We discuss CSP's amplitudes as a new infrared deformation of ordinary massless amplitudes, which is controlled by the scale of the Pauli-Lubanski vector squared, as opposed to the familiar mass deformation. Finally, we explore under which conditions it is possible to relax some assumptions, such as strict on-shell factorisation, analyticity, or others. In particular, we also investigate how continuous-spin particles may couple to gravity and electromagnetism, in a loose version of $S$-matrix principles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous-Spin Particles, On Shell Bellazzini, Brando De Angelis, Stefano Romano, Marcello High Energy Physics - Theory High Energy Physics - Phenomenology We study on-shell scattering amplitudes for continuous-spin particles (CSPs). Poincaré invariance, little-group $ISO(2)$ covariance, analyticity, and on-shell factorisation (unitarity) impose stringent conditions on these amplitudes. We solve them by realizing a non-trivial representation for all little-group generators on the space of functions of bi-spinors. The three-point amplitudes are uniquely determined by matching their high-energy limit to that of definite-helicity (ordinary) massless particles. Four-point amplitudes are then bootstrapped using consistency conditions, allowing us to analyze the theory in a very transparent way, without relying on any off-shell Lagrangian formulation. We present several examples that highlight the main features of the resulting scattering amplitudes. We discuss CSP's amplitudes as a new infrared deformation of ordinary massless amplitudes, which is controlled by the scale of the Pauli-Lubanski vector squared, as opposed to the familiar mass deformation. Finally, we explore under which conditions it is possible to relax some assumptions, such as strict on-shell factorisation, analyticity, or others. In particular, we also investigate how continuous-spin particles may couple to gravity and electromagnetism, in a loose version of $S$-matrix principles. |
| title | Continuous-Spin Particles, On Shell |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2406.17017 |