Mapping the transverse spin sum rule in position space
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910114064105472 |
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| author | Lorcé, Cédric Mukherjee, Asmita Singh, Ravi Won, Ho-Yeon |
| author_facet | Lorcé, Cédric Mukherjee, Asmita Singh, Ravi Won, Ho-Yeon |
| contents | We discuss in detail the relativistic spatial distribution of transverse angular momentum, including both orbital and intrinsic spin contributions. Using the quantum phase-space formalism, we begin with the definition of the three-dimensional spatial distributions of transverse orbital angular momentum and intrinsic spin in a generic Lorentz frame. By integrating these three-dimensional spatial distributions over the longitudinal axis, we derive for the first time the relativistic spatial distributions of transverse orbital angular momentum, intrinsic spin, and total angular momentum for spin-0 and spin-1/2 targets in the transverse plane. We verify the transverse spin sum rule about the relativistic center of spin for spin-0 and spin-1/2 systems, and find that the transverse total angular momentum distribution is non-trivial, even for spin-0 targets. We also show how the distributions of transverse orbital angular momentum, intrinsic spin, and total angular momentum change with the target momentum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mapping the transverse spin sum rule in position space Lorcé, Cédric Mukherjee, Asmita Singh, Ravi Won, Ho-Yeon High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory We discuss in detail the relativistic spatial distribution of transverse angular momentum, including both orbital and intrinsic spin contributions. Using the quantum phase-space formalism, we begin with the definition of the three-dimensional spatial distributions of transverse orbital angular momentum and intrinsic spin in a generic Lorentz frame. By integrating these three-dimensional spatial distributions over the longitudinal axis, we derive for the first time the relativistic spatial distributions of transverse orbital angular momentum, intrinsic spin, and total angular momentum for spin-0 and spin-1/2 targets in the transverse plane. We verify the transverse spin sum rule about the relativistic center of spin for spin-0 and spin-1/2 systems, and find that the transverse total angular momentum distribution is non-trivial, even for spin-0 targets. We also show how the distributions of transverse orbital angular momentum, intrinsic spin, and total angular momentum change with the target momentum. |
| title | Mapping the transverse spin sum rule in position space |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2505.20468 |