Covariant Spinor Formalism for Multipole Expanded Form Factor
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917462371467264 |
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| author | Huang, Hong Tan, Tuo Wang, Yi-Ning Yu, Jiang-Hao |
| author_facet | Huang, Hong Tan, Tuo Wang, Yi-Ning Yu, Jiang-Hao |
| contents | We present a systematic technique for constructing Lorentz covariant orbital-spin ($LS$) bases for matrix elements of local operators and the associated form factors, thereby extending the traditional multipole expansion to a Lorentz covariant formalism. In the spinor-helicity formalism, matrix elements of local operators for spin-$j$ particles can be treated as several massive 3-point scattering amplitudes, each of which can be further decomposed into different $LS$ partial wave amplitudes. We obtain explicit complete and linearly independent $LS$ amplitude bases for scalar, vector, and rank 2 tensor form factor of particles with spin-$\frac{1}{2}$, $1$, and $\frac{3}{2}$. In the Breit frame, it recovers the traditional multipole expansion expression, and we show the explicit equivalence among the traditional multipole expansion, canonical $LS$ expansion, and the $\mathrm{SO}(3)$ Zemach tensor expansion. Finally noting covariant structures built from the relativistic external wave functions and momenta of the initial and final state particles, we give a universal construction formula for form factor of arbitrary Lorentz tensor operators for arbitrary external spin particles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04030 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Covariant Spinor Formalism for Multipole Expanded Form Factor Huang, Hong Tan, Tuo Wang, Yi-Ning Yu, Jiang-Hao High Energy Physics - Phenomenology We present a systematic technique for constructing Lorentz covariant orbital-spin ($LS$) bases for matrix elements of local operators and the associated form factors, thereby extending the traditional multipole expansion to a Lorentz covariant formalism. In the spinor-helicity formalism, matrix elements of local operators for spin-$j$ particles can be treated as several massive 3-point scattering amplitudes, each of which can be further decomposed into different $LS$ partial wave amplitudes. We obtain explicit complete and linearly independent $LS$ amplitude bases for scalar, vector, and rank 2 tensor form factor of particles with spin-$\frac{1}{2}$, $1$, and $\frac{3}{2}$. In the Breit frame, it recovers the traditional multipole expansion expression, and we show the explicit equivalence among the traditional multipole expansion, canonical $LS$ expansion, and the $\mathrm{SO}(3)$ Zemach tensor expansion. Finally noting covariant structures built from the relativistic external wave functions and momenta of the initial and final state particles, we give a universal construction formula for form factor of arbitrary Lorentz tensor operators for arbitrary external spin particles. |
| title | Covariant Spinor Formalism for Multipole Expanded Form Factor |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2605.04030 |