Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929682196201472 |
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| author | Hu, Chang Hu, Yifan Shen, Jiyuan |
| author_facet | Hu, Chang Hu, Yifan Shen, Jiyuan |
| contents | In recent work, we derived a direct expression for one-loop tensor reduction using generating functions and Feynman parametrization in projective space, avoiding recursive relations. However, for practical applications, this expression still presents two challenges: (1) While the final reduction coefficients are expressed in terms of the dimension D and Mandelstam variables, the given expression explicitly contains irrational functions; (2) The expression involves an auxiliary vector R, which can be eliminated via differentiation $\frac{\partial}{\partial R}$, but the presence of irrational terms making differentiation cumbersome. (3) Most practical applications require the tensor form with Lorentz indices.
In this paper, we provide a rational form of the reduction coefficients with Lorentz indices, free from recursion. Additionally, We provide a pure Wolfram Mathematica implementation of the code. Our practical tests demonstrate that this direct expression achieves significantly higher computational efficiency compared to the traditional Passarino-Veltman (PV) reduction or other recursion-based methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Hu, Chang Hu, Yifan Shen, Jiyuan High Energy Physics - Theory High Energy Physics - Phenomenology In recent work, we derived a direct expression for one-loop tensor reduction using generating functions and Feynman parametrization in projective space, avoiding recursive relations. However, for practical applications, this expression still presents two challenges: (1) While the final reduction coefficients are expressed in terms of the dimension D and Mandelstam variables, the given expression explicitly contains irrational functions; (2) The expression involves an auxiliary vector R, which can be eliminated via differentiation $\frac{\partial}{\partial R}$, but the presence of irrational terms making differentiation cumbersome. (3) Most practical applications require the tensor form with Lorentz indices. In this paper, we provide a rational form of the reduction coefficients with Lorentz indices, free from recursion. Additionally, We provide a pure Wolfram Mathematica implementation of the code. Our practical tests demonstrate that this direct expression achieves significantly higher computational efficiency compared to the traditional Passarino-Veltman (PV) reduction or other recursion-based methods. |
| title | Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2501.11150 |