Loop integrals in de Sitter spacetime: The parity-split IBP system and $\mathrm{d}\log$-form differential equations
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913044874919936 |
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| author | Chen, Jiaqi Feng, Bo Qin, Zhehan Tao, Yi-Xiao |
| author_facet | Chen, Jiaqi Feng, Bo Qin, Zhehan Tao, Yi-Xiao |
| contents | We develop integration-by-parts (IBP) reduction and differential equations for massive loop integrals of cosmological correlators in de Sitter (dS) spacetime, demonstrating the feasibility of this approach. We identify a structural property of the dS IBP system: for an $n$-propagator family, it splits into $2^n$ closed subsystems classified by the parity of the propagator indices. We further formulate a Baikov representation for loop integrals in dS space and derive the corresponding dimensional recurrence relations. In flat spacetime, intersection theory shows that $\mathrm{d}\log$-form master integrands lead to $\mathrm{d}\log$-form differential equations. Motivated by fibration intersection theory, we conjecture that this construction extends to dS integrands involving Hankel functions. We verify this conjecture in the one-loop bubble family and determine the associated alphabet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Loop integrals in de Sitter spacetime: The parity-split IBP system and $\mathrm{d}\log$-form differential equations Chen, Jiaqi Feng, Bo Qin, Zhehan Tao, Yi-Xiao High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We develop integration-by-parts (IBP) reduction and differential equations for massive loop integrals of cosmological correlators in de Sitter (dS) spacetime, demonstrating the feasibility of this approach. We identify a structural property of the dS IBP system: for an $n$-propagator family, it splits into $2^n$ closed subsystems classified by the parity of the propagator indices. We further formulate a Baikov representation for loop integrals in dS space and derive the corresponding dimensional recurrence relations. In flat spacetime, intersection theory shows that $\mathrm{d}\log$-form master integrands lead to $\mathrm{d}\log$-form differential equations. Motivated by fibration intersection theory, we conjecture that this construction extends to dS integrands involving Hankel functions. We verify this conjecture in the one-loop bubble family and determine the associated alphabet. |
| title | Loop integrals in de Sitter spacetime: The parity-split IBP system and $\mathrm{d}\log$-form differential equations |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2604.14549 |