All order factorization for virtual Compton scattering at next-to-leading power
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912209686233088 |
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| author | Schoenleber, Jakob Szafron, Robert |
| author_facet | Schoenleber, Jakob Szafron, Robert |
| contents | We discuss all-order factorization for the virtual Compton process at next-to-leading power (NLP) in the $Λ_{\rm QCD}/Q$ and $\sqrt{-t}/Q$ expansion (twist-3), both in the double-deeply-virtual case and the single-deeply-virtual case. We use the soft-collinear effective theory (SCET) as the main theoretical tool. We conclude that collinear factorization holds in the double-deeply virtual case, where both photons are far off-shell. The agreement is found with the known results for the hard matching coefficients at leading order $α_s^0$, and we can therefore connect the traditional approach with SCET. In the single-deeply-virtual case, commonly called deeply virtual Compton scattering (DVCS), the contribution of non-target collinear regions complicates the factorization. These include momentum modes collinear to the real photon and (ultra)soft interactions between the photon-collinear and target-collinear modes. However, such contributions appear only for the transversely polarized virtual photon at the NLP accuracy and in fact it is the only NLP $\sim (Λ_{\rm QCD}/Q)^1 \sim (\sqrt{-t}/Q)^1$ contribution in that case. We therefore conclude that the DVCS amplitude for a longitudinally polarized virtual photon, where the leading power $\sim (Λ_{\rm QCD}/Q)^0 \sim (\sqrt{-t}/Q)^0$ contribution vanishes, is free of non-target collinear contributions and the collinear factorization in terms of twist-3 GPDs holds in that case as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All order factorization for virtual Compton scattering at next-to-leading power Schoenleber, Jakob Szafron, Robert High Energy Physics - Phenomenology We discuss all-order factorization for the virtual Compton process at next-to-leading power (NLP) in the $Λ_{\rm QCD}/Q$ and $\sqrt{-t}/Q$ expansion (twist-3), both in the double-deeply-virtual case and the single-deeply-virtual case. We use the soft-collinear effective theory (SCET) as the main theoretical tool. We conclude that collinear factorization holds in the double-deeply virtual case, where both photons are far off-shell. The agreement is found with the known results for the hard matching coefficients at leading order $α_s^0$, and we can therefore connect the traditional approach with SCET. In the single-deeply-virtual case, commonly called deeply virtual Compton scattering (DVCS), the contribution of non-target collinear regions complicates the factorization. These include momentum modes collinear to the real photon and (ultra)soft interactions between the photon-collinear and target-collinear modes. However, such contributions appear only for the transversely polarized virtual photon at the NLP accuracy and in fact it is the only NLP $\sim (Λ_{\rm QCD}/Q)^1 \sim (\sqrt{-t}/Q)^1$ contribution in that case. We therefore conclude that the DVCS amplitude for a longitudinally polarized virtual photon, where the leading power $\sim (Λ_{\rm QCD}/Q)^0 \sim (\sqrt{-t}/Q)^0$ contribution vanishes, is free of non-target collinear contributions and the collinear factorization in terms of twist-3 GPDs holds in that case as well. |
| title | All order factorization for virtual Compton scattering at next-to-leading power |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2407.09263 |