Reconstruction of the Dipole Amplitude in the Dipole Picture as a mathematical Inverse Problem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911275763630080 |
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| author | Hänninen, Henri Kykkänen, Antti Schlüter, Hjørdis |
| author_facet | Hänninen, Henri Kykkänen, Antti Schlüter, Hjørdis |
| contents | We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To this formulation of the problem, we apply standard inverse problems methods and algorithms to reconstruct known dipole amplitudes from simulated reduced cross section data with realistic precision. The main difference of this approach to previous works is that this implementation does not require any fit parametrization of the dipole amplitude. The freedom from parametrization also enables us for the first time to quantify the uncertainties of the inferred dipole amplitude in a novel more general framework. This mathematical approach to small-$x$ phenomenology opens a path to parametrization bias free inference of the dipole amplitude from HERA and Electron--Ion Collider data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstruction of the Dipole Amplitude in the Dipole Picture as a mathematical Inverse Problem Hänninen, Henri Kykkänen, Antti Schlüter, Hjørdis High Energy Physics - Phenomenology Mathematical Physics Nuclear Theory 65R32 We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To this formulation of the problem, we apply standard inverse problems methods and algorithms to reconstruct known dipole amplitudes from simulated reduced cross section data with realistic precision. The main difference of this approach to previous works is that this implementation does not require any fit parametrization of the dipole amplitude. The freedom from parametrization also enables us for the first time to quantify the uncertainties of the inferred dipole amplitude in a novel more general framework. This mathematical approach to small-$x$ phenomenology opens a path to parametrization bias free inference of the dipole amplitude from HERA and Electron--Ion Collider data. |
| title | Reconstruction of the Dipole Amplitude in the Dipole Picture as a mathematical Inverse Problem |
| topic | High Energy Physics - Phenomenology Mathematical Physics Nuclear Theory 65R32 |
| url | https://arxiv.org/abs/2509.05005 |