Inferring the initial condition for the Balitsky-Kovchegov equation
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| Format: | Preprint |
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2023
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| _version_ | 1866910363653505024 |
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| author | Casuga, Carlisle Karhunen, Mikko Mäntysaari, Heikki |
| author_facet | Casuga, Carlisle Karhunen, Mikko Mäntysaari, Heikki |
| contents | We apply Bayesian inference to determine the posterior likelihood distribution for the parameters describing the initial condition of the small-$x$ Balitsky-Kovchegov evolution equation at leading logarithmic accuracy. The HERA structure function data is found to constrain most of the model parameters well. In particular, we find that the HERA data prefers an anomalous dimension $γ\approx 1$ unlike in previous fits where $γ>1$ which led to e.g. the unintegrated gluon distribution and the quark-target cross sections not being positive definite. The determined posterior distribution can be used to propagate the uncertainties in the non-perturbative initial condition when calculating any other observable in the Color Glass Condensate framework. We demonstrate this explicitly for the inclusive quark production cross section in proton-proton collisions and by calculating predictions for the nuclear modification factor for the $F_2$ structure function in the EIC and LHeC/FCC-he kinematics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_10491 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inferring the initial condition for the Balitsky-Kovchegov equation Casuga, Carlisle Karhunen, Mikko Mäntysaari, Heikki High Energy Physics - Phenomenology Nuclear Theory We apply Bayesian inference to determine the posterior likelihood distribution for the parameters describing the initial condition of the small-$x$ Balitsky-Kovchegov evolution equation at leading logarithmic accuracy. The HERA structure function data is found to constrain most of the model parameters well. In particular, we find that the HERA data prefers an anomalous dimension $γ\approx 1$ unlike in previous fits where $γ>1$ which led to e.g. the unintegrated gluon distribution and the quark-target cross sections not being positive definite. The determined posterior distribution can be used to propagate the uncertainties in the non-perturbative initial condition when calculating any other observable in the Color Glass Condensate framework. We demonstrate this explicitly for the inclusive quark production cross section in proton-proton collisions and by calculating predictions for the nuclear modification factor for the $F_2$ structure function in the EIC and LHeC/FCC-he kinematics. |
| title | Inferring the initial condition for the Balitsky-Kovchegov equation |
| topic | High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2311.10491 |