Some inverse problems in particle physics

Description

Luigi Del Debbio's 2026 lecture notes tackle inverse problems, the task of recovering a whole function from a limited set of measurements, in particle physics. Two examples anchor the lectures. Physicists must extract parton distribution functions, which describe how momentum is shared inside the proton, from scattering data or from lattice QCD calculations. They must also pull spectral functions out of lattice correlation data. Both jobs are ill-posed: finite data cannot pin down an infinite-dimensional answer without added assumptions.

Del Debbio frames the work probabilistically: every assumption sits openly in a prior, and results emerge as posterior probabilities with honest error bars. Three strategies get detailed treatment: the Backus-Gilbert method, Gaussian processes, and neural-network fits. Readers see how bigger datasets, more precise data, and different priors each move the answer. The lectures suit graduate students needing rigorous uncertainty estimates in precision phenomenology.

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Source: https://europepmc.org/article/MED/PMC13457332