Ground-state energy of pionic hydrogen to one loop

J. Gasser (Bern University) , M.A. Ivanov (JINR Dubna) , E. Lipartia (Lund University , JINR Dubna , Tbilisi University) , M. Mojzis (Massachusetts University , Comenius University) , A. Rusetsky (Bern University

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classification ✦ hep-ph

keywords energyexpansionframeworkground-statehydrogenlow-energynext-to-leadingorder

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We investigate the ground-state energy of the pi- p atom (pionic hydrogen) in the framework of QCD+QED. In particular, we evaluate the strong energy-level shift. We perform the calculation at next-to-leading order in the low-energy expansion in the framework of the relevant effective field theory. The result provides a relation between the strong energy shift and the pion-nucleon S-wave scattering lengths - evaluated in pure QCD - at next-to-leading order in isospin breaking and in the low-energy expansion. We compare our result with available model calculations.

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QED radiative corrections in inverse beta decay from virtual pions
hep-ph 2026-04 unverdicted novelty 4.0

Pion-induced QED radiative corrections in inverse beta decay are small, at or below nucleon form factor uncertainties, enabling sub-permille theoretical precision for charged-current neutrino-nucleon scattering above 10 MeV.