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The spectral energy distribution of giant lobes shows one main peak detectedby the Wilkinson Microwave Anisotropy Probe at low energy of $10^{-5}$ eV and afaint $\gamma$-ray flux imaged by Fermi Large Area Telescope at energy $\geq$100 MeV. On the other hand, Pierre Auger Observatory associated someultra-high-energy cosmic rays with the direction of Centaurus A and IceCubereported 28 neutrino-induced events in a TeV - PeV energy range, although noneof them related with this direction. In this work we describe the spectra foreach of the lobes, the main peak with synchrotron radiation, and thehigh-energy emission with $pp$ interactions. Obtaining a good description ofthe main peak, we deduce the magnetic fields, electron densities and the age ofthe lobes. Describing successfully the $\gamma$-ray emission by pp interactionsand considering as targets those thermal particles in the lobes with density inthe range $10^{-10}$ to $10^{-4}\, {\rm cm}^{-3}$, we calculate the number ofultra-high-energy cosmic rays. Although $\gamma$-spectrum is well describedwith any density in the range, only when $10^{-4}\, {\rm cm}^{-3}$ isconsidered, the expected number of events is very similar to that observed byPierre Auger Observatory, otherwise we obtain an excessive luminosity. Inaddition, correlating the $\gamma$-ray and neutrino fluxes through ppinteractions we calculate the number of high-energy neutrinos expected inIceCube. Our analysis indicates that neutrinos above 1 TeV cannot be producedin the lobes of Centaurus A, which is consistent with the results recentlypublished by IceCube Collaboration.

Correlation of $\gamma$-ray and high-energy cosmic ray fluxes from the giant lobes of Centaurus A