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Context. Very recent gamma-ray observations of G120.1+1.4 (Tycho’s) supernova remnant (SNR) by Fermi-LAT and VERITAS have provided new fundamental pieces of information for understanding particle acceleration and nonthermal emission in SNRs. Aims. We want to outline a coherent description of Tycho’s properties in terms of SNR evolution, shock hydrodynamics, and multiwavelength emission by accounting for particle acceleration at the forward shock via first-order Fermi mechanism. Methods. We adopt here a quick and reliable semi-analytical approach to nonlinear diffusive shock acceleration. It includes magnetic field amplification due to resonant streaming instability and the dynamical backreaction on the shock of both cosmic rays (CRs) and self-generated magnetic turbulence. Results. We find that Tycho’s forward shock accelerates protons up to at least 500 TeV, channelling into CRs about 10% of its kinetic energy. Moreover, the CR-induced streaming instability is consistent with all the observational evidence of very efficient magnetic field amplification (up to ~300 μG). In such a strong magnetic field, the velocity of the Alfvén waves scattering CRs in the upstream is expected to be enhanced and to make accelerated particles feel an effective compression factor lower than 4, in turn leading to an energy spectrum steeper than the standard prediction ∝ E-2. This effect is crucial for explaining GeV-to-TeV gamma-ray spectrum as the result of neutral pions decay produced in nuclear collisions between accelerated nuclei and the background gas. Conclusions. The self-consistency of such hadronic scenario, along with the inability of the concurrent leptonic mechanism (inverse Compton scattering of relativistic electrons on several photon backgrounds) to reproduce both the shape and the normalization of the detected gamma-ray emission, represents the first clear and direct radiative evidence that hadron acceleration occurs efficiently in young Galactic SNRs.