Constraints on the T2K neutrino flux prediction from hadron production measurements at NA61/SHINE

New measurements of hadron production with a proton beam on a 2 cm carbon target at 31 GeV/c performed by the NA61/SHINE collaboration are shown. The inelastic and production cross section are presented. Multiplicities of π± , K± , KS0 , proton and Λ are shown. These measurements are fundamental to reduce the uncertainties on the neutrino flux at the T2K experiment. The procedure used to tune the T2K flux prediction with the measured spectra is explained as well.