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The T2K neutrino beam predictions require precise knowledge of the hadron production in proton-carbon interactions at 31 GeV/c. Currently one of the largest errors in flux estimates comes from the poor constraints of particle yields off the target. The NA61/SHINE experiment addresses this source of uncertainty for T2K with hadron production measurements obtained using data taken in 2007 and 2009 with a thin graphite target of 2 cm length (about 0.04 of an interaction length λI). Measurements of π ± and K yields from the 2007 dataset were already used by the T2K experiment to tune neutrino beam simulations and reduce uncertainties. New results on π±, K±, p, K S and Λ production from the NA61/SHINE 2009 data analyses with smaller statistical and systematic errors were recently published. They allow for further reduction of neutrino and antineutrino flux uncertainties in T2K. Finally we discuss the total T2K beam uncertainty for neutrino and antineutrino mode with detailed decomposition of sources of errors that affect the flux predictions. 1. The T2K beam production The experimental setup of the T2K consists of three main components: the neutrino beamline, the near detector complex, and far detector. The first two are situated at the J-PARC (Japan Proton Accelerator Research Complex) facility in Tokai, while the far detector SuperKamiokande is placed nearly 295 km away from the production point of the neutrino beam, in Kamioka mine. More details about near and far detectors may be found in [3]. J-PARC is equipped with three accelerators: a linear accelerator (LINAC), a Rapid Cycle Synchrotron (RCS) and a Proton Synchrotron called Main Ring (MR) [4]. The design energies of the three acceleration stages are 400 MeV, 3 GeV and 30 GeV, respectively. The neutrino beamline consists of two complementary subsystems. These are: the primary and secondary beamlines. The main aim of the primary beamline is to tune proton beam coming from MR, bent it towards the direction of Kamioka by 80.70, and focus the beam onto the target. A well tuned proton beam is of great importance for the stable neutrino beam production, thus in J-PARC facility there are several beam monitors placed in order to control the proton beam intensity, profile, position or loss. Three sections constitute the secondary beamline: the target station, decay volume and beam dump. The target station is equipped with three magnetic horns and the graphite target, 90 cm in length, is inserted inside the first one. The proton beam is directed towards graphite target, and as a result many hadrons are produced, amongst of which charged pions and kaons are crucial. While charged pions decays are responsible for the low energy neutrinos, charged kaons generate the high energy tail of the T2K beam, and

Recent T2K flux predictions with NA61/SHINE thin graphite target measurements