This paper, together with a subsequent paper, questions the so-called LSND anomaly: a 3.8 {sigma} excess of anti-electronneutrino interactions over standard backgrounds, observed by the LSND Collaboration in a beam dump experiment with 800 MeV protons. That excess has been interpreted as evidence for the anti-muonneutrino{to} anti-electronneutrino oscillation in the {Delta}m2 range from 0.2 eV2 to 2 eV2. Such a {Delta}m2 range is incompatible with the widely accepted model of oscillations between three light neutrino species and would require the existence of at least one light sterile neutrino. In this paper, new data on pion production by protons on nuclei are presented, and four decades old data on pion production by neutrons on nuclei are recalled, that together increase significantly the estimates of standard backgrounds in the LSND experiment, and decrease the significance of the LSND anomaly from 3.8 {sigma} to 2.9 {sigma}. In a subsequent paper, in addition the LSND Collaborations data analysis will be questioned, rendering a further reduction of the significance of the LSND anomaly.
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