Revisiting the 'LSND anomaly' II: critique of the data analysis

This paper, together with a preceding paper, questions the so-called ``LSND anomaly'': a $3.8\ensuremath{\sigma}$ excess of ${\overline{\ensuremath{\nu}}}_{\mathrm{e}}$ 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 ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{\mathrm{e}}$ oscillation in the $\ensuremath{\Delta}{m}^{2}$ range from $0.2\text{ }\text{ }{\mathrm{eV}}^{2}$ to $2\text{ }\text{ }{\mathrm{eV}}^{2}$. Such a $\ensuremath{\Delta}{m}^{2}$ 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 a preceding paper, it was concluded that the estimates of standard backgrounds must be significantly increased. In this paper, the LSND Collaboration's estimate of the number of ${\overline{\ensuremath{\nu}}}_{\mathrm{e}}$ interactions followed by neutron capture, and of its error, is questioned. The overall conclusion is that the significance of the ``LSND anomaly'' is not larger than $2.3\ensuremath{\sigma}$.