  The $\beta$ decay of one-neutron halo nucleus $^{11}$Be was investigated
using the Warsaw Optical Time Projection Chamber (OTPC) detector to measure
$\beta$-delayed charged particles. The results of two experiments are reported.
In the first one, carried out in LNS Catania, the absolute branching ratio for
$\beta$-delayed $\alpha$ emission was measured by counting incoming $^{11}$Be
ions stopped in the detector and the observed decays with the emission of
$\alpha$ particle. The result of 3.27(46)\% is in good agreement with the
literature value. In the second experiment, performed at the HIE-ISOLDE
facility at CERN, bunches containing several hundreds of $^{11}$Be ions were
implanted into the OTPC detector followed by the detection of decays with the
emission of charged particles. The energy spectrum of $\beta$-delayed $\alpha$
particles was determined in the full energy range. It was analysed in the
R-matrix framework and was found to be consistent with the literature. The best
description of the spectrum was obtained assuming that the two $3/2^+$ and one
$1/2^+$ states in $^{11}$B are involved in the transition. The search for
$\beta$-delayed emission of protons was undertaken. Only the upper limit for
the branching ratio for this process of $(2.2 \pm 0.6_{\rm stat} \pm 0.6_{\rm
sys}) \times 10^{-6}$ could be determined. This value is in conflict with the
result published in [Ayyad et al. Phys. Rev. Lett. 123, 082501 (2019)] but does
agree with the limit reported in [Riisager et al., Eur. Phys. J. A (2020)
56:100]
