  Background: Measurements of $\beta$ decay provide important nuclear structure
information that can be used to probe isospin asymmetries and inform nuclear
astrophysics studies. Purpose: To measure the $\beta$-delayed $\gamma$ decay of
$^{26}$P and compare the results with previous experimental results and
shell-model calculations. Method: A $^{26}$P fast beam produced using nuclear
fragmentation was implanted into a planar germanium detector. Its
$\beta$-delayed $\gamma$-ray emission was measured with an array of 16
high-purity germanium detectors. Positrons emitted in the decay were detected
in coincidence to reduce the background. Results: The absolute intensities of
$^{26}$P $\beta$-delayed $\gamma$-rays were determined. A total of six new
$\beta$-decay branches and 15 new $\gamma$-ray lines have been observed for the
first time in $^{26}$P $\beta$-decay. A complete $\beta$-decay scheme was built
for the allowed transitions to bound excited states of $^{26}$Si. $ft$ values
and Gamow-Teller strengths were also determined for these transitions and
compared with shell model calculations and the mirror $\beta$-decay of
$^{26}$Na, revealing significant mirror asymmetries. Conclusions: A very good
agreement with theoretical predictions based on the USDB shell model is
observed. The significant mirror asymmetry observed for the transition to the
first excited state ($\delta=51(10)\%$) may be evidence for a proton halo in
$^{26}$P.
