  We present the precision calibration of 35 Hamamatsu R11410-22
photomultiplier tubes (PMTs) with xenon scintillation light centred near 175
nm. This particular PMT variant was developed specifically for the LUX-ZEPLIN
(LZ) dark matter experiment. A room-temperature xenon scintillation cell
coupled to a vacuum cryostat was used to study the full-face PMT response at
both room and low temperature $\textrm{($\sim$ -100$^\circ$C)}$, in particular
to determine the quantum efficiency (QE) and double photoelectron emission
(DPE) probability in LZ operating conditions. For our sample with an average QE
of $\textrm{(32.4$\pm$2.9)%}$ at room temperature, we find a relative
improvement of $\textrm{(17.9$\pm$5.2)%}$ upon cooling (where uncertainty
values refer to the sample standard deviation). The mean DPE probability in
response to single vacuum ultraviolet (VUV) photons is
$\textrm{(22.6$\pm$2.0)%}$ at low temperature; the DPE increase relative to
room temperature, measured here for the first time, was
$\textrm{(12.2$\pm$3.9)%}$. Evidence of a small triple photoelectron emission
probability $\textrm{($\sim$0.6%)}$ has also been observed. Useful correlations
are established between these parameters and the QE as measured by the
manufacturer. The single VUV photon response is also measured for one ETEL
D730/9829QB, a PMT with a more standard bialkali photocathode used in the
ZEPLIN-III experiment, for which we obtained a cold DPE fraction of
$\textrm{(9.1$\pm$0.1)%}$. Hence, we confirm that this effect is not restricted
to the low-temperature bialkali photocathode technology employed by Hamamatsu.
This highlights the importance of considering this phenomenon in the
interpretation of data from liquid xenon scintillation and electroluminescence
detectors, and from many other optical measurements in this wavelength region.
