Detectors using liquid xenon as target are widely deployed in rare event searches. Conclusions on the interacting particle rely on a precise reconstruction of the deposited energy which requires calibrations of the energy scale of the detector by means of radioactive sources. However, a microscopic calibration, i.e. the translation from the number of excitation quanta into deposited energy, also necessitates good knowledge of the energy required to produce single scintillation photons or ionisation electrons in liquid xenon. The sum of these excitation quanta is directly proportional to the deposited energy in the target. The proportionality constant is the mean excitation energy and is commonly known as $W$-value. Here we present a measurement of the $W$-value with electronic recoil interactions in a small dual-phase xenon time projection chamber with a hybrid (photomultiplier tube and silicon photomultipliers) photosensor configuration. Our result is based on calibrations at $mathcal{O}(1-10 , mathrm{keV})$ with internal $^{37}$Ar and $^{83text{m}}$Kr sources and single electron events. We obtain a value of $W=11.5 , ^{+0.2}_{-0.3} , mathrm{(syst.)} , mathrm{eV}$, with negligible statistical uncertainty, which is lower than previously measured at these energies. If further confirmed, our result will be relevant for modelling the absolute response of liquid xenon detectors to particle interactions.
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