We report on a new measurement of the energy resolution that can be attained
in liquid xenon when recording only the scintillation light. Our setup is
optimised to maximise light collection, and uses state-of-the-art, high-PDE,
VUV-sensitive silicon photomultipliers. We find a value of 2.7% +- 0.3% FWHM at
511 keV, a result much better than previous measurements and very close to the
Poissonian resolution that we expect in our setup (3.0% +- 0.7% FWHM at 511
keV). Our results are compatible with a null value of the intrinsic energy
resolution in xenon, with an upper bound of 1.5% FWHM at 95% CL at 511 keV, to
be compared with 3--4% FWHM in the same region found by theoretical estimations
which have been standing for the last twenty years. Our work opens new
possibilities for apparatus based on liquid xenon and using scintillation only.
In particular it suggests that modular scintillation detectors using liquid
xenon can be very competitive as building blocks in segmented calorimeters,
with applications to nuclear and particle physics as well as Positron Emission
Tomography technology