  The evaluation of vacuum expectation values (VEVs) in massive integrable
quantum field theory (QFT) is a nontrivial renormalization-group "connection
problem" -- relating large and short distance asymptotics -- and is in general
unsolved. This is particularly relevant in the context of entanglement entropy,
where VEVs of branch-point twist fields give universal saturation predictions.
We propose a new method to compute VEVs of twist fields associated to
continuous symmetries in QFT. The method is based on a differential equation in
the continuous symmetry parameter, and gives VEVs as infinite form-factor
series which truncate at two-particle level in free QFT. We verify the method
by studying U(1) twist fields in free models, which are simply related to the
branch-point twist fields. We provide the first exact formulae for the VEVs of
such fields in the massive uncompactified free boson model, checking against an
independent calculation based on angular quantization. We show that logarithmic
terms, overlooked in the original work of Callan and Wilczek [Phys. Lett. B333
(1994)], appear both in the massless and in the massive situations. This
implies that, in agreement with numerical form-factor observations by Bianchini
and Castro-Alvaredo [Nucl. Phys. B913 (2016)], the standard power-law
short-distance behavior is corrected by a logarithmic factor. We discuss how
this gives universal formulae for the saturation of entanglement entropy of a
single interval in near-critical harmonic chains, including log log
corrections.
