  In this short note, we derive a precise tail expansion for Gaussian
multiplicative chaos (GMC) associated to the 2d GFF on the unit disk with zero
average on the unit circle (and variants). More specifically, we show that to
first order the tail is a constant times an inverse power with an explicit
value for the tail exponent as well as an explicit value for the constant in
front of the inverse power; we also provide a second order bound for the tail
expansion. The main interest of our work consists of two points. First, our
derivation is based on a simple method which we believe is universal in the
sense that it can be generalized to all dimensions and to all log-correlated
fields. Second, in the 2d case we consider, the value of the constant in front
of the inverse power is (up to explicit terms) nothing but the Liouville
reflection coefficient taken at a special value. The explicit computation of
the constant was performed in the recent rigorous derivation with A. Kupiainen
of the DOZZ formula \cite{KRV1,KRV}; to our knowledge, it is the first time one
derives rigorously an explicit value for such a constant in the tail expansion
of a GMC measure. We have deliberately kept this paper short to emphasize the
method so that it becomes an easily accessible toolbox for computing tails in
GMC theory.
