Critical and subcritical fusion asymptotics for Sine$_β$ correlation functions

We determine the first correction to the leading Vandermonde fusion law for the correlation functions of the Sine$*β$ process in the critical and and subcritical regimes $mβ\leq1$. When $mβ<1$, the normalized correction is of order $|\varepsilon|^{1+mβ}$, with a strictly negative coefficient given b