  We analyze the applicability of the Fermi-golden-rule description of
quasiparticle relaxation in a closed diffusive quantum dot with
electron-electron interaction. Assuming that single-particle levels are already
resolved but the initial stage of quasiparticle disintegration can still be
described by a simple exponential decay, we calculate the average inelastic
energy relaxation rate of single-particle excitations and its mesoscopic
fluctuations. The smallness of mesoscopic fluctuations can then be used as a
criterion for the validity of the Fermi-golden-rule description. Technically,
we implement the real-space Keldysh diagram technique, handling correlations in
the quasi-discrete spectrum non-perturbatively by means of the non-linear
supersymmetric sigma model. The unitary symmetry class is considered for
simplicity. Our approach is complementary to the lattice-model analysis of Fock
space: thought we are not able to describe many-body localization, we derive
the exact lowest-order expression for mesoscopic fluctuations of the relaxation
rate, making no assumptions on the matrix elements of the interaction. It is
shown that for the quasiparticle with the energy $\varepsilon$ on top of the
thermal state with the temperature $T$, fluctuations of its energy width become
large and the Fermi-golden-rule description breaks down at
$\max\{\varepsilon,T\}\sim\Delta\sqrt{g}$, where $\Delta$ is the mean level
spacing in the quantum dot, and $g$ is its dimensionless conductance.
