  We prove analytically and show numerically that the dynamics of the
Fermi-Pasta-Ulam-Tsingou chain is characterised by a transient Burgers
turbulence regime on a wide range of time and energy scales. This regime is
present at long wavelengths and energy per particle small enough that
equipartition is not reached on a fast time scale. In this range, we prove that
the driving mechanism to thermalisation is the formation of a shock that can be
predicted using a pair of generalised Burgers equations. We perform a
perturbative calculation at small energy per particle, proving that the energy
spectrum of the chain $E_k$ decays as a power law, $E_k\sim k^{-\zeta(t)}$, on
an extensive range of wavenumbers $k$. We predict that $\zeta(t)$ takes first
the value $8/3$ at the Burgers shock time, and then reaches a value close to
$2$ within two shock times. The value of the exponent $\zeta=2$ persists for
several shock times before the system eventually relaxes to equipartition.
During this wide time-window, an exponential cut-off in the spectrum is
observed at large $k$, in agreement with previous results. Such a scenario
turns out to be universal, i.e. independent of the parameters characterising
the system and of the initial condition, once time is measured in units of the
shock time.
