  In slow roll inflation, the running of the spectral tilt is generically
proportional to the square of the deviation from scale invariance, $\alpha_s
\propto (n_s-1)^2$, and it is therefore currently undetectable. We present a
mechanism able to generate a much larger running within slow roll. The
mechanism is based on a curvaton field with a large mass term, and a time
evolving normalization. This may happen for instance to the angular direction
of a complex field in presence of an evolving radial direction. At the price of
a single tuning between the mass term and the rate of change of the
normalization, the curvaton can be made effectively light at the CMB scales,
giving a spectral tilt in agreement with observations. The lightness is not
preserved at later times, resulting in a detectable running of the spectral
tilt. This mechanism shows that fields with a large mass term do not
necessarily decouple from the inflationary physics, and provides a new tool for
model building in inflation.
