Paper here. Lay summary here. Some bits from the latter:

The problem is this. The Pioneer 10 and 11 spacecraft were launched towards Jupiter and Saturn in the early 1970s. After their respective flybys, they continued on escape trajectories out of the Solar System, both decelerating under the force of the Sun's gravity. But careful measuremenrs show that the spacecraft are slowing faster than they ought to, as if being pulled by an extra unseen force towards the Sun.

Spacecraft engineers' first thought was that heat emitted by the spacecraft could cause exactly this kind of deceleration. But when they examined the way heat was produced on the craft, by on board plutonium, and how this must have been emitted, they were unable to make the numbers add up.

Now Frederico Francisco at the Instituto de Plasmas e Fusao Nuclear in Lisbon Portugal, and a few pals, say they've worked out where the thermal calculations went wrong.