Using our current methods of exoplanet detection...
How long would it take to notice a wobble from the Alpha Centauri
stars that indicate the presence of a planet, especially one about
the size of Earth? Has the transit method been tried yet?
The fact that not even massive Jupiter-type worlds have been found
around the nearest star system to us does make one wonder.
I know they have found binary star systems with planets, but maybe
Alpha Centauri is one of those whose gravitational interactions kept planets from forming, or maybe they did form but got flung out or
absorbed ages ago.