After flying through heavy precipitation at FL200; an A320 Captain's airspeed developed a 15 KT discrepancy from the First Officer's which increased to 90 KTS as the descent continued to the landing.

Narrative

Descending on the Arrival we began to encounter heavy precipitation at about FL200. Autopilot and Auto Throttles were off. At about 11;000 FT began to notice an IAS discrepancy between Captain and First Officer indicators. It started at about 15 KTS difference; but increased as we continued our descent to over 40 KTS by about 2000 FT. At approximately 10;000 FT we were given heading 080 to intercept RWY 09 LOC and given a descent to 8000 FT. This was at the same time we were attempting to ascertain which IAS was correct. In the process I didn't completely turn on the LOC and overshot by 1.2 miles according to the First Officer. ATC queried and gave us heading 020 back to LOC. After determining the faulty IAS was the Captain's; I flew the standby IAS and the rest of the approach was basically uneventful. When stabilized on short final the airspeed on the Captain's side indicated about 90 KTS with red bar (i.e. well in the stall zone) while the First Officers and standby were indicating about 140 KTS. Coincidentally the ground speed on both ND's indicated correctly based on winds and airspeed on the First Officer and standby indicators.Couple of things I would do different; immediately get ATC in the loop; and since the First Officer's IAS seemed normal should have had him fly the rest of approach. As an Airbus pilot I am becoming very concerned; particularly in light of the recent A330 loss; with the IAS issues following precipitation or icing encounters. My situation might have been drastically different if both IAS indicators would have failed.