An A320 Captain reported possibly landing without a clearance after he was distracted by a wake vortex encounter and concern with the tight spacing on the preceding aircraft.

Narrative

We were cleared for a visual approach to the runway behind an Airbus A320. Because we were vectored in tight behind the A320; we requested S-turns to give us some extra spacing. We were also advised that there would be an Embraer jet departing another runway prior to our arrival. On short final; we encountered wake turbulence from the preceding A320 and I was busy stabilizing the aircraft while; at the same time; paying attention to our separation from the departing Embraer jet. As my comfort level with regard to spacing from the departing Embraer jet was beginning to diminish; I began to prepare myself for a go-around. Shortly thereafter; it became apparent to me that the Embraer jet would be airborne and beyond the intersection of our runway and his prior to us touching down. I then decided to continue the approach and land the aircraft. After arriving at the gate; I questioned my First Officer if he remembered receiving a landing clearance because I did not remember receiving one. He did not remember receiving a landing clearance either. I believe that I landed without a clearance; unintentionally; because of a number of factors. First of all; I was task-saturated at a critical point of the flight - on short final. Because of the tight spacing behind the A320; the wake turbulence encounter and the need for ensuring adequate separation from the departing Embraer jet; I was distracted and failed to remember to obtain a landing clearance (at least I think I failed to obtain the landing clearance). Although I am dissatisfied with myself and the fact that I unintentionally landed without a clearance (or at least I think I did); I do feel that safety was at the top of my priority list in that my attention was focused on stabilizing the aircraft and avoiding a potential separation conflict with the departing Embraer jet.