Stereo sound separation into three sources Whenever we listen stereo songs, one part of the audio like voice hear at the center of the head, and other parts are nearby left ear and right ear. If I represent center part by C, and other parts by L' and R', We may model our original left and right channel as,



L' + C = L    and,

R' + C = R. 

As, common part of L and R channel comes in C vector, L' and R' are uncorrelated. Now we can say, (alpha + beta = pi/2)

Is this modelling correct as per the listening scenario for stereo sound?
Partially correct. Human auditory spatial perception is rather complicated. A good book on the topic would be Spatial Hearing.  How and where we localize things depends on a great many factors. For left/right localization the main effects are interaural time difference and interaural level difference. Time differences is the strongest queue. Whatever comes earlier on the left ear will be solidly localized on the left unless even if the sound is louder on the right (within reason). 
If left &amp; right signals are perfectly time aligned than your model is simplified model.