再求建議 If I should follow up 謝謝

Started my first interview with hiring director and manager (two ppl) on early Apirl. One week later, interviewed by 4 future coworkers. On the third week, I was asked for reference. I gave three professional references (all of them are from work 6 years ago). I was asked for a direct supervisor within last 5 years and I gave one with my last company (call it A) which is in the different industry from what I am applying for (call it B).  most of my career are in the same industry with company B which I am applying. then I was asked again to provide a reference from the most recent company within the same industry wth B. I told them I lost connection with my boss but offered to find a director from other areas (not my boss, I do not want my boss to be my reference) whom I worked closely on many projects within the past 5 years and I was told OK.. I gave last Tueday(3/14). 

My question is if I should ask for their decision (maybe offer to provide more information) or just wait for a answer?  Out of job for a while and really want to get this offer, also this is most close one.

Any suggestions are greatly appreciated.