I am applying to doctoral programs in the US.
I have a paper currently under review, and, it seems that the status will remain under review after I submit my application packages.
My question is: If my paper is accepted or revised or rejected, then should I notify the schools to which I am applying that this paper was accepted or revised or rejected?
Short answer: no (don't bother). More nuanced answer: it depends. Is your paper of earth-shaking significance in some way? Is it going to appear in some renowned journal (Nature, PNAS, Lancet, Journal of the ACM, etc.)? If not, it is little more than a waste of time to try to add the information to your application. Late information is rarely added to application packets (which these days are anyway handled almost entirely online -- convenient in certain ways but makes for an additional hassle when it comes to adding to or correcting an application or supporting documentation).
However, if you have corresponded with some professor you would like to work with at the grad school that you are applying to, and have reason to believe this professor might be interested and able to influence the admissions committee, then I would certainly take the time to send a polite e-mail to this person indicating that your paper was accepted in such-and-such notable journal or conference. I would however avoid bringing up a rejection, and would also not take the trouble in case of acceptance of a less important article (or one in a less-respectable forum; e.g., an op-ed in your college newspaper).
