I have applied almost a month after the deadline (Jan 9), but still got accepted. Currently I'm in my last year of masters in Italy. After a discussion with my thesis supervisor he recommended me to apply here. I contacted faculty member (in mid December) and he encouraged me to apply. I have co-authored on paper published in JHEP (although I did not apply for high energy physics, I'm going for the condensed matter theory). Even though I do not recommend applying late, it is still possible to get accepted (But you should contact the administration so that they consider your application for current cycle).

Did not submit GRE scores

I have been hired for research here since graduating with a B.S. in May

hep-ex/ astroparticle ex

My 3rd recommender uploaded his recommendation almost a month late so this is most likely why.

Nuclear theory. 7 months of experimental particle physics research, a semester of research in applied mathematics, current project in gravitational theory. 5 graduate courses taken. 4 years in physics and math education(TA, SI, Tutor, Mentor, etc…)