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How important is the role of publications to get an admit into top 20 programs with an otherwise descent profile? Would love to know answers specific to the context of international students in addition to the experience of domestic students. I am applying to HEP-ex.
They are nice but not necessary at all. As metaphyx said, if you have one, it's a good addition to your profile and it will help solidify your profile to the professors (i.e. you have produced results, not just "look good on paper"). However, tons of people are admitted to top schools without any publications at all.