Ask HN: Research on different search box UIs?

I'm building an application with search functionality prime and center.

I've perused the web for inspiration. Some sites put the search button inside the search box, some one the left, others on the right. Google places the search and I'm feeling lucky button under the search box. I would imagine Google has done A/B experimentation on this, or maybe it's just some product manager's / designer / engineers intuition.

Is there any academic literature on this? Is there statistical data on what's the most common pattern?

Thank you!