I have had this same problem twice now.  Just this last weekend the screw came out.   Actually you probably did not break anything off but the pressurized screw came out of the socket?   The first time this happened I was able to work it back into the whole.  As you screw the screw in it puts preasure on a spot inside. The tighter you screw the nut in the tighter the pan is etc.

I sent mine in to Arca Swill (after calling them) to have it repaired hopefully for good.
The office is located in Chicago.

I have a backup that has not caused me this problem.

My problem is that no matter how much I try to tighten this knob I cannot get it to lock the head.  It will still pan albeit with some tension.  Is this normal?  Is there any remedy other than sending back?  I love the head otherwise but this has been frustrating.

I have  a  fairly new Arca  Swiss B1 ball head, and  the knob that controls  the pannning has  failed in the middle of an  extended photo shoot in Vermont(of course). There is a little screw at the end of the  knob and it has broken off into the collar in the head that apparently stops the head from panning around. Is this a user repairable problem, or does it have to be sent back to Arca
Swiss or somewhere else.
BTW, is this  a common failure with Arca B1 heads?
Thanks.

This is the website of the company that will work on your
Ball head (b1)  Precision Camera in Niles, IL
I got mine back yesterday.  Bob who owns the company said you will need to send it to him or Arca Swiss (who in turn will give it to him) to be repaired.

This is his website  with good tips on care and treatmend of
the Arca Swiss ball heads
http://www.precisioncameraworks.com/
It only took a short time to get my ball head back.