Notch Filter - Bandwidth vs pole / zero location vs Q factor
In this paper by Nehora, "A Minimal Parameter Adaptive Notch Filter With
Constrained Poles and Zeros" IEEE Trans ASSP, vol 33, No 4, 1985 link

The Bandwidth is given as
$$BW=\pi(1-\rho) $$
where $\rho$ is the radius of the pole. The zero is assumed to be on the unit circle. 

Excerpt from the relevant section of that paper:



And the references 1 through 3:



Another paper gives the same bandwidth and it is listed as the 3dB bandwidth - see (Yong, Kechu, Xiaofan, "A gradient algorithm for complex adaptive notch filters" - Intl Conf on Signal Processing, 2004) link.

Yet another paper with bandwidth details is by Regalia,"A Complex Adaptive Notch Filter" IEEE Sig Proc Letters, Vol 17, No 11, 2010, Link. 
Note that Regalia's notch filter is based on All-pass filters and so it has a different equation for bandwidth.

The relevant section from the Regalia paper: