I'm working on a paper that needs to be bound

$$ Pr left[|vec x^top Q vec y| >= tright]$$ from where $ Q $ is a matrix (random symmetric) and $ vec x, vec y $ are real mean zero subgauss random vectors. As far as I understand it, the Hanson-Wright inequality ties this as $$ 2 exp left (-c cdot min left ( frac {t ^ 2} {k ^ 4 || Q || _F ^ 2}, frac {t} {k ^ 2 || Q | | _2} right) right) $$ from where $ k $ is the subgaussian parameter and $ c $ is an absolute constant.

But I'm trying to derive an actual numerical limit. Is there a paper that gives an actual value of $ c $preferably a close? It may be different for the two sides of min (). Many Thanks.