What is the mouse down selector in CSS?

I figured out that this behaves like a mousedown event:

button:active:hover {}

I think you mean the active state

 button:active{
  //some styling
 }

These are all the possible pseudo states a link can have in CSS:

a:link {color:#FF0000;}    /* unvisited link, same as regular 'a' */
a:hover {color:#FF00FF;}   /* mouse over link */
a:focus {color:#0000FF;}   /* link has focus */
a:active {color:#0000FF;}  /* selected link */
a:visited {color:#00FF00;} /* visited link */

See also: http://www.w3.org/TR/selectors/#the-user-action-pseudo-classes-hover-act

Pro-tip Note: for some reason, CSS syntax needs the :active snippet after the :hover for the same element in order to be effective

http://www.w3schools.com/cssref/sel_active.asp