What he ^^ said, without this you will have no charge, this excites the field windings that starts the charge process, it's the earth from the warning light, when charging thats why the light extinguishes as two lives(It would charge if revved hard enough as well) It's just snapped as they commonly do you should find the connector on the back of the alternator still. Best bet is to use a ring connector and a nut and use another piece of wire to connect again to the blue wire.

Martin