The indications from the details you have given is that the scanner is causing the hum due to it being grounded by the coax which in turn is grounded by the mast. This is probably all caused by what ever power supply your using to power the scanners. My bet is that it isn't grounded and your experiencing a ground loop issue from the power supply.
My suggestion would be to find a good ground to make sure the negative of the power supply is tied to ground. By any chance does the power supply have only a 2 conductor power cord? If your power supply does have a 3 wire power cord, then you need to look further.
I would start with making sure the power outlet your plugged into has a good ground connection. You can test this real fast by looking at the outlet with a volt meter. You will notice that the outlet should have a long slot and a short slot. The short slot is the hot leg and the long slot is the neutral.
If you take a volt meter from the round pin (ground) to the short slot, you should see 120 volts AC.
If you take the volt meter from the long slot to the round pin, you should see nothing.
Now put the meter in the Ohms position, and short the test leads together. You should see 0 Ohms. Take the test leads and go from the round ground pin to the long neutral slot. You should see close to zero Ohms again. If not, your missing the ground connection at that outlet.
If in your testing of the outlet in the first few steps, you don't get the 120 volts and no volts in the locations I told you to measure them in, stop. The outlet is wired wrong. Trying to use an Ohm meter on a circuit that has voltage on it will damage or blow the meter up.