@plainsane - I don't think Verizon would have been as precise as to cut only the common wire. If this is the issue, I'm betting the whole bundle is cut.
@scarittagle - if you have an ohm meter you could disconnect the common and a zone wire from the Rachio unit and then temporarily connect those same two wires together in the valve box by undoing their existing connections. Then using the ohm meter measure resistance across those two wires back at the Rachio unit. If the resistance is infinite (futile) then one, or more than likely both, are cut. No ohm meter, then probably time to call out an irrigation repair company/person. To help keep the time on the job and the repair bill lower, when they show up, take them to where Verizon trenched the cable and have them trace the wiring from the Rachio or the valve box, which ever is closest to the trench. When they get to the trench then dig out the wiring cable, I bet it is sliced in two.