Why doesn't the 'V' curve of a synchronous motor touch the D.C. field current axis?
I guess you talk about the fact that the V-curve bottom tip does not becomes zero at zero excitation current.

Torque production and saliency

The fact that this happens can be ascribed to the saliency of the rotor. Torque(and therefore active power) is produced in two ways:


reluctance torque - comes from the asymmetry of the rotor. During one rotation the rotor iron will have different distances from the stator. In simple terms it could be just a piece of iron that is attracted to magnet, if you rotate the magnet around, the iron will follow (even though it itself has no excitation windings or permanent magnets)
full-pole torque - comes from the fact that the rotor itself becomes a magnet. The rotor becomes magnetized by the excitation current, or an embedded permanent magnet. If there is no excitation current or no PM, this component will be zero.


Torque is directly proportional to active power(rotation speed is needed for conversion).

V-curve

The V-curve is used to describe the power output of a synchronous machine with regard to the excitation current. The bottom tip of the V is pure active power output from the machine. The arms of the V are under- and overexcited regimes which generate reactive power output.


V-curve, Source: Wikimedia(CC)

Your case

The V-curve shown above is for non-salient machines. That means machines that have a rotor that is same along the whole circumference. From this we conclude that there is no reluctance torque, and therefore no reluctance torque related active power.

In your case however if you have a salient rotor, you will get power because there will be reluctance torque and therefore active power, even when your armature(excitation) current is zero.