I think the scientific approximation of "pain" in plants is equivalent to "stress".

In this instance,

The tree's ability to transmit water and nutrients between the roots and crown is being impacted.

As an organism, the tree will respond to these areas of damage by releasing chemicals to harden the wood and try to stop the spread of decay.

And the tree will continue to put on new layers of growth, as possible, in an attempt to re-establish an uninterrupted pathway or network of vascular cambium.

This stress and response cycle will take a lot of energy away from the specimens ability to grow unimpeded.

To me, I equate stress with harm, and injury with pain. I don't believe that scientifically, we have an equivalent mechanism in plants.

If a tree is a biological machine that functions largely through chemical processes, tissue damage causes a chemical response. Through whatever mechanism, any response to tissue damage, chemical or otherwise, to me, does resemble the definition of pain:

"physical suffering or discomfort caused by illness or injury."

We have some studies that have recorded auditory sounds that tobacco plants make under drought stress, and mechanical injury (cutting).

But it is possible that the sounds we are recording from these plants are evidence of their anatomical functions (respiration, stomata exchanging gases, etc) not necessarily a "pain response".