dna - Does an annealing temp higher than primer's Tm contribute to primer dimer?

I don't think primer dimers are your primary concern here. Usually in my experiences, I get primer dimers all the time, even if the reaction works and I get my bands of interest.

Maybe you ought to troubleshoot other aspects of your PCR that might account for why your reaction isn't working. Have you tried using a positive control with your primers? You may try varying the parameters of your PCR as well. Remember, standard Tms are calculated according to a 50mM salt concentration: is that what you're using?

Generally, if the annealing temperature is above the predicted Tms of your primers, this represents a more restrictive and selective amplification of your target. You usually use a high annealing temperature if you're seeing lots of non-specific products. Since you're seeing no products at all, consider lowering the Tm to that of your primers (50º).

If you start seeing non-specific products at that Tm, I'd do what we call a "Touchdown" PCR -- that is, you start the reaction at a higher annealing temperature, and as each cycle progresses, it "touches down" to a lower annealing temperature. The principle behind this is that it starts it off at a restrictive temperature -- so your yield is very low initially, but then by gradually decreasing the "restrictiveness" of the reaction, your yield will improve. This will still prevent non-specific amplification b/c the less restrictive amplification will be on the fragments already amplified from the restrictive condition. Remember, biology is not exact science. Just because something says the Tm is such and such does not mean it's absolute and doesn't give you some margin of error. For example, we exploit that margin of error to optimize our experiments in the example I outlined above.

Anyways, (might have went on a tangent a little bit) you also have to consider how you designed your primers. Primers wil high self-complementarity will self-anneal at higher Tms.