Well, first of all: that was the normal relation for impedance transformers: Z_T=sqrt(Z_L*Z_A) with T denoting the characteristic impedance of the transformer line, L the line impedance which you want to obtain in the end (e.g. 50Ohms) and Z_A the impedance of the antenna at its footpoint. As I mentioned, then the transformer length has to be lambda/4 (with lambda being the effective wavelength on the substrate). Google impedance transformer or quarter-wave transformer to get more information.
Then, let me first state my opinion based on my experience: UWB antennas are difficult to simulate (with HFSS, I do not have experience with other tools) because the solving frequency is far away from the full bandwidth which you want results of. Therefore, the result can be almost arbitrarily wrong. The paper shows very good agreement with measurement, maybe they were lucky.
That being said, there are a few basic mistakes in your model: first, the way you applied the waveport is wrong. The width of the waveport has to be about 3 times the width of the problem domain (i.e. the width of your microstrip line) and about 5 times the height of the substrate. The way you applied it (with just the height of the substrate and the width of the line) is how a lumped port would be modelled -- that however can not be applied on radiating boundary. So, I think the waveport is the way to go in your case, but it has to be larger.
Also, all outermost surfaces will become Perfect E in HFSS, unless defined otherwise. So, the radiating boundary will stay radiating, but the ground surface, where you did not apply anything else will become Perfect E -- extending your ground plane all the way under your antenna. Clearly you do not want that. Also, as a rule of thumb, the radiation boundary has to be about lambda/4 (or in my experience rather lambda/3) away from the antenna structure at all places (except for the waveport, of course). There again, you see why UWB is difficult to simulate, because either the radiation boundary makes your model very electrically large for the highest frequency or the boundary is to near for the low frequency.
So, in my opinion you need to make your air container (at least somewhat) larger and away from the ground plane and then apply the radiation boundary all around.
The third problem, at least by looking at your problem, is that the line does not really connect to the disc, because that is built by several segments. So, I would always let the line extend into the disc and then use the "unite button" to make one single area of both. But that might not be a problem for you, depending on the settings for the resolution of the disc.
So, that is all I can tell you, I haven't actually tried to simulate your model, but I think that would be the way to go. Also, please, if you're gonna be writing a publication, make sure to include all information necessary to reproduce your results. The publication of your antenna is for example missing information on the thickness of the copper plating, which in my experience can have a big impact on the solutions.