A What Are the Key Unresolved Issues in the Two-Higgs-Doublet Model?

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TarasZ
Hi! My question is for people familiar with the two-Higgs-doublet model (2HDM). What phenomenological or theoretical problems of this model are important to work on?

I am a postgraduate student. I have studied the Higgs sector of the Standard Model (SM) and the Higgs sectors of some of its extensions for some time. As I know, the 2HDM is now the most studied extension of the SM. I have read a few articles on the 2HDM, but have not been able to find out what particluar processes predicted by the 2HDM I should study.
 
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What does your advisor say?
 
At the beginning of my postgraduate course my advisor suggested studying the Higgs sectors of some of the SM extensions. I agreed, and now I have two articles on these topics. Then I found out that the 2HDM was much more popular than the extensions I had studied. I talked to my advisor and suggested we study the 2HDM. He agreed. However, he had never studied this model -- that is why it's up to me to choose what particular problem I will study in the 2HDM.

Now my advisor is visiting the LAL laboratory in Orsay, and he will try to talk with some experts on the 2HDM there, however, he is not sure he will do that)
 
Again what's your aim (not necessary to say exactly what you're doing just the general idea of it)?
What articles did you end up with? What's more popular than the extensions you studied (=what additional information is already there that wasn't in the articles)? Nevertheless, for working on something new from the scratch (neither you nor your advisor have any deep background on the topic), two articles are not enough to give you the necessary foundations from which on you'll start building your own research.. I guess you'll have to invest a couple of months working on existing stuff...
 
I am going to derive the differential distributions or the differential cross-sections of some particular processes predicted by the 2HDM, and then to compare the calculated distributions or cross-sections to those measured at the LHC. I have read the following articles on the 2HDM: arxiv.org/abs/1106.0034v3, arxiv.org/abs/hep-ph/9701257v1, arxiv.org/abs/1607.02402v2, etc.

Before I decided to study the 2HDM, I worked chiefly on the SM extension allowing for any possible CP properties of a spin-zero neutral Higgs boson. However, this extension has been studied for decades, and thus it's difficult to do principally new research in this extension. Predicitons of the 2HDM are now actively tested at the LHC, and it makes the model popular.
 
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