I Strongest Prediction of GUTs possible with Current Tech?

I don't understand the question very well...
A GUT (if exists) can be anywhere... For example extrapolation of the Standard Model to higher energies can give you a prediction of GUT at around [itex]10^{16}\text{GeV}[/itex]. Of course that's a very rough thing to say because the SM does not predict the intersection of all the coupling (running) constants anywhere in the spectrum, they just get very close together at around that energy.
There are several GUT models that have made predictions that we were able to test and rule them out. For example the SU(5) GUT predicted a "fast" decay of proton something that we ruled out by not observing such a decay. Of course you can enhance the model and make it so that it fits the current experimental limits.

Now new scenarios may be implemented...For example allowing for SUSY to be at some energy scale and playing around with its parameters you can obtain a GUT I could say almost anywhere (speculative statement)? I mean you can set the scale of SUSY anywhere on the spectrum, at that scale then and based on how many particles you give to your SUSY, there can be a change of slope of the coupling constants' running and so you can tune them to meet anywhere by playing around with those 2. Also some other GUTs can result to higher groups than the Standard Model at lower energies, and those higher groups get broken into the Standard Model at some energy scale, which we know today it should be higher than 1TeV (so the scheme would be GUT->HigherGroup->StandardModel). That's the reason why LHC has two experiments (namely the CMS and ATLAS) that are dedicated to looking for signatures of such new physics scenarios at the TeV scale.
So if you ask about when we will test GUTs, I would say "we did it yesterday, still doing it now and for sure will keep on doing it in the future'.

How you search for such stuff? Well GUTs predict new particles, and so searching for those new particles can help you to test those GUTs. You do that by looking for excesses that cannot be explained/predicted by the Standard Model+statistical fluctuations. So any excess that has been found is a good indicator for new physics to exist. Of course the excesses at the moment are not statistically reliable (otherwise we would speak for new physics)... One excess I know of is the 3.9sigma deviation [not high enough yet] from the Standard Model of the fraction of the branching ratios of Bmeson decays to D or D* and taus/muons: [itex]R = \frac{\text{Br}(B\rightarrow D^{(*)}\tau \nu)}{\text{Br}(B\rightarrow D^{(*)} \mu \nu)}[/itex] obtained by combining the excesses found at BaBar,Belle and LHCb...Such excesses I know could point at some models that break the universality of weak interactions (eg favoring taus to muons).
For future technology I don't know much... our current technology has yet to reach its peak. Also making high predictions about where technology will be in 10years from now is not my thing. However nothing "big" concerning High Energy Physics is going to be built-to-operate in the next 1 or 2 decades. And higher precision measurements and a more optimal way to make them can be [and is] done in the meantime...

 

I am by no means a theoretician and so I don't know how they choose their fields of interest, I guess it depends on personal preferences and funding. In fact I am not sure that theoreticians really have any connection to experiments; the connection (at least as I see it) is done by phenomenologists who take theories and try to create testable models out of them. For example again SUSY is a theory, MSSM,NMSSM,NNMSSM etc are susy models.
and...Well judging from how many theoreticians have turned into string theory I am not sure that the main motivation is a "breakthrough" that would come from an experiment... I think it's more like how attractive the whole concept and field is to them... some people love topology and geometry...
The question is vast and cannot get a complete answer...there is not a single string theory for example [something that I don't find attractive] and that's the reason why they decided to give birth to Mtheory of which they knew nothing about but somehow [not knowing how at all] connected their different string theories.

 

That's why I said that they don't care about the experiment. Even if the experiment proves their theory unnatural, they have contributed to a field of mathematics.

 

I think (mainly speculation!) a lot of influence comes from the research done at the place one does his masters education (European system).
For example someone that gets several lecture from someone like Carlo Rovelli would be more inclined to study loops.
While a lot of people at my current institution pursue strings because that's what the hep-th group specialises in.

The messy bit with e.g. strings is that there is a lot we don't know yet. There are some no-go theorems but they have several assumptions that can be used to circumvent them. E.g. the Maldacena-Nunez no-go can be avoided by including negative tension sources which are readily available.
The theorists I conversed with will be pragmatic about their results, is it negative then they wonder is there something general to say here?
Are they positive? Great, but why do I find a good solution here and not there, what's the difference?

About experimental verification/tests, we are only uncovering the tip of the iceberg. Who knows what happens when somebody finds an unexpected result. And surely people try to find such tests or directions where they can be viable.

 

When my office is a mess, and I can't find something, it is futile to look for that particular thing. The only viable option is to straighten up the whole office, file everything, and hope that what I'd like to find shows up.

Looking for a GUT is like that. You try everything and maybe eventually you find something interesting.



Seriously. There is no short cut. Proton decay experiments are probably the most targeted at GUTs particularly and keep ruling them out to higher degrees of precision. LHC measurements of the beta functions of the coupling constants provide some hints, but only at incrementally higher energy scales. There is no smoking gun associated with GUTs in general which can resolve the issue one way or the other once and for all and never will be in our lifetimes.

 

Science has ups and downs like anything else. One day you discover a new particle, the next, it's all about weasel control and suicidal robots and there's no way in heck you're going to get the data you need on schedule to discover anything. http://dispatchesfromturtleisland.blogspot.com/2016/04/weasel-shuts-down-lhc-japanese.html

 

yeh, but you have to understand something essential... for each theory that is proven natural, at least another one [or several hundrends] are proved unnatural. The reason is also kind of recent, with the mainstream topic in theoretician circles being the diphoton excess that was seen at ~750GeV. Although that excess is not yet considered important and the bets are against it (I heard something like 20:1, so betting on its unimportance wouldn't return you much money), there have been several hundreds of papers trying to explain it in the last few months [the number of papers can also give you an idea of how chaotic your room looks like ]... Not all of them will be right and maybe none is going to be... So yes... it may be or it may not seem fun... but when you are clueless your only option is to search.
In fact asking for the GUT that exists is lame; if I knew it I would be a nobel prize winner for sure. Asking for a GUT that has the best odds to exist is not a good question... a few years ago I would say supersymmetry (I really liked MSSM at TeV scale), but now I am skeptical [without having lost all my faith or motivation for searching for it while excluding most of its parameter space].

 

We already have a theory of QG. It's called String Theory. And it potentially also is a GUT :P

 

it can be from 0 to infinity? So I guess it should contain the measured one.... (currently fighting with ambiguities in my compiler, they are for sure not good)

 

I would focus on something different: the tension between metastability of the standard model vacuum, and the hints of gauge coupling unification. The latter suggests a GUT, the former suggests something like the neutrino minimal standard model (nu MSM). They differ on whether or not there are new physics scales between the electroweak scale and the Planck scale. This is a contradiction in the hints that the data gives us, and so how it is resolved should be important.