After a homeless young man, who thinks he brings a misfortune whenever he is, meets his idol and becomes a member of a group with super-powered people, called Core-holders, he starts thinking that this is turnaround in his life. Its awesome, its everything he ever wanted and? Core-holders start mysteriously dying. Of course.

>>there is no short way to describe what Core-holders are

That's a potentially fatal problem with your concept. Core-holders are central to your story. Anyone who reads your logline needs to be able to understand what differentiates them from the crowd of other characters in other films with ultra or super powers.

Since I, for one, have no clear idea what they are either, I am at a loss as to what to suggest. Other than, first and foremost, come up with a sharply focused and succinct definition of what a Core-holder is/does.

Hi everyone!
This was a huge help, thank you a lot!
Here is my thing- I?m working from outline, and although I can change a lot of it, I want to stick to the core of the story. If I should summarize that story in some kind of logline, it would be like this:

After a strongest Core-holder- a cheerful heroin, is condemned by law for execution , an obsessed by her comic-book fanboy is willing to do anything to spare her from such fate, even if it means to eliminate all of the other core-holders and become a villain only she could defeat.

Here are my issues- there is no short way to describe what Core-holders are -which is a small group of people enhanced by mysterious artifacts (Cores), controlled by government, and used as energy source
-the fact that main character is a killer, should be a big reveal in the story (and this one is ruining me the most)
-it is a bit like a buddy-cop story where main character(the killer) and the strongest Core-holder(that cheerful heroin) share most of the screen time (or page space?) which makes it SO hard to distinct which one is main character.
-and I can?t make Core-holders just a superheroes, the way the Cores work is a key to climax of the story

As my task is to write a script out of this, I want my logline to be at least OK, and now I see how horrid the logline I posted is (sorry!). I tried to exploit one layer of the story as a irony factor of the logline.

I know this is not scriptwriting forum, but bad logline=bad script, and for now I?m bit helpless.
OK, I end this rant here.
For any smallest advice- BIG thank you!
And again, I hope this is readable.

Great points Nir, you are spot on about my draft as well.