I determined a parameter for an experiment – shall I ask for authorship? I am working in an experimental-physics group. They are going to publish a paper soon. So far, I see five authors on first draft (PhD student, postdoc, collaborator, collaborator, PI).

I am not sure whether I should ask my PI to consider putting my name on the paper or not. I was working on the project for only a month and then the PI gave me another project right after I finished it. I was not involved in any analysis of the paper, but I was working on finding a good parameter for the experiment.

Initially, when I was working on the project, I thought I would be one the authors, however, one year and half later, the first and second author of this project did too much work, so it seems like that I did nothing on this experiment compared to them.

Is it worth it to ask my PI to consider me in the paper?
Whether or not you should be an author on the paper is not about whether you did something, but whether you contributed intellectually. For example, a lab technician who washed the petri dishes and while everyone was working on the experiment in the background turned the dial of the radio to the station that everyone wanted to listened to (i.e., determined one parameter that was crucial to the experiment), did contribute to the experiment. But it was not an intellectual contribution, and so authorship is probably not warranted.

Without more details in your question, it is hard to tell whether you should or should not be an author on the paper. But, this is worth a conversation with your adviser. It's likely going to be a slightly awkward conversation, but it is one in which you can talk about the norms in your field, what qualifies as an "intellectual contribution" and why or why not everyone on the paper should or should not be an author.