UX & Agile: What criteria could change the complexity of a UX user story?

I'm part of a cross functional dev team, we are applying Agile and also we are trying to adopt UX. Now, we have a difficult moment to estimate the UX user stories. What criteria can be involved to estimate the complexity points? Also I'm interested in listening to other similar experiences (UX Designers that apply Agile).

I will clarify my context ^^:

My team (formed by 4 Dev, 2 QA, 4 Business Analysts, 1 UX Designer) are developing applications that are used internal by employees.

Usually a business request was firstly analysed by the Business Analysts, but now we want to improve the experience of our users and also make research in this scope (here we want to intergrate the UX Designer role).

We want to bring the design process before starting the developing one and this UX activity to be also marked in our backlog.

For example this sprint we created a UX Research user story with the purpose to improve the way that users search for a document inside of one our apps (the tasks that were included in this user story: to create a research plan, run interviews, run usability tests, synthetize data).

The estimation of this user story was made by our "inside feeling", but now we want to define some criteria (for example when we estimate a development user story our criteria are the time, rank of unknown, risks, knowledge level).

Also we can't mark this activity in a "sprint zero" because the journey between research and a tested prorototype can take months in some complex situations.