Current alert e-mail template does not contain any option to Analyze the alert in user specific project. The button link "Analyze Further" leads to a prefabricated project. Another option how to achieve this, could be to put a custom link to Alert notes. If the notes would be a part of template it could fit too.
Or prepare the specific element in the e-mail template leading to the specific project in Workspace and assigned by URL at Alert definition page.