clicked_id doesn't return an id but remains inactive with a messsage Uncaught ReferenceError: clicked_id is not defined at HTMLButtonElement

Question

Why on long press the alert doesn't "fire" and show alert "button", just this one word being an ID? I want to use vanilla js. Here can be an possible answer, but I do not know how to add combine it with a code below?

onClick to get the ID of the clicked button

Currently the returned message is "Uncaught ReferenceError: clicked_id is not defined at HTMLButtonElement.".

I know how to make it work for one button, writing here var button = document.getElementById(button);
What I am trying to do and failing is to make it work for several various buttons and being activated based on clicked_id.

<button id="button">click</button>
<script>
    (function(window, document, undefined){
     'use strict';
     var start;
     var end;
     var delta;
     var button = document.getElementById(clicked_id);  
    
     button.addEventListener("mousedown", function(){
       start = new Date();
     });
    
     button.addEventListener("mouseup", function() {
         end = new Date();
         delta = end - start;
         if (delta > 0 && delta < 500) {
             alert("less than half second:");
         }
         if (delta > 500 && delta < 1000) {
             alert("more than half second and less than a second:");
         }
         if (delta > 1000) {
             alert(this_id);
         }
     });
})(window, document);
</script>