PHP can't reach ajax data

Question

I have the form that consists of input text and button. I need to get the text from the input field and pass into the php variable. I use ajax, callback function responds to me but php doesn't get the data. Here is occurring such an error - Notice: Undefined index: site_input.

<form>
    <div class="input-group">
      <input type="text" class="form-control" placeholder="URL" value="">
        <span class="input-group-btn">
          <button id="start" class="btn" type="button">Start</button>
        </span>
    </div> 
</form>

//jQuery
 $("#start").click(function(){
        $(document).ready(function(){
            if(status == 0) {
            $("#start").css("background-color", "red");
            $("#start").text("Stop");
             var site = $(".form-control").val();
            $.ajax({
                url: "index.php",
                data: {
                    "site_input" : site
                },
                type: "POST",
                success: function(data) {
                    alert("OK");
                }
            });
            status = 1;   
        }
//index.php
$a =isset($_POST['site_input'])?$_POST['site_input']:'not yet';
echo $a ;
$value = $_POST['site_input'];
echo $value;