When I use Luke to search my Lucene index using a standard analyzer, I can see the field I am searchng for contains values of the form MY_VALUE. When I search for field:\"MY
I don't think you'll be able to use the standard analyser for this use case.
Judging what I think your requirements are, the keyword analyser should work fine for little effort (the whole field becomes a single term).
I think some of the confusion arises when looking at the field with luke. The stored value is not what's used by queries, what you need are the terms. I suspect that when you look at the terms stored for your field, they'll be "my" and "value".
Hope this helps,
It doesn't look like you used the StandardAnalyzer to index that field. In Luke you'll need to select the analyzer that you used to index that field in order to match MY_VALUE correctly.
Incidentally, you might be able to match MY_VALUE by using the KeywordAnalyzer.