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In answering your question, the first thing to establish is the make/model of vibrato on your LTD M-50. The absence of the letters FR from the guitar model name suggests a non-locking fulcrum vibrato rather than a licensed Floyd Rose.
Remove the spring cavity cover plate. Inspect the vibrato sustain block for embossed identifier letters and/or numbers. This could be Sung-il, Ping Well, Gotoh or any number of other SE Asian brands.
If, for example, you find P. W. 26, it should be easy to source the matching arm from an official ESP/LTD retailer.