Massless Limit of Massive Field Theory: Right or Wrong?

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Taking the massless limit of a massive field theory does not always yield the correct massless theory, as the outcome depends on the specific context and definitions involved. Careful consideration is necessary due to potential ambiguities that can arise during this process. In certain scenarios, the massless limit may lead to incorrect conclusions or results. Therefore, it is crucial to approach this limit with caution and a thorough understanding of the underlying principles. Ultimately, the massless limit is not universally reliable in producing the "right" massless theory.
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If I take the massless limit of a massive field theory (e.g. considering cross-sections or other observables), do I always obtain the "right" massless theory?
 
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It depends what you mean exactly as well as the context. In general, great care must be taken when you take this limit as there are a number of ambiguities that can and will arise.

In some cases, the answer is most likely no!
 

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