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I've never heard of a field dedicated to the study of research methods. There are journals dedicated to advances in methodology (e.g., , ), but the closest concept I've encountered to a field dedicated to researching research is Thomas Kuhn's classic work The Structure of Scientific Revolutions and other similar philosophical works, which discuss how science, as a field, progresses and evolves.
I would guess that the reason for the lack of such a field is such research is part and parcel of the actual work done in the field. In order to study biochemistry, one must understand how to study biochemistry; in order to study mathematics, one must know the types of questions and the methods used to find answers in mathematics. Each field is unique, and each field will find specific methods that will optimally serve the needs of that specific field. While there may be broadly-applicable research techniques, each field will solve the problem of "how to do research" differently, in the way that best suits that field.