In the last paragraph, the author states that "the professor presented the Higgs field with such certainty that for a long while I had no idea it had yet to be established experimentally." In this context, for a scientific theory to be established most nearly means that it is validated, or proven.
Choices B, C, and D are incorrect because in the context of the last paragraph describing a scientific theory as being "established experimentally," the word "established" means validated, or proven, not founded (choice B), introduced (choice C), or enacted (choice D).