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The study of $\mathrm{T}\overline{\mathrm{T}}$-perturbed quantum fieldtheories is an active area of research with deep connections to fundamentalaspects of the scattering theory of integrable quantum field theories,generalised Gibbs ensembles, and string theory. Many features of thesetheories, such as the peculiar behaviour of their ground state energy and theform of their scattering matrices, have been studied in the literature.However, so far, very few studies have approached these theories from theviewpoint of the form factor program. From the perspective of scatteringtheory, the effects of a $\mathrm{T}\overline{\mathrm{T}}$ perturbation (andhigher spin versions thereof) is encoded in a universal deformation of thetwo-body scattering matrix by a CDD factor. It is then natural to ask how theseperturbations influence the form factor equations and, more generally, the formfactor program. In this paper, we address this question for free theories,although some of our results extend more generally. We show that the formfactor equations admit general solutions and how these can help us study thedistinct behaviour of correlation functions at short distances in theoriesperturbed by irrelevant operators.

Form Factors and Correlation Functions of $\mathrm{T}\overline{\mathrm{T}}$-Deformed Integrable Quantum Field Theories