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In this paper we compute higher particle form factors of branch point twistfields. These fields were first described in the context of massive1+1-dimensional integrable quantum field theories and their correlationfunctions are related to the bi-partite entanglement entropy. We find analyticexpressions for some form factors and check those expressions for consistency,mainly by evaluating the conformal dimension of the corresponding twist fieldin the underlying conformal field theory. We find that solutions to the formfactor equations are not unique so that various techniques need to be used toidentify those corresponding to the branch point twist field we are interestedin. The models for which we carry out our study are characterized by staircasepatterns of various physical quantities as functions of the energy scale. Asthe latter is varied, the beta-function associated to these theories comesclose to vanishing at several points between the deep infrared and deepultraviolet regimes. In other words, renormalisation group flows approach thevicinity of various critical points before ultimately reaching the ultravioletfixed point. This feature provides an optimal way of checking the consistencyof higher particle form factor solutions, as the changes on the conformaldimension of the twist field at various energy scales can only be accounted forby considering higher particle form factor contributions to the expansion ofcertain correlation functions.

Higher particle form factors of branch point twist fields in integrable quantum field theories