Critical structure factors of bilinear fields in O(N) vector models

We compute the two-point correlation functions of general quadratic operators in the high-temperature phase of the three-dimensional O(N) vector model by using field-theoretical methods. In particular, we study the small- and large-momentum behavior of the corresponding scaling functions, and give general interpolation formulas based on a dispersive approach. Moreover, we determine the crossover exponent phi(T) associated with the traceless tensorial quadratic field, by computing and analyzing its six-loop perturbative expansion in fixed dimension. We find phi(T)=1.184(12), phi(T)=1.271(21), and phi(T)=1.40(4) for N=2,3,5, respectively.