Deuteron Matrix Elements in Chiral Effective Theory at Leading Order

We consider matrix elements of two-nucleon operators that arise in chiral effective theories of the two-nucleon system. Generically, the short-distance piece of these operators scales as 1/r^n, with r the relative separation of the two nucleons. We show that, when evaluated between the leading-order wave functions obtained in this effective theory, these two-nucleon operators are independent of the cutoff used to renormalize the two-body problem for n=1 and 2. However, for n greater than or equal to 3 general arguments about the short-distance behavior of the leading-order deuteron wave function show that the matrix element will diverge.