Anomalous scaling exponents of a white-advected passive scalar

For Kraichnan's problem of passive scalar advection by a velocity field delta correlated in time, the limit of large space dimensionality d >> 1 is considered. Scaling exponents of the scalar field are analytically found to be zeta(2n) = (n) zeta(2) - 2(2 - zeta(2))n(n - 1)/d, while those of the dissipation field are mu(n) = -2(2 - zeta(2))n(n - 1)/d for orders n << d. The refined similarity hypothesis zeta(2n) = n zeta(2) + mu(n) is thus established by a straightforward calculation for the case considered.