  We have investigated the impact of long-range forces induced by unparticle
operators of scalar, vector and tensor nature coupled to fermions in the
interpretation of solar neutrinos and KamLAND data. If the unparticle couplings
to the neutrinos are mildly non-universal, such long-range forces will not
factorize out in the neutrino flavour evolution. As a consequence large
deviations from the observed standard matter-induced oscillation pattern for
solar neutrinos would be generated. In this case, severe limits can be set on
the infrared fix point scale, Lambda_u, and the new physics scale, M, as a
function of the ultraviolet (d_UV) and anomalous (d) dimension of the
unparticle operator. For a scalar unparticle, for instance, assuming the
non-universality of the lepton couplings to unparticles to be of the order of a
few per mil we find that, for d_UV=3 and d=1.1, M is constrained to be M >
O(10^9) TeV (M > O(10^10) TeV) if Lambda_u= 1 TeV (10 TeV). For given values of
Lambda_u and d, the corresponding bounds on M for vector [tensor] unparticles
are approximately 100 [3/Sqrt(Lambda_u/TeV)] times those for the scalar case.
Conversely, these results can be translated into severe constraints on
universality violation of the fermion couplings to unparticle operators with
scales which can be accessible at future colliders.
