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Topological interactions of a vector unparticle

Recently Georgi argued that hypothetical conformally invariant hidden sector weakly interacting with ordinary particles will have unusual manifestations at low energies in terms of effective degrees of freedom called unparticles. In this paper we consider Aharonov-Bohm type of interactions due to the vector unparticle coupled to elementary fermions. An unusual feature of these interactions is that quantum mechanical phase shift is path-dependent, although no classical force is acting on a particle. In recent papers [1] and [2], Georgi argued that a hypothetical hidden sector with an infrared conformal fixed point (see e.g. [3] as an example of such a theory) can be described by low-energy effective degrees of freedom that have properties qualitatively very different from those of ordinary particles. He named these degrees of freedom unparticles. Among the distinct properties of unparticles are the unusual scaling of the apparent phase space volume, unconventional missing energy spectra and novel interference patterns. These and related issues has been subsequently considered in much details by many authors. All the previous studies have been concentrated on the effects of local interactions of unparticles with the ordinary particles. In this brief note we would like to discuss topological, Aharonov-Bohm type of interactions [4] associated with a vector unparticle coupled to elementary fermions. Following [1],[2], we consider an effective low-energy interaction of a vector unparticle field Uμ (we assume it is transverse, ∂Uμ = 0) with the standard model fermions f , Lint = cf ΛdU−1 Ψ̄fγ ΨfUμ . (1) Here 1 < dU < 2 is the scaling dimension of the unparticle operator and Λ is a mass parameter related to the dynamics of the conformal sector. Unparticle propagator is determined by its scaling dimension, Π(q) = iAdU 2 sin(πdU) (