  Coupling the scale invariant unparticle sector to flavour physics and
assuming that it remains scale invariant we investigate its consequences in
heavy flavour physics. A drastic feature of unparticle physics is an unusual
phase leading to novel CP violating phenomena. We consider the CP asymmetry in
the leptonic decay B^+ -> tau^+ nu and the hadronic decay B_d -> D^+D^-, taking
into account constraints of branching ratios and time dependent CP asymmetries.
Generic plots are shown and it turns out that there exist parameters for which
the CP violation is maximal. A prediction of a large CP asymmetry in B_d ->
D^+D^- is difficult to achieve in other models without contradicting the
current data in other channels. The prediction of a CP asymmetry in leptonic
decays, such as B^+ -> tau^+ nu, is novel. We identify the CP compensating mode
due to the unparticles and show explicitly that it exactly cancels the CP
asymmetry of B^+ -> tau^+ nu as demanded by CPT invariance. Building up on
earlier works we investigate the breaking of scale invaricance, due to the
coupling to the Higgs and the size of the effects in the weak sector resorting
to a dimensional analysis. An enhancement is observed on the grounds of the
relevance of the unparticle interaction operator as compared to the weak
four-Fermi term.
