Direct CP violation of $B \to l \nu$ in unparticle physics

We have investigated the effects of unparticles in decays $B \to l \nu$. It is found that the direct CP violation in the decays, which is zero in SM, can show up due to the CP conserving phase intrinsic in unparticle physics. For $l=\tau$, the direct CP asymmetry can reach 30% for the scalar unparticle contribution, and 100% for the longitudinal vector unparticle contribution under the constraints of ${\rm Br}(B\to\tau\nu)$ and $\nu e$ elastic scattering. If both unparticle-lepton coupling universality and unparticle-quark coupling universality are assumed the constraint from $Br(\pi\to \mu\nu)$ leads that the direct CP violation in $B\to l\nu$ can only reach at most 8% and 1% for scalar and vector unparticle contributions respectively if $d_{\cal U} < 2$. If the direct CP violation is observed in the future it would give strong evidence for the existence of unparticle stuff.