CP-Conserving Unparticle Phase Effects on the Unpolarized and Polarized Direct CP Asymmetry in $b \to d \ell^+\ell^-$ Transition

Abstract

We examine the unparticle CP-conserving phase effects on the direct CP asymmetry for both polarized and unpolarized lepton in the inclusive $b\to d \ell^+ \ell^-$ transition, where the flavor changing neutral currents are forbidden at tree level but are induced by one-loop penguin diagrams. The averaged polarized and unpolarized CP asymmetries depict strong dependency on the unparticle parameters. In particular, a sizable discrepancy corresponding to the standard model is achieved when the scale dimension value is $1<d_{\UP}< 2$. We see that the unparticle stuff significantly enhances, suppresses or changes the sign of the CP asymmetry depending on the definite value of the scaling dimension $d_{\UP}$. Especially, when $d_{\UP}\sim 1.1$ the CP asymmetries vanish.