OnD→Xul+l−within the Standard Model and frameworks like the littlest Higgs model withTParity

Abstract

The $D\ensuremath{\rightarrow}{X}_{u}{l}^{+}{l}^{\ensuremath{-}}$ transitions---branching ratios, forward-backward (FB) asymmetry ${A}_{\mathrm{FB}}^{c}$, the $CP$ asymmetry ${A}_{CP}^{c}$, and the $CP$ asymmetry in the forward-backward asymmetry ${A}_{\mathrm{FB}}^{CP}$---have two sources: for ${D}^{\ifmmode\pm\else\textpm\fi{}}$ they represent a pure $\ensuremath{\Delta}C=1$ $\ensuremath{\Delta}Q=0$ current interaction whereas neutral $D$ mesons can also communicate via their antihadron. Standard model (SM) contributions to $\mathrm{BR}(D\ensuremath{\rightarrow}{X}_{u}{l}^{+}{l}^{\ensuremath{-}})$ come primarily from long distance dynamics, which overshadow short distance contributions by several orders of magnitude; still they fall much below the present upper experimental bounds. Even the SM contributions to ${A}_{\mathrm{FB}}^{c}$, ${A}_{CP}^{c}$, and ${A}_{\mathrm{FB}}^{CP}$ are tiny, quite unlike in beauty hadrons. The branching ratios are hardly dented by contributions from the littlest Higgs models with $T$ parity (LHT) even in the short distance regime, let alone in the SM long distances dynamics. Yet the asymmetries ${A}_{\mathrm{FB}}^{c}$, ${A}_{CP}^{c}$, and ${A}_{\mathrm{FB}}^{CP}$ in these new physics models can be enhanced over SM predictions, as they arise purely from short distance dynamics; this can occur, in particular, for ${A}_{\mathrm{FB}}^{c}$ and ${A}_{\mathrm{FB}}^{CP}$, which get enhanced by orders of magnitudes. Even such enhancements hardly reach absolute sizes for observable experimental effects for ${A}_{\mathrm{FB}}^{c}$ and ${A}_{CP}^{c}$. However, LHT contributions to ${A}_{\mathrm{FB}}^{CP}$ could be measured in experiments like the LHCb and the SuperB Collaboration. These results lead us to draw further conclusions on flavor-changing neutral-current interactions within LHT-like models through some simple scaling arguments that encapsulate the essence of flavor dynamics in and beyond the standard model.