On $D\to X_u{l}^{+}{l}^{-}$ within the Standard Model and Frameworks like the Littlest Higgs Model with T Parity

Abstract

The $D\to X_u{l}^{+}{l}^{-}$ transitions -- branching ratios, forward-backward asymmetry $A_{FB}^c$, the CP asymmetry $A_{CP}^c$ and the CP asymmetry in the forward-backward asymmetry $A_{FB}^{CP}$ -- have two sources: for $D^{\pm }$ they represent a pure $\Delta C=1$ & $\Delta Q=0$ current interaction whereas neutral $D$ mesons can also communicate via their anti-hadron. Standard Model (SM) contributions to BR$(D\to X_u{l}^{+}{l}^{-})$ 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 $A_{FB}^c$, $A_{CP}^c$ and $A_{FB}^{CP}$ 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 $A_{FB}^c$, $A_{CP}^c$ and $A_{FB}^{CP}$ 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 $A_{FB}^c$ and $A_{FB}^{CP}$ which get enhanced by orders of magnitudes. Even such enhancements hardly reach absolute sizes for observable experimental effects for $A_{FB}^c$ and $A_{CP}^c$. However LHT contributions to $A_{FB}^{CP}$ could be measured in experiments like the LHCb and the SuperB Collaboration. These results lead us to draw further conclusions on FCNCs within LHT-like models through some simple scaling arguments that encapsulate the essence of flavour dynamics in and beyond the Standard Model.

24 Pages, 12 figures. V2 contains corrections to the Appendix A. V3 fixes an error in eq. 10

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