CP Violation in Charmed Meson Decays into Final States with $η'$

TL;DR

This work provides Standard Model predictions for direct CP asymmetries in singly Cabibbo-suppressed charm decays to η′ final states, using approximate SU(3)F symmetry with linear breaking. The authors develop a topological decomposition of CKM-subleading amplitudes, including penguin and hairpin contributions, and impose redefinitions to manage linear dependencies, enabling robust CP-violation sum rules. They derive SU(3)F-limit relations between CP asymmetries and give improved variants that account for phase-space and branching-ratio effects. A global frequentist fit to branching ratios and limited CP-asymmetry data yields sub-percent predictions for the CP asymmetries, showing correlations between charged and neutral modes and highlighting the key parameter |C̄18/ T̂18| that governs penguin-to-tree effects. The results offer a framework for interpreting future measurements from LHCb, Belle II, and BESIII to test the SM and potentially reveal new physics through deviations from the predicted correlations or through an extracted penguin-to-tree ratio.

Abstract

We derive Standard Model predictions for the CP asymmetries of singly-Cabibbo suppressed $D\rightarrow Pη'$ decays, where $P=K,π,η$. Our predictions are based on the approximate SU(3)$_F$ symmetry of QCD and include first-order symmetry-breaking effects in a systematic way. The underlying symmetry leads to correlations between different decay modes. To this end we predict the correlations between $ a_{\rm CP}^{\rm dir}(D^+\to π^+ η')$ and $a_{\rm CP}^{\rm dir}(D_s^+ \to K^+ η')$ as well as $a_{\rm CP}^{\rm dir}(D^0\to π^0 η')$ and $ a_{\rm CP}^{\rm dir}(D^0\to ηη')$. Our results can be used to probe the Standard Model with future measurements by LHCb, Belle II and BESIII. At the same time, such future measurements permit the extraction of the key theory parameter related to the ratio of color-suppressed to color-favoured contributions to the decay amplitudes. Future data on both branching ratios and CP asymmetries will automatically improve our predictions and thereby also their sensitivity to physics beyond the Standard Model.

Figures (4)

• Figure 1: $\Delta \chi^2$ profile of $|\overline{C}_{18}/\hat{T}_{18}|$.
• Figure 2: Correlations between predicted CP asymmetries for the charged (left) and neutral (right) modes. The red line represents the $SU(3)_F$ limit sum rules Eqs. (\ref{['eq:su3limSR-1']}, \ref{['eq:su3limSR-2']}). The blue line indicates the modified sum rules Eqs. (\ref{['eq:improvedSR1']}, \ref{['eq:improvedSR2']}) which partially account for SU(3)$_F$-breaking effects. The contour lines represent the $68.30\%$ and $95.45\%$ confidence levels.
• Figure 3: Predictions for CP asymmetries as a function of the SU(3)$_F$ limit parameter ratio $\left| \overline{C}_{18} / \hat{T}_{18} \right|$. The filled green areas represent the $1\sigma$ and $2\sigma$ confidence levels. The gray band in $a_{CP}^{\textrm{dir}}(D^+\to\pi^+\eta')$ corresponds to the $1\sigma$ experimental input. The plots can be used as a tool in order to interpret future determinations of CP asymmetries in terms of allowed intervals for $\left| \overline{C}_{18} / \hat{T}_{18} \right|$ and check their consistency.
• Figure 4: $SU(3)_F$-breaking topologies contributing to $\mathcal{A}_{b}$. The subscripts $ij$ indicate the mixed singlet-octet contributions, i.e., $18$ or $81$. The Feynman diagrams are created with JaxoDraw Binosi:2003yfBinosi:2008ig.