Discerning new physics in charm meson leptonic and semileptonic decays

Current experimental information on the charm-meson decay observables in which the $c\to s\ell {\nu }_{\ell }$ transitions occur is well compatible with the Standard Model predictions. Recent precise lattice calculations of the $D_s$-meson decay constant and form factors in $D\to K\ell \nu$ decays offer a possibility to search for small deviations from the Standard Model predictions in the next generation of high-intensity flavor experiments. We revisit constraints from these processes on the new physics contributions in the effective theory approach. We investigate new physics effects which might appear in the differential distributions for the longitudinally and transversely polarized $K^{*}$ in $D\to K^{*}\ell {\nu }_{\ell }$ decays. Present constraints from these observables are rather weak, but could be used to constrain new physics effects in the future. In the case of $D\to K\ell \nu$ we identify observables sensitive to the new physics contribution coming from the scalar Wilson coefficient, namely the forward-backward asymmetry and the transversal muon polarizations. By assuming that new physics only modifies the second lepton generation, we identify the allowed region for the differential decay rate for the process $D\to K\mu {\nu }_{\mu }$ and find that it is allowed to deviate from the Standard Model prediction by only a few percent. The lepton flavor universality violation can be tested in the ratio $R_{\mu /e}(q^2)\equiv \frac{d{\mathrm{\Gamma }}^{(\mu )}}{d{q}^2}/\frac{d{\mathrm{\Gamma }}^{(e)}}{d{q}^2}$. If the first lepton generation behaves as in the Standard Model, we find (using the current constraint on the scalar Wilson coefficient) that the ratio $R_{\mu /e}(q^2)$ is currently allowed to be within the range (0.9,1.2), depending on the value of $q^2$.

Figure 1

Allowed regions of the effective couplings $c_P^{(\tau )}$ (upper panel) and $c_P^{(\mu )}$ (lower panel), extracted from the branching fraction of the decay mode $D_s\to \tau (\mu )\nu$, respectively. The 68% (95%) C.L. regions of the parameters are shown in darker (lighter) shades.

Figure 2

Allowed regions of the effective coupling $c_P^{(\mu )}$, extracted from the ratio $R_{L/T}$. The color coding is the same as in Fig. 1.

Figure 3

Allowed regions of the effective coupling $c_S^{(\mu )}=c_R^{(\mu )}+c_L^{(\mu )}$ extracted from the branching fraction of the decay mode $D\to K{\mu }^{+}\nu$. The color coding is the same as in Fig. 1.

Figure 4

Upper panel: The differential decay rate for the process $D\to K\mu {\nu }_{\mu }$. The thin red band shows the SM prediction, while its width represents the uncertainty. The (wider) grey band corresponds to the deviations that result from the presently allowed scalar Wilson coefficient from Fig. 3. Lower panel: The SM prediction and allowed deviations in the ratio $R_{\mu /e}(q^2)\equiv \frac{d{\mathrm{\Gamma }}^{(\mu )}}{d{q}^2}/\frac{d{\mathrm{\Gamma }}^{(e)}}{d{q}^2}$ assuming $c_S^{(e)}=0$.

Figure 5

Comparison of the shape of the forward-backward asymmetry $A_{FB}^{(\mu )}(q^2)$ in the SM (red) with the deviations (grey) induced by currently allowed values of the $c_S^{(\mu )}$ couplings. Colored bands represent the form-factor uncertainties.