Rare radiative charm decays in the standard model and beyond

Flavor changing neutral current (FCNC) decays involving charm quarks, i.e. $c\to u$ transitions, are rare in the standard model (SM) since they are loop suppressed. Furthermore, the GIM mechanism sets, e.g., CP asymmetries to approximate zero in the SM. On the other hand, branching ratios are controlled by non-perturbative contributions. Hence, rare charm decays can be used, first, as a probe of physics beyond the standard model (BSM) and, second, to probe models and frameworks which are employed to calculate non-perturbative SM contributions.

We give predictions for radiative decays of $D$ mesons into a vector meson in the SM, in leptoquark (LQ) and supersymmetric (SUSY) models in section 2. Section 3 is on baryonic ${\Lambda }_c\to p\gamma$ decays and their opportunities for future polarization measurements. A summary is given in section 4.

To include corrections to the perturbative Wilson coefficients we employ two frameworks: (1) a QCD based approach, worked out for $b$ physics in [6, 7], and (2) a hybrid model of the heavy quark effective theory and chiral perturbation theory using experimentally measured parameters [8, 9]. In the first approach, we compute the leading power corrections $\sim \frac{1}{m_D}$, shown in figure 1.

They involve the spectator quark and depend on ${\lambda }_D$, the first negative moment of the $D$ meson light-cone distribution amplitude. The parameter ${\lambda }_D\sim O\left(0.1\text{GeV}\right)$ can presently only be estimated.

The branching ratios of $D\to \rho \gamma$, as predicted in both SM approaches, are shown in figure 2.

The parameter ${\lambda }_D$ can be constrained by measuring the branching ratio of the charged decay $D^{+}\to {\rho }^{+}\gamma$. The branching ratio of the neutral decay $D^0\to {\rho }^0\gamma$ in approach (1) is subject to larger uncertainties due to the color suppressed combination of Wilson coefficients. In approach (2), the predictions cover predictions from other approaches [10, 11], see [2]. Compared to the measured $D^0\to {\rho }^0\gamma$ branching ratio (1), predictions in both approaches are too low. This may be addressed to unknown corrections. However, a (B)SM interpretation of data is feasible for CP asymmetries. For $D^0\to {\rho }^0\gamma$, the $|A_{CP}^{\text{SM}}|<2\times {10}^{-2}$ if the measured branching ratio is explained by the SM, see figure 2. Since the uncertainties of the present experimental data are controlled by statistics future experiments will test the SM.

The approaches (1) and (2) can be probed with WA induced radiative decays of neutral $D$ mesons. In table 1 predictions and data are given for the branching ratios of $D^0\to (\varphi ,{\overline{K^{\ast }}}^0)\gamma$ decays.

The data and the SM predictions are consistent. However, a slow convergence of the expansions in $\frac{1}{m_D}$, ${\alpha }_s$ is indicated.

As two BSM scenarios, we study scalar and vector LQ models, see [2], and SUSY models for which we use the mass insertion approximation [13]. In both models, the Wilson coefficients $C_{7,8}^{\left(\prime \right)}$ are loop induced, correlated and constrained by other observables [2, 5]. The induced branching ratios and CP asymmetries are given in table 2.

Generically, contributions from SUSY models can be larger than LQ model contributions since the SUSY Wilson coefficients are enhanced by the gluino mass. Specifically, LQs can induce $A_{CP}^{\text{LQ}}\lesssim O\left(10\%\right)$, whereas SUSY induced observables can be close to the experimental data (1).

In SUSY models, $A^{\gamma }$ can be different from the SM prediction, including a sign flip, pointing out an opportunity for future polarization measurements with baryons.

Motivated by the first measurement of a rare radiative charm decay, we have presented a work of $D\to V\gamma$ and ${\Lambda }_c\to p\gamma$ [2]. For $D\to V\gamma$, we have given improved SM predictions including power corrections and updating a hybrid model. Predictions for branching ratios are uncertain, whereas CP asymmetries are approximate SM null tests. Branching ratios, however, test non-perturbative QCD approaches, once further rare and weak annihilation induced radiative decays of $D$ mesons are measured. On the other hand, measurements of CP asymmetries will constrain or reveal BSM physics, e.g. LQ and SUSY models. For ${\Lambda }_c\to p\gamma$, we have explored opportunities with an additional angular observable for future colliders, e.g. an FCC-ee.

I thank the organisers for the wonderful conference. I am grateful to Gudrun Hiller for a very enjoyable collaboration and Ivan Nisandzic for reading the manuscript. This project is in part supported by the DFG Research Unit FOR 1873 “Quark Flavour Physics and Effective Field Theories”.