Model-independent analysis of $b\to d$ processes

We perform a model-independent analysis of $|\Delta b|=|\Delta d|=1$ processes to test the standard model and probe flavor patterns of new physics. Constraints on Wilson coefficients are obtained from global fits to $B^+ \to \pi^+ \,\mu^+\mu^-$, $B^0_s\to \bar{K}^{*0}\, \mu^+\mu^-$, $B^0\to\mu^+\mu^-$, and radiative $B \to X_d \,\gamma$ decays data. The fits are consistent with the standard model but leave sizable room for new physics. Besides higher-statistics measurements and more data in theory-friendly bins of the dilepton mass, further complementary observables such as angular distributions of $B_s^0 \to \bar{K}^{*0}\,\ell^+ \ell^-$, $B \to \rho\,\ell^+ \ell^-$ or the baryonic modes $\Xi_b \to \Sigma\,\ell^+ \ell^-$, $\Omega_b^- \to \Xi^- \, \ell^+ \ell^-$ are necessary to resolve the significant degeneracy in the fit for the semileptonic four-fermion operators. Assuming minimal quark flavor violation, the $b \to s$ global fit implies tight constraints on the $b \to d$ couplings, and hence allows to test this paradigm with improved data. Another benefit from $|\Delta b|=|\Delta d|=1$ processes is to shed light on the $B$-anomalies in $|\Delta b|=|\Delta s|=1$ modes from a new angle. Specifically, studies of lepton flavor-specific and dineutrino modes are informative on the lepton flavor structure. Rare $b \to d \, \ell \ell, \nu \bar \nu$ decays can be studied at high luminosity flavor facilities LHCb, Belle II, and a future $Z$-factory.