  Recent experimental data on several observables in semileptonic $B$-meson
decays are found to be in tension with the corresponding Standard Model
predictions. Most of these deviations are related to $b \to c$ and $b \to s$
flavour changing transitions. In this work, we estimate possible New Physics
effects in $b \to d \mu^+ \mu^-$ flavour changing neutral currents. We
parametrize NP contributions in a model-independent way and determine the
allowed ranges of corresponding Wilson coefficients from the data on the
exclusive $B^\pm \to \pi^\pm \mu^+ \mu^-$ decays measured recently by the LHCb
collaboration. Afterwards, we investigate the impact of these results on other
$b \to d$ processes such as the leptonic $B^0 \to \mu^+ \mu^-$ decays and $B^0
- \bar B^0$ mixing. As an example, we consider a simplified $Z^\prime$ model
that is found to be consistent with current $b \to d$ data in the certain
regions of the NP parameter space. In addition, we estimate the correlations
between the partial decay widths of $B \to \pi \mu^+ \mu^-$ and $B \to K \mu^+
\mu^-$ processes to be used for an independent determination of CKM matrix
elements as well as for a combined New Physics analysis of both $b \to d$ and
$b \to s$ transitions.
