  Charge-dependent two- and three-particle correlations measured in Xe-Xe
collisions at $\sqrt{s_{\mathrm{NN}}} = 5.44$ TeV are presented. Results are
obtained for charged particles in the pseudorapidity range $|\eta|<0.8$ and
transverse momentum interval $0.2 \le p_{\rm T}<5.0$ GeV/$c$ for different
collision centralities. The three-particle correlator ${\gamma_{\alpha\beta}}
\equiv {\langle \cos(\varphi_\alpha + \varphi_\beta - 2{\Psi_{\rm 2}})
\rangle}$, calculated for different combinations of charge sign $\alpha$ and
$\beta$, is expected to be sensitive to the presence of the Chiral Magnetic
Effect (CME). Its magnitude is similar to the one observed in Pb-Pb collisions
in contrast to a smaller CME signal in Xe-Xe collisions than in Pb-Pb
collisions predicted by Monte Carlo (MC) calculations including a magnetic
field induced by the spectator protons. These observations point to a large
non-CME contribution to the correlator. Furthermore, the charge dependence of
${\gamma_{\alpha\beta}}$ can be described by a blast wave model calculation
that incorporates background effects and by the Anomalous Viscous Fluid
Dynamics model with values of the CME signal consistent with zero. The Xe-Xe
and Pb-Pb results are combined with the expected CME signal dependence on the
system size from the MC calculations including a magnetic field to obtain the
fraction of CME contribution in ${\gamma_{\alpha\beta}}$, $f_{\rm CME}$. The
CME fraction is compatible with zero for the 30% most central events in both
systems and then becomes positive; averaging over the 0-70% centrality interval
yields an upper limit of 2% (3%) and 25% (32%) at 95% (99.7%) confidence level
for the CME signal contribution to ${\gamma_{\alpha\beta}}$ in Xe-Xe and Pb-Pb
collisions, respectively.
