Abstract
We explore the constraints imposed by the cancellation of triangle anomalies
on models in which the flavour anomalies reported by LHCb and other experiments
are due to an extra U(1)' gauge boson Z'. We assume universal and rational
U(1)' charges for the first two generations of left-handed quarks and of
right-handed up-type quarks but allow different charges for their
third-generation counterparts. If the right-handed charges vanish, cancellation
of all the triangle anomalies requires all the quark U(1)' charges to vanish,
if there are no fermions beyond those in the Standard Model (SM), or if there
is only one SM-singlet dark matter (DM) fermion. There are non-trivial
anomaly-free models with more than one such `dark' fermion, or with a single DM
fermion if right-handed up-type quarks have non-zero U(1)' charges. In some of
the latter models the U(1)' couplings of the first- and second-generation
quarks all vanish, weakening the LHC Z' constraint, and in some other models
the DM particle has purely axial couplings, weakening the direct DM scattering
constraint. We also consider models in which anomalies are cancelled via extra
vector-like leptons, showing how the prospective LHC Z' constraint may be
weakened because the \$Z' \mu^+ \mu^-\$ branching ratio is suppressed
relative to other decay modes, facilitating an explanation of the anomaly in
the anomalous magnetic moment of the muon. The various possibilities are
illustrated by benchmark models.
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