NLO+NLL Collider Bounds, Dirac Fermion and Scalar Dark Matter in the B-L
  Model
  Baryon and lepton numbers being accidental global symmetries of the Standard
Model (SM), it is natural to promote them to local symmetries. However, to
preserve anomaly freedom, only combinations of B-L are viable. In this spirit,
we investigate possible dark matter realizations in the context of the
$U(1)_{B-L}$ model: (i) Dirac fermion with unbroken B-L; (ii) Dirac fermion
with broken B-L; (iii) scalar dark matter; (iv) two component dark matter. We
compute the relic abundance, direct and indirect detection observables and
confront them with recent results from Planck, LUX-2016, and Fermi-LAT and
prospects from XENON1T. In addition to the well known LEP bound
$M_{Z^{\prime}}/g_{BL} \gtrsim 7$ TeV, we include often ignored LHC bounds
using 13 TeV dilepton (dimuon+dielectron) data at next-to-leading order plus
next-to-leading logarithmic accuracy. We show that, for gauge couplings smaller
than $0.4$, the LHC gives rise to the strongest collider limit. In particular,
we find $M_{Z^{\prime}}/g_{BL} > 8.7$ TeV for $g_{BL}=0.3$. We conclude that
the NLO+NLL corrections improve the dilepton bounds on the $Z^{\prime}$ mass
and that both dark matter candidates are only viable in the $Z^{\prime}$
resonance region, with the parameter space for scalar dark matter being fully
probed by XENON1T. Lastly, we show that one can successfully have a minimal two
component dark matter model.
