  Recently, deviations in flavor observables of B -> D(*) tau nu have been
shown between the predictions in the Standard Model and the experimental
results reported by BaBar, Belle, and LHCb collaborations. One of the solutions
to this anomaly is obtained in a class of leptoquark model with a scalar
leptoquark boson S_1, which is a SU(3)_c triplet and SU(2)_L singlet particle
with -1/3 hypercharge interacting with a quark-lepton pair. With well-adjusted
couplings, this model can explain the anomaly and be compatible with all flavor
constraints. In such a case, the S_1 boson can be pair-produced at CERN's Large
Hadron Collider (LHC) and subsequently decay as S_1 -> t tau, b nu, c tau. This
paper explores the current 8 and 13 TeV constraints, as well as the detailed
prospects at 14 TeV, of this flavor-motivated S_1 model. From the current
available 8 and 13 TeV LHC searches, we obtain constraints on the S_1 boson
mass for M_{S_1} < 400 GeV - 640 GeV depending on values of the leptoquark
couplings to fermions. Then we study future prospects for this scenario at the
14 TeV LHC using detailed cut analyses and evaluate exclusion/discovery
potentials for the flavor-motivated S_1 leptoquark model from searches for the
(b nu) (b nu) and (c tau) (c tau) final states. In the latter case, we consider
several scenarios for the identification of charm jets. As a result, we find
that the S_1 leptoquark origin of the B -> D(*) tau nu anomaly can be probed
with mass less than around 600/800 GeV at the 14 TeV LHC with 300/3000 fb^-1 of
accumulated data.
