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 CERNs 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.
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