The measurement of sparticle masses in the Minimal Supersymmetric Standard Model at the LHC is analysed, in the scenario where the lightest neutralino decays into three quarks. Such decays, occurring through the baryon-number violating coupling lambda_ijk, pose a severe challenge to the capability of the LHC detectors since the final state has no missing energy signature and a high jet multiplicity. We focus on the case of non-zero lambda_212 which is the most difficult experimentally. The proposed method is valid over a wide range of SUGRA parameter space with lambda_212 between 10^{-5}-0.1. Simulations are performed of the ATLAS detector at the Large Hadron Collider. Using the lightest neutralino from the decay chain left-squark to quark + next-to-lightest neutralino to right-slepton + lepton + quark and finally to lightest neutralino + lepton pair + quark, we show that the lightest and next-to-lightest neutralino masses can be measured by 3-jet and 3-jet + lepton pair invariant mass combinations. At the SUGRA point M_0=100 GeV, M_{1/2}=300 GeV, A_0=300 GeV, tan beta=10, sign of mu positive and with lambda_212=0.005, we achieve statistical (systematic) errors of 3 (3), 3 (3), 0.3 (4) and 5 (12) GeV respectively for the masses of the lightest neutralino, next-to-lightest neutralino, right-slepton and left-squark, with an integrated luminosity of 30 fb^{-1}.
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