We search for evidence of physics beyond the Standard Model in the production of final states with multiple high transverse momentum jets, using 20.3 fb$^{-1}$ of proton-proton collision data recorded by the ATLAS detector at $\sqrt{s} = 8$ TeV. No excess of events beyond Standard Model expectations is observed, and upper limits on the visible cross-section for non-Standard Model production of multi-jet final states are set. Using a wide variety of models for black hole and string ball production and decay, the limit on the cross-section times acceptance is as low as 0.16 fb at the 95% CL for a minimum scalar sum of jet transverse momentum in the event of about 4.3 TeV. Using models for black hole and string ball production and decay, exclusion contours are determined as a function of the production mass threshold and the gravity scale. These limits can be interpreted in terms of lower-mass limits on black hole and string ball production that range from 4.6 to 6.2
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