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One of the uncertainties in interpretation of ultra-high energy cosmic ray(UHECR) data comes from the hadronic interaction models used for air showerMonte Carlo (MC) simulations. The number of muons observed at the ground fromUHECR-induced air showers is expected to depend upon the hadronic interactionmodel. One may therefore test the hadronic interaction models by comparing themeasured number of muons with the MC prediction. In this paper, we present theresults of studies of muon densities in UHE extensive air showers obtained byanalyzing the signal of surface detector stations which should have high$\it{muon \, purity}$. The muon purity of a station will depend on both theinclination of the shower and the relative position of the station. In 7 years'data from the Telescope Array experiment, we find that the number of particlesobserved for signals with an expected muon purity of $\sim$65% at a lateraldistance of 2000 m from the shower core is $1.72 \pm 0.10{\rm (stat.)} \pm 0.37{\rm (syst.)}$ times larger than the MC prediction value using the QGSJET II-03model for proton-induced showers. A similar effect is also seen in comparisonswith other hadronic models such as QGSJET II-04, which shows a $1.67 \pm 0.10\pm 0.36$ excess. We also studied the dependence of these excesses on lateraldistances and found a slower decrease of the lateral distribution of muons inthe data as compared to the MC, causing larger discrepancy at larger lateraldistances.

Study of muons from ultra-high energy cosmic ray air showers measured with the Telescope Array experiment