One of the uncertainties in interpretation of ultra-high energy cosmic ray ( UHECR ) data comes from the hadronic interaction models used for air shower Monte Carlo ( MC ) simulations .
The number of muons observed at the ground from UHECR-induced air showers is expected to depend upon the hadronic interaction model .
One may therefore test the hadronic interaction models by comparing the measured number of muons with the MC prediction .
In this paper , we present the results of studies of muon densities in UHE extensive air showers obtained by analyzing the signal of surface detector stations which should have high \it { muon purity } .
The muon purity of a station will depend on both the inclination 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 particles observed for signals with an expected muon purity of \sim 65 % at a lateral distance of 2000 m from the shower core is 1.72 \pm 0.10 { ( stat . ) } \pm 0.37 { ( syst . ) } times larger than the MC prediction value using the QGSJET I \hskip { -1.0 pt } I-03 model for proton-induced showers .
A similar effect is also seen in comparisons with other hadronic models such as QGSJET I \hskip { -1.0 pt } I-04 , which shows a 1.67 \pm 0.10 \pm 0.36 excess .
We also studied the dependence of these excesses on lateral distances and found a slower decrease of the lateral distribution of muons in the data as compared to the MC , causing larger discrepancy at larger lateral distances .