Sensitivity of EAS measurements to the energy spectrum of muons

We have studied how the energy spectrum of muons at production affects some of the most common measurements related to muons in extensive air shower studies, namely, the number of muons at the ground, the slope of the lateral distribution of muons, the apparent muon production depth, and the arrival time delay of muons at ground. We found that by changing the energy spectrum by an amount consistent with the difference between current models (namely EPOS-LHC and QGSjet-II.04), the muon surface density at ground increases $5\%$ at $20^\circ$ zenith angle and $17\%$ at $60^\circ$ zenith angle. This effect introduces a zenith angle dependence on the reconstructed number of muons which might be experimentally observed. The maximum of the muon production depth distribution at $40^\circ$ increases $\sim10\text{ g/cm}^2$ and $\sim0\text{ g/cm}^2$ at $60^\circ$, which, from pure geometrical considerations, increases the arrival time delay of muons. There is an extra contribution to the delay due to the subluminal velocities of muons of the order of $\sim3$ ns at all zenith angles. Finally, changes introduced in the logarithmic slope of the lateral density function are less than 2%.