The upsilon mass resolution, as measured by the PHENIX Muon Arms is limited by 1) the multiple scattering and energy straggling in the absorber material in front of the tracking stations, 2) the multiple scattering within the tracking volumes, and 3) the resolution of the tracking chamber planes. This paper gives the quantitative limits of the mass resolution caused by these effects. It also gives the mass resolution comparison of tracking stations which are composed of either three or six fine resolution planes at each station, as well as the mass resolution if there are three fine resolution planes at the first and last stations and six fine resolution planes in the middle station.