A new pixel detector for the CMS experiment was built in order to cope with the instantaneous luminosities anticipated for the Phase~I Upgrade of the LHC. The new CMS pixel detector provides four-hit tracking with a reduced material budget as well as new cooling and powering schemes. A new front-end readout chip mitigates buffering and bandwidth limitations, and allows operation at low comparator thresholds. In this paper, comprehensive test beam studies are presented, which have been conducted to verify the design and to quantify the performance of the new detector assemblies in terms of tracking efficiency and spatial resolution. Under optimal conditions, the tracking efficiency is $99.95pm0.05,%$, while the intrinsic spatial resolutions are $4.80pm0.25,mu mathrm{m}$ and $7.99pm0.21,mu mathrm{m}$ along the $100,mu mathrm{m}$ and $150,mu mathrm{m}$ pixel pitch, respectively. The findings are compared to a detailed Monte Carlo simulation of the pixel detector and good agreement is found.
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