ResBos2 and the CDF W Mass Measurement

The recent CDF $W$ mass measurement of 80,433 $\pm$ 9 MeV is the most precise direct measurement. However, this result deviates from the Standard Model predicted mass of 80,359.1 $\pm$ 5.2 MeV by $7\sigma$. The CDF experiment used an older version of the ResBos code that was only accurate at NNLL+NLO, while the ResBos2 code is able to make predictions at N${}^3$LL+NNLO accuracy. We determine that the data-driven techniques used by CDF capture most of the higher order corrections, and using higher order corrections would result in a decrease in the value reported by CDF by at most 10 MeV.