The ionizing photon production efficiency, $xi_{ion}$, is a critical parameter that provides a number of physical constraints to the nature of the early Universe, including the contribution of galaxies to the timely completion of the reionization of the Universe. Here we use KECK/MOSFIRE and ZFOURGE multi-band photometric data to explore the $xi_{ion}$ of a population of galaxies at $zsim2$ with $log_{10}(M_*/M_odot)sim9.0-11.5$. Our 130 Halpha detections show a median $log_{10}(xi_{ion}[Hz/erg])$ of $24.8pm0.5$ when dust corrected using a Calzetti et al. (2000) dust prescription. Our values are typical of mass/magnitude selected $xi_{ion}$ values observed in the $zsim2$ Universe. Using BPASSv2.2.1 and Starburst99 stellar population models with simple parametric star-formation-histories (SFH), we find that even with models that account for effects of stellar evolution with binaries/stellar rotation, model galaxies at $log_{10}(xi_{ion}[Hz/erg])lesssim25.0$ have low H$alpha$ equivalent widths (EW) and redder colors compared to our $zsim2$ observed sample. We find that introducing star-bursts to the SFHs resolve the tension with the models, however, due to the rapid time evolution of $xi_{ion}$, H$alpha$ EWs, and rest-frame optical colors, our Monte Carlo simulations of star-bursts show that random distribution of star-bursts in evolutionary time of galaxies are unlikely to explain the observed distribution. Thus, either our observed sample is specially selected based on their past SFH or stellar models require additional mechanisms to reproduce the observed high UV luminosity of galaxies for a given production rate of hydrogen ionizing photons.
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