We investigate the loss of low-mass stars in two of the faintest globular clusters known, AM 4 and Palomar 13 (Pal 13), using HST/WFC3 F606W and F814W photometry. To determine the physical properties of each cluster --- age, mass, metallicity, extinction, present day mass function (MF) --- we use the maximum likelihood color-magnitude diagram (CMD) fitting program MATCH and the Dartmouth, Padova and BaSTI stellar evolution models. For AM 4, the Dartmouth models provide the best match to the CMD and yield an age of >13 Gyr, metallicity log Z/Z_solar = -1.68 +/- 0.08, a distance modulus (m-M)_V = 17.47 +/- 0.03 and reddening A_V = 0.19 +/- 0.02. For Pal 13 the Dartmouth models give an age of 13.4 +/- 0.5 Gyr, log Z/Z_solar = -1.55 +/- 0.06, (m-M)_V = 17.17 +/- 0.02 and A_V = 0.43 +/- 0.01. We find that the systematic uncertainties due to choice in assumed stellar model greatly exceed the random uncertainties, highlighting the importance of using multiple stellar models when analyzing stellar populations. Assuming a single-sloped power law MF, we find that AM 4 and Pal 13 have spectral indices alpha = +0.68 +/- 0.34 and alpha = -1.67 +/- 0.25 (where a Salpeter MF has alpha = +1.35), respectively. Comparing our derived slopes with literature measurements of cluster integrated magnitude (M_V) and MF slope indicates that AM 4 is an outlier. Its MF slope is substantially steeper than clusters of comparable luminosity, while Pal 13 has a MF in line with the general trend. We discuss both primordial and dynamical origins for the unusual MF slope of AM 4 and tentatively favor the dynamical scenario. However, MF slopes of more low luminosity clusters are needed to verify this hypothesis.
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