  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.
