  The blazar 3C 279 exhibited twin $\gamma$-ray flares of similar intensity in
2013 December and 2014 April. In this work, we present a detailed
multi-wavelength analysis of the 2013 December flaring event. Multi-frequency
observations reveal the uncorrelated variability patterns with X-ray and
optical-UV fluxes peaking after the $\gamma$-ray maximum. The broadband
spectral energy distribution (SED) at the peak of the $\gamma$-ray activity
shows a rising $\gamma$-ray spectrum but a declining optical-UV flux. This
observation along with the detection of uncorrelated variability behavior rules
out the one-zone leptonic emission scenario. We, therefore, adopt two
independent methodologies to explain the SED: a time dependent lepto-hadronic
modeling and a two-zone leptonic radiative modeling approach. In the
lepto-hadronic modeling, a distribution of electrons and protons subjected to a
randomly orientated magnetic field produces synchrotron radiation. Electron
synchrotron is used to explain the IR to UV emission while proton synchrotron
emission is used to explain the high energy $\gamma$-ray emission. A
combination of both electron synchrotron self Compton emission and proton
synchrotron emission is used to explain the X-ray spectral break seen during
the later stage of the flare. In the two-zone modeling, we assume a large
emission region emitting primarily in IR to X-rays and $\gamma$-rays to come
primarily from a fast moving compact emission region. We conclude by noting
that within a span of 4 months, 3C 279 has shown the dominance of a variety of
radiative processes over each other and this reflects the complexity involved
in understanding the physical properties of blazar jets in general.
