  According to general understanding, the proton as one of the main ingredients
of the nucleus is composed of one down and two up quarks bound together by
gluons, described by Quantum Chromodynamics (QCD). In this view, heavy quarks
do not contribute to the primary wave function of the proton. Heavy quarks
arise in the proton perturbatively by gluon splitting and the probability
gradually increases as $Q^2$ increases (extrinsic heavy quarks). In addition,
the existence of non-perturbative intrinsic charm quarks in the proton has also
been predicted by QCD. In this picture, the heavy quarks also exist in the
proton's wave function. In fact, the wave function has a five-quark structure $
\vert u u d c \bar{c}\rangle $ in addition to the three-quark bound state $
\vert u u d\rangle $. So far, many studies have been done to confirm or reject
this additional component. One of the recent studies has been done by the NNPDF
collaboration. They established the existence of an intrinsic charm component
at the 3-standard-deviation level in the proton from the structure function
measurements. Most of the studies performed to calculate the contribution of
the intrinsic charm so far have been based on the global analyses of the
experimental data. In this article, for the first time we directly calculate
this contribution by an analytic method. We estimate a $x^{c\bar{c}} = (1.36
\pm 0.67)\% $ contribution for the $ \vert u u d c \bar{c}\rangle $ component
of the proton.
