  In this paper we propose the study of the $W^+W^-$ and $\mu^+\mu^-$
production by two-photon interactions in $pp$ collisions at LHC energies to
constrain the photon flux associated to an ultrarelativistic proton. We
consider the current parametrizations for the photon distribution of the proton
and estimate the effective photon - photon luminosities for elastic,
semielastic and inelastic processes. Moreover, we present predictions for the
rapidity and invariant mass distributions for the two-photon production of
$W^+W^-$ and $\mu^+\mu^-$ in $\gamma \gamma$ interactions at LHC energies. We
demonstrate that the semielastic and inelastic predictions are strongly
dependent on the description of the inelastic photon flux, and that the
relative contribution of the different processes depends on the invariant mass
of the final state. Our results implies that a dedicated experimental analysis
of the two-photon production of $W^+W^-$ and $\mu^+\mu^-$ with the tagging of
one of the protons in the final state can be useful to constrain the magnitude
of the inelastic component of the photon distribution.
