  We study the infrared (IR) structure of $SU(N) \times U(1)$ (QCD $\times$
QED) gauge theory with $n_f$ quarks and $n_l$ leptons within the framework of
perturbation theory. In particular, we unravel the IR structure of the form
factors and inclusive real emission cross sections that contribute to inclusive
production of color neutral states, such as a pair of leptons or single W/Z in
Drell-Yan processes and a Higgs boson in bottom quark annihilation, in Large
Hadron Collider (LHC) in the threshold limit. Explicit computation of the
relevant form factors to third order and the use of Sudakov's $K+G$ equation in
$SU(N)\times U(1)$ gauge theory demonstrate the universality of the cusp
anomalous dimensions ($A_I , I = q, b$). The abelianization rules that relate
$A_I$ of $SU(N)$ with those from $U(1)$ and $SU(N)\times U(1)$ can be used to
predict the soft distribution that results from the soft gluon emission
subprocesses in the threshold limit. Using the latter and the third order form
factors, we can obtain the collinear anomalous dimensions ($B_I$ ) and the
renormalisation constant $Z_b$ to third order in perturbation theory. The form
factors, the process independent soft distribution functions can be used to
predict fixed and resummed inclusive cross sections to third order in couplings
and in leading logarithmic approximation respectively.
