  The $HZ\gamma $ coupling, which is highly sensitive to the new physics beyond
the standard model, is studied through the process $pp\rightarrow p\gamma
p\rightarrow pHX$ at the LHC. To this purpose, an effective Lagrangian, in a
model independent approach, with dimension six operators is considered in this
paper. New interaction terms regarding beyond the standard model physics
include the Higgs boson anomalous vertices in both CP-even and CP-odd
structures. A detailed numerical analysis is performed to scrutinize the
accurate constraints on the effective $HZ\gamma $ couplings and to discuss how
far the corresponding bounds can be improved. This is achieved by testing all
the efficient Higgs decay channels and increasing the integrated luminosity at
three different forward detector acceptance regions. The numerical results
propose that the Higgs photoproduction at the LHC, as a complementary channel,
has a great potential of exploring the $HZ\gamma $ couplings.
