  Recent analyses suggest that in TeV scales that will be made accessible at
the LHC copious amounts of color scalar parton bound states may be produced.
Would this be the case, the scalars would leave long enough to interact and
this could lead to new physics. These interaction could be direct, but also
take place with a mediation of the dense parton medium through which they
propagate. Since multiple processes would have to be included, the latter case
is too convoluted to be treated with perturbative methods applied to the
Standard Model. We explore a possibility of describing such interaction by a
nonlocal Lagrangian which is an infinite polynomial in the field variables,
momentum and mass. We treat all scalars as identical, use a O(N)-symmetric
Lagrangian, where N is the number of scalars and discuss the problem in 1/N
expansion. Nonrenormalizable by all traditional criteria, such model still
requires only a limited set of multiplicative renormalizations, provided that
the parameters in the Lagrangian are not treated as an infinite set of
independent coupling constants, but as finite expansion coefficients of the
Lagrangian in powers of field variables, mass and momenta. The necessary
constraints on the relative magnitudes of these coefficients can be determined
order by order in a double series in the single coupling constant and 1/N.
