By Edward L. Bernays
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Extra resources for [Article] Manipulating Public Opinion: The Why and The How
65). Above we have factorized the hard part from the remaining functions, which are still linked via soft momenta. Fully Factorized Form Here we will use the soft approximation to factorize the jets Jp from the soft function, which, by power counting, are connected only through soft gluons. We could factorize the eikonal jet Jβ from S in an analogous way, but we choose not to do so here because eventually we will combine all soft and eikonal functions to form an eikonal cross section. From the arguments given in Sec.
The above considerations are most relevant when Q becomes very large, Q → ∞. In this limit, due to Eq. 1), we can neglect masses since they become vanishingly small. Up and down quarks have masses of a few MeV at scales of the order of ΛQCD , where we do not expect perturbation theory to be reliable anyway. Thus, studying the theory with all masses at their physical values is equivalent to studying the corresponding massless theory with external particles on shell. Corrections to the so identified leading behavior for infrared safe quantities, Eq.
Ti denote numerator suppression factors which are summarized below. • Soft three-point vertices suppress the scaling by λ. 22) (3) where vS is the number of soft three-point vertices. • On the other hand, jet three-point vertices give a suppression of λ1/2 , unless the gluons involved are scalar polarized in covariant gauges. 23) (3) where vJ is the number of jet 3-point vertices, and sJ denotes the number of soft lines attached to the jet. 24) 2 J due to scalar polarized gluons lJ , linking jet lines and the hard scattering.