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Ok, I actually found the answer. As the question was up-voted, I'm going to write it down. I would argue as follows. Let's say that we want to define the cross section at an arbitrary renormalization scale. Then we put $$ \sigma=\sigma(s,M,a_{s}(M)) $$ as these are the only variables on which the cross section can explicitly depend (of course we are ...


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this paper might help.$^1$ It's written pedagogically and hence is easier to read. It goes on to discuss a lot more than just color decomposition too. $^1$ Scattering Amplitudes, Henriette Elvang, Yu-tin Huang.


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Working in dimensional regularization, in the MS bar scheme consider the renormalization group equation for the strong coupling $$\mu\frac{d\alpha}{d\mu}=-\beta_0\alpha(\mu)^2-\beta_1\alpha(\mu)^3-\beta_2\alpha(\mu)^4+\ldots$$ Reordering terms we get an expression we can integrate ...


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Even if a theory is naively (classically) scale invariant (eg: the scalar theory with $\lambda \phi^4$ interaction therm), quantum mechanically, the 4-point scattering amplitude depends on the energy of the scattering particles (as can be shown by a one-loop computation. Tree level computations are the classical approximation). Suppose the scattering ...


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The bare coupling vanishes in the continuum limit, because the renormalized quantities are associated with measurements over very large scales (compared to the lattice spacing). One way to think about this is that since QCD is confining, the coupling at the scale of the lattice spacing must vanish if the coupling at the continuum scale is to remain finite. ...


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Perturbative QCD is a subfield of particle physics in which the theory of strong interactions, Quantum Chromodynamics (QCD), is studied by using the fact that the strong coupling constant \alpha_s is small in high energy or short distance interactions, thus allowing Perturbation theory techniques to be applied It has been used for high energies, and is ...


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It is not limited to the Parton distribution functions (pdfs) only. The difference between LO and NLO event generators is that at the hard scattering level the formers use tree level matrix elements while the latter use one loop matrix elements*. The utility is that when you generate events with NLO matrix elements you improve the precision by lowering the ...



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