The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action k . The ordinary effective action 0 can be obtained by integrating the flow equation from an ultraviolet scale k = down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.
We study W boson scattering in the same-and opposite-sign channels under the assumption that no resonances are present in the collider processes pp → l AE ν l l AE ν l jj and pp → l AE ν l l ∓ ν l jj, respectively. Basic selection cuts together with a restriction on the combination of the final lepton and jet momenta (the Warsaw cut) make it possible to argue that at the LHC a luminosity of 100 fb −1 and a center-of-mass energy of ffiffi ffi s p ¼ 13 TeV will allow us to constrain the leading effective Lagrangian coefficients at the permil level. We also discuss limits on the other coefficients of the effective Lagrangian as well as stronger constraints provided by higher energy and luminosity.
We consider a model in which Goldstone bosons, described by a SU(N) chiral
nonlinear sigma model, are coupled to an N-plet of colored fermions by means of
a Yukawa interaction. We study the one-loop renormalization group flow and show
that the non-Gaussian UV fixed point, which is present in the purely bosonic
model, is lost because of fermion loop effects unless N is sufficiently large.
We then add four-fermion contact interactions to the lagrangian and show that
in this case there exist several non-Gaussian fixed points. The strength of the
contact interactions, predicted by the requirement that the theory flows
towards a fixed point in the UV, is compared to the current experimental
bounds. This toy model could provide an important building block of an
asymptotically safe model of the weak interactions.Comment: 7 pages, 3 figures, 1 tabl
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