We compute of the lowest order quantum radiative correction to the mass of the kink in $phi^4$ theory in 1+1 dimensions using an alternative renormalization procedure which has been introduced earlier. We use the standard mode number cutoff in conjun
ction with the above program. Our results show a small correction to the previously reported values.[The paper has been withdraw by the authors because a new version is been written to better emphasize on renormalization in problems with nontrivial background. The new version has been submitted by our new co-author (arXiv:1205.2775).]
The production of W bosons decaying into a tau lepton and a neutrino with the tau lepton decaying hadronically has been observed in LHC pp collisions at sqrt(s) = 7 TeV with the CMS detector. The selection criteria provide a statistically significant
signal on the top of QCD multi-jet and electroweak backgrounds. A data-driven method for the estimation of the QCD multi-jet background has been employed.
In this paper we discuss the effects of nontrivial boundary conditions or backgrounds, including non-perturbative ones, on the renormalization program for systems in two dimensions. Here we present an alternative renormalization procedure such that t
hese non-perturbative conditions can be taken into account in a self-contained and, we believe, self-consistent manner. These conditions have profound effects on the properties of the system, in particular all of its $n$-point functions. To be concrete, we investigate these effects in the $lambda phi^4$ model in two dimensions and show that the mass counterterms turn out to be proportional to the Greens functions which have nontrivial position dependence in these cases. We then compute the difference between the mass counterterms in the presence and absence of these conditions. We find that in the case of nontrivial boundary conditions this difference is minimum between the boundaries and infinite on them. The minimum approaches zero when the boundaries go to infinity. In the case of nontrivial backgrounds, we consider the kink background and show that the difference is again small and localized around the kink.
