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We present the initial release of ARGES, a toolkit for obtaining renormalisation group equations in perturbation theory. As such, ARGES can handle any perturbatively renormalisable four-dimensional quantum field theory. Notable further features include a symbolic rather than numeric computation, input of unconventional scalar and Yukawa sectors, an interactive evaluation and disentanglement as well as capabilities to inject algebraic simplification rules. We provide a conceptual and practical introduction into ARGES, and highlight similarities and differences with complementary packages.
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We consider the calculation of threshold effects due to Kaluza Klein and winding modes in string theory. We show that for a large radius of compactification these effects may be approximated by an effective field theory applicable below the string cut-off scale. Using this formalism we show that the radiative contribution to gauge couplings involving only massive Kaluza Klein and winding modes may be calculated to all orders in perturbation theory and determine the full two loop contribution involving light modes and estimate the magnitude of the higher-order contributions. For the case of the weakly coupled heterotic string we also discuss how an improved calculation can be made incorporating the string theory threshold corrections which avoids the limitations of the effective field theory approach. Using this formalism we determine the implications for gauge coupling unification for one representative model including the effects of two loop corrections above the compactification scale. Finally we discuss the prospects for gauge unification in Type I models with a low string scale and point out potential fine tuning problems in this case.
We discuss the errors introduced by level truncation in the study of boundary renormalisation group flows by the Truncated Conformal Space Approach. We show that the TCSA results can have the qualitative form of a sequence of RG flows between different conformal boundary conditions. In the case of a perturbation by the field phi(13), we propose a renormalisation group equation for the coupling constant which predicts a fixed point at a finite value of the TCSA coupling constant and we compare the predictions with data obtained using TBA equations.
Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. After a discussion of the types of corrections that could possibly appear and elucidating on the theory behind neutrino mass sum rules, we estimate and explicitly compute the impact of radiative corrections, as these appear in general and thus hold for whole groups of models. We discuss all neutrino mass sum rules currently present in the literature, which together have realisations in more than 50 explicit neutrino flavour models. We find that, while the effect of the renormalisation group running can be visible, the qualitative features do not change. This finding strongly backs up the solidity of the predictions derived in the literature, and it thus marks a very important step in deriving testable and reliable predictions from neutrino flavour models.
We discuss an approach for accessing bound state properties, like mass and decay width, of a theory within the functional renormalisation group approach. An important cornerstone is the dynamical hadronization technique for resonant interaction channels. The general framework is exemplified and put to work within the two-flavour quark-meson model. This model provides a low-energy description of the dynamics of two-flavour QCD with quark and hadronic degrees of freedom. We compare explicitly the respective results for correlation functions and observables with first principle QCD results in a quantitative manner. This allows us to estimate the validity range of low energy effective models. We also present first results for pole masses and decay widths. Next steps involving real-time formulations of the functional renormalisation group are discussed.
The application of the exact renormalisation group to symmetric as well as asymmetric many-fermion systems with a short-range attractive force is studied. Assuming an ansatz for the effective action with effective bosons, describing pairing effects a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations has been derived. The phase transition to a phase with broken symmetry is found at a critical value of the running scale. The mean-field results are recovered if boson-loop effects are omitted. The calculations with two different forms of the regulator are shown to lead to a similar results. We find that, being quite small in the case of the symmetric many-fermion system the corrections to mean field approximation becomes more important with increasing mass asymmetry.
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