Two-loop diagrams in Yang-Mills theory

A calculation of the renormalisation constants of the Yang-Mills field to O(g⁴) is presented. The function β(g) is hence evaluated to O(g⁵) and possible implications for gauge theories of the strong interactions discussed.     

Low-energy predictions from grand unified theories

A theoretical framework to compute low-energy processes in a spontaneously broken gauge theory is devised. It applies in any gauge and uses conventional renormalisation schemes. Application of the method to SU(5) gives a range for M_X of 4.10¹³ GeV < M_X < 1.3 · 10¹⁵ GeV with a best value of 6.6 · 10¹⁴ GeV.     

Aspects of the functional renormalisation group

We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.     

AnomalousZ′ effects in the WW channel at NLC

We consider the virtual signals of aZ′ of very general type in the processe ⁺ e ^?→W ⁺ W ^? at a future linear collider (NLC). We show that possible deviations from the SM predictions in this channel are related to similar deviations in the purely leptonic one in a way that is only characteristic of thisZ′ model, and not in general of possible competitor models with anomalous gauge couplings.     

Gradient properties of the renormalisation group equations in multicomponent systems

The existence of a metric, which enables the renormalisation group β functions of a multicomponent field theory to be written as a gradient, has very important implications for the asymptotic behavior of the renormalisation group equations. It is shown that a very simple metric exists in a field theory with n-component Bose fields and arbitrary φ⁴ interaction, when the β functions are calculated perturbatively up to and including the 2-loop diagrams. This same metric is shown to work for all irreducible diagrams, but it must and can be modified to accommodate reducible 3-loop contributions. The prospects and outlook of this aspect of the renormalisation group are discussed.     

AnomalousZ�� effects in the WW channel at NLC

We consider the virtual signals of aZ?? of very general type in the processe ⁺ e ^???W ⁺ W ^? at a future linear collider (NLC). We show that possible deviations from the SM predictions in this channel are related to similar deviations in the purely leptonic one in a way that is only characteristic of thisZ?? model, and not in general of possible competitor models with anomalous gauge couplings.     

A contribution to the problem of effective particle-hole interactions

Various effects arising in nuclear-structure calculations and leading all to a renormalisation of the nucleon-nucleon interaction are reviewed. A new treatment is proposed for the renormalisation due to mixing of the particle-hole subspace and then particle ?n hole (n=2, 3, 4 etc.) subspaces.     

Horizontal interactions and their symmetries in GUTs

Using very general assumptions we find and discuss a large class of unified models with horizontal symmetries. We classify them and show on the basis of renormalisation group equations that the typical horizontal mass scale must be at least 10⁹–10¹³ GeV, depending on the model. A class of nonsupersymmetric theories with horizontal symmetries is discovered which predicts a proton lifetimeτ _p ≧10³³ and sin² θ _w ?0.23. It is also argued that supersymmetric unified models involving horizontal symmetries are unlikely to meet present experimental and theoretical requirements—contrary to ordinary supersymmetric theories without horizontal sector.     

Models for strong interactions in 6−ϵ dimensions

We explore the possibility that high energy physics is an infrared phenomenon, with strong interactions determined by an infrared stable fixed point of the renormalisation group. Models ofφ³ interactions with SU(n) and SU (3) ×SU (3) internal symmetries are shown to illustrate this idea. Corrections to a Gell-Mann Okubo mass formula are calculated to first order in ? in 6?? dimensions.     

The rotating mass matrix,the strong CP problem and Higgs decay

We first show that the rotating mass matrix hypothesis suggested earlier, where the massive eigenvector of a rank-one mass matrix changes with renormalisation scale, is consistent with the latest experimental data on fermion mass hierarchy and mixing, including the CP violating KM phase. We obtain thereby a smooth trajectory for the massive eigenvector as a function of the scale. Using this trajectory we next study Higgs decay and find suppression of \(\varGamma(H\rightarrow c\bar{c})\) compared to the standard model predictions for a range of Higgs masses. We also give limits for flavour-violating decays, including a relatively large branching ratio for the τ ^? μ ⁺ mode.     

On neutral currents in two-Z-boson gauge models

A systematic procedure is considered for the phenomenological analysis of neutral current interactions in an arbitrary two-Z-boson gauge model by means of a general neutral current effective Lagrangian. Expressions for two gauge boson masses and their mixing angle have been obtained directly through the effective Lagrangian parameters. A general classification of possible types of two-Z-boson gauge models is presented in accordance with the form of the effective Lagrangian.     

Asymptotic behaviour of supersymmetric Yang-Mills theories in the two-loop approximation

A calculation of the renormalisation group function β(g) to O(g⁵) for a supersymmetric Yang-Mills theory is presented. It is found that in no case do both the leading terms in the perturbation expansion of β(g) vanish.     

Full one-loop corrections to the relic density in the MSSM: A few examples

We show the impact of the electroweak, and in one instance the QCD, one-loop corrections on the relic density of dark matter in the MSSM which is provided by the lightest neutralino. We cover here some of the most important scenarios: annihilation into fermions for a bino-like neutralino, annihilation involving gauge bosons in the case of a mixed neutralino, the neutralino–stau co-annihilation region and annihilation into a bottom quark pair. The corrections can be large and should be taken into account in view of the present and forthcoming increasing precision on the relic density measurements. Our calculations are made possible thanks to a newly developed automatic tool for the calculation at one-loop of any process in the MSSM. We have implemented a complete on-shell gauge invariant renormalisation scheme, with the possibility of switching to other schemes. In particular we will report on the impact of different renormalisation schemes for tanβ$\tan \beta$.     

Virtual effects of Higgs particles

The possibility of observing Higgs particles through virtual effects is considered in detail for a general gauge theory. The effect of charged Higgs particles on low-energy weak interaction processes, like muon decay, tau decay, nuclear beta decay, pion decay, and some higher-order processes is analyzed. The effect of flavor-changing neutral Higgs particles on rare decay modes of the muon and kaon, μe conversion, K^o-$\text{K}$^o and D^o-$\text{D}$^o mixing is also studied. We discuss constraints on possible extensions of the Weinberg-Salam model and experiments sensitive to their Higgs particles. In particular, we analyze the neutral Higgs which couple to fermions in the minimal SU(2)_L×SU(2)_R×U(1) model and find that they probably have mass greater than 100 GeV.     

Z′ mass limits,masses and coupling of higgs bosons,and Z′ decays in an E6 superstring based model

We demonstrate that current phenomenological constraints on Z-Z′ mixing for an E₆ grand unified group with low energy gauge group SU(2)_L×U(1)_Y×U(1)_Y, allow only a narrow range of Higgs vacuum expectation values consistent with possibilities favored by renormalization group expectations. Modest improvements in bounds on this mixing will lead to substantial bounds on the Z′ mass if alternative renormalization group solutions are not found. We then explore the constraints upon relations between Higgs masses in this model. In addition we explore the couplings of these Higgs to the gauge particles of the theory and emphasize the associated implications for Higgs detection in decays of the Z′.     

Discriminating between Z′-boson effects and effects of anomalous gauge couplings in the double production of W ± bosons at a linear collider

The potential of the International Linear electron-positron Collider (ILC) for seeking, in the annihilation production of W ^±-boson pairs, signals induced by new neutral gauge bosons predicted by models belonging to various classes and featuring an extended gauge sector is studied. Limits that will be obtained at ILC for the parameters and masses of Z′ bosons are compared with present-day and future data from the Large Hadron Collider (LHC). The possibility of discriminating between the effects of Z-Z′ mixing and signals induced by anomalous gauge couplings (AGC) is demonstrated within theoretically motivated trilinear gauge models involving several free anomalous parameters. It is found that the sensitivity of ILC to the effects of Z-Z′ mixing in the process e ⁺ e ^? → W ⁺ W ^? and its ability to discriminate between these two new-physics scenarios, Z′ and AGC, become substantially higher upon employing polarized initial (e ⁺ e ^?) and final (W ^±) states.     

Photon-Z mixing in the Weinberg-Salam model: Effective charges and the a = −3 gauge

We study some properties of the Weinberg-Salam model connected with the photon-Z mixing. We solve the linear Dyson-Schwinger equations between full and 1PI boson propagators. The task is made easier by the two-point function Ward identities that we derive to all orders and in any gauge. Some aspects of the renormalization of the model are also discussed. We display the exact mass-dependent one-loop two-point functions involving the photon and Z field in any linear ξ-gauge. The special gauge a = ξ^?1 = ?3 is shown to play a peculiar role. In this gauge, the Z field is multiplicatively renormalizable (at the one-loop level), and one can construct both electric and weak effective charges of the theory from the photon and Z propagators, with a very simple expression similar to that of the QED Petermann, Stueckelberg, Gell-Mann and Low charge.