Prediction for α3(Mz)\alpha_3(M_z) in a string-inspired model

We apply the Renormalisation Group Evolution (RGE) to analyze the phenomenological implications of an extended supersymmetric model, for the value of the unification scale and the strong coupling at the electroweak scale. The model we consider is predicted to exist in Calabi-Yau string compactifications with Wilson line mechanism for $E_6$ symmetry breaking, contains additional matter beyond the MSSM spectrum and avoids the ``doublet-triplet'' splitting problem in the Higgs sector. The calculation is analytical in two-loop order and includes the effects of the heavy thresholds due to the additional matter considered. The value of $\alpha_3(M_z)$ can be brought within the experimental limits without a significant change of the unification scale from the MSSM prediction.Comment: 9 pages, LaTeX, 3 figure

Unification and Extra Space-Time Dimensions

We analyse the phenomenological implications of a particular class of supersymmetric models with additional space-time dimensions below the unification scale. Assuming the unification of the gauge couplings and using a two-loop calculation below the scale of the additional space-time dimensions, we show that the value of $\alpha_3(M_z)$ is further increased from the two-loop Minimal Supersymmetric Standard Model prediction. We consider whether decompactification threshold effects could bring $\alpha_3(M_z)$ into agreement with experiment and discuss the associated level of fine tuning needed.Comment: 11 pages, LaTeX, submitted to Phys. Lett.

Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds

We perform a detailed analysis of one-loop corrections to the self-energy of the (off-shell) gauge bosons in six-dimensional N=1 supersymmetric gauge theories on orbifolds. After discussing the Abelian case in the standard Feynman diagram approach, we extend the analysis to the non-Abelian case by employing the method of an orbifold-compatible one-loop effective action for a classical background gauge field. We find that bulk higher derivative and brane-localised gauge kinetic terms are required to cancel one-loop divergences of the gauge boson self energy. After their renormalisation we study the momentum dependence of both the higher derivative coupling h(k^2) and the {\it effective} gauge coupling g_eff(k^2). For momenta smaller than the compactification scales, we obtain the 4D logarithmic running of g_eff(k^2), with suppressed power-like corrections, while the higher derivative coupling is constant. We present in detail the threshold corrections to the low energy gauge coupling, due to the massive bulk modes. At momentum scales above the compactification scales, the higher derivative operator becomes important and leads to a power-like running of g_eff(k^2) with respect to the momentum scale. The coefficient of this running is at all scales equal to the renormalised coupling of the higher derivative operator which ensures the quantum consistency of the model. We discuss the relation to the similar one-loop correction in the heterotic string, to show that the higher derivative operators are relevant in that case too, since the field theory limit of the one-loop string correction does not commute with the infrared regularisation of the (on-shell) string result.Comment: 1+45 pages, 2 figures, JHEP style file, version to be published in JHE

Renormalization Group for Non-minimal ϕ2R\phi^2 R Couplings and Gravitational Contact Interactions

Theories of scalars and gravity, with an Einstein-Hilbert term and non-minimal interactions, $M^2R/2 -\alpha\phi^2R/12$, have graviton exchange induced contact interactions. These modify the renormalization group, leading to a discrepancy between the conventional calculations in the Jordan frame that ignore this effect (and are found to be incorrect), and the Einstein frame in which $\alpha$ does not exist. Thus, the calculation of quantum effects in the Jordan and Einstein frames does not generally commute with the transition from the Jordan to the Einstein frame. In the Einstein frame, though $\alpha$ is absent, for small steps in scale $\delta\mu/\mu$ infinitesimal contact terms $\sim \delta\alpha$ are induced, that are then absorbed back into other couplings by the contact terms. This modifies the $\beta$-functions in the Einstein frame. We show how correct results can be obtained in a simple model by including this effect.Comment: 11 pages, 4 figures. arXiv admin note: text overlap with arXiv:2009.1478

On gauge unification in Type I/I' models

We discuss whether the (MSSM) unification of gauge couplings can be accommodated in string theories with a low (TeV) string scale. This requires either power law running of the couplings or logarithmic running extremely far above the string scale. In both cases it is difficult to arrange for the multiplet structure to give the MSSM result. For the case of power law running there is also enhanced sensitivity to the spectrum at the unification scale. For the case of logarithmic running there is a fine tuning problem associated with the light closed string Kaluza Klein spectrum which requires gauge mediated supersymmetry breaking on the ``visible'' brane with a dangerously low scale of supersymmetry breaking. Evading these problems in low string scale models requires a departure from the MSSM structure, which would imply that the success of gauge unification in the MSSM is just an accident.Comment: 10 pages, LaTeX, 2 figures; minor change

Higher Derivative Operators as Counterterms in Orbifold Compactifications

In the context of 5D N=1 supersymmetric models compactified on S_1/Z_2 or S_1/(Z_2 x Z_2') orbifolds and with brane-localised superpotential, higher derivative operators are generated radiatively as one-loop counterterms to the mass of the (brane or zero mode of the bulk) scalar field. It is shown that the presence of such operators which are brane-localised is not related to the mechanism of supersymmetry breaking considered (F-term, discrete or continuous Scherk-Schwarz breaking) and initial supersymmetry does not protect against the dynamical generation of such operators. Since in many realistic models the scalar field is commonly regarded as the Higgs field, and the higher derivative operators seem a generic presence in orbifold compactifications, we stress the importance of these operators for solving the hierarchy problem.Comment: Contribution to the Conference "Supersymmetry 2005", Durham; 13 pages, LaTe

Quantum scale invariance in gauge theories and applications to muon production

We discuss quantum scale invariance in (scale invariant) gauge theories with both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST invariance is checked in two apparently unrelated approaches using a scale invariant regularisation (SIR). These approaches are then shown to be equivalent. Secondly, for the Abelian case we discuss both UV and IR quantum corrections present in such theories. We present the Feynman rules in a form suitable for offshell Green functions calculations, together with their one-loop renormalisation. This information is then used for the muon production cross section at one-loop in a quantum scale invariant theory. Such a theory contains not only new UV poles but also IR poles. While the UV poles bring new quantum corrections (in the form of counterterms), finite or divergent, that we compute, it is shown that the IR poles do not bring new physics. The IR quantum corrections, both finite and divergent, cancel out similarly to the way the IR poles themselves cancel in the traditional approach to IR divergences (in the cross section, after summing over virtual and real corrections). Hence, the evanescent interactions induced by the scale-invariant analytical continuation of the SIR scheme do not affect IR physics, as illustrated at one-loop for the muon production ($e^+ e^- \to \mu^+\mu^-$) cross section.Comment: 20 page

Quadratic Divergences in Kaluza-Klein Theories

We investigate the so-called ``Kaluza-Klein regularisation'' procedure in supersymmetric extensions of the standard model with additional compact dimensions and Scherk-Schwarz mechanism for supersymmetry breaking. This procedure uses a specific mathematical manipulation to obtain a finite result for the scalar potential. By performing the full calculation, we show that the finiteness of this result is not only a consequence of the underlying supersymmetry, but also the result of an implicit fine-tuning of the coefficients of the terms that control the ultraviolet behaviour. The finiteness of the Higgs mass at one-loop level seems therefore to be an artefact of the regularisation scheme, and quadratic divergences are expected to reappear in higher orders of perturbation theory.Comment: 10 pages, LaTe

Higher Derivative Operators from Scherk-Schwarz Supersymmetry Breaking on T^2/Z_2

In orbifold compactifications on T^2/Z_2 with Scherk-Schwarz supersymmetry breaking, it is shown that (brane-localised) superpotential interactions and (bulk) gauge interactions generate at one-loop higher derivative counterterms to the mass of the brane (or zero-mode of the bulk) scalar field. These brane-localised operators are generated by integrating out the bulk modes of the initial theory which, although supersymmetric, is nevertheless non-renormalisable. It is argued that such operators, of non-perturbative origin and not protected by non-renormalisation theorems, are generic in orbifold compactifications and play a crucial role in the UV behaviour of the two-point Green function of the scalar field self-energy. Their presence in the action with unknown coefficients prevents one from making predictions about physics at (momentum) scales close to/above the compactification scale(s). Our results extend to the case of two dimensional orbifolds, previous findings for S^1/Z_2 and S^1/(Z_2 x Z_2') compactifications where brane-localised higher derivative operators are also dynamically generated at loop level, regardless of the details of the supersymmetry breaking mechanism. We stress the importance of these operators for the hierarchy and the cosmological constant problems in compactified theories.Comment: 23 pages, LaTeX, one figure, published version in JHE