349 research outputs found

    Decoupling of Heavy Kaluza-Klein Modes In Models With Five-Dimensional Scalar Fields

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    We investigate the decoupling of heavy Kaluza-Klein modes in ϕ4\phi^{4} theory and scalar QED with space-time topology R3,1×S1\mathbb{R}^{3,1} \times S^{1}. We calculate the effective action due to integrating out heavy KK modes. We construct generalized RGE's for the couplings with respect to the compactification scale MM. With the solutions to the RGE's we find the MM-scale dependence of the effective theory due to higher dimensional quantum effects. We find that the heavy modes decouple in ϕ4\phi^{4} theory, but do not decouple in scalar QED. This is due to the zero mode of the 5-th component A5A_{5} of the 5-d gauge field. Because A5A_{5} is a scalar under 4-d Lorentz transformations, there is no gauge symmetry protecting it from getting mass and A54A_{5}^{4} interaction terms after loop corrections. In light of these unpleasant features, we explore S1/Z2S^{1}/\mathbb{Z}_{2} compactifications, which eliminate A5A_{5}, allowing for the heavy modes to decouple at low energies. We also explore the possibility of decoupling by including higher dimensional operators. It is found that this is possible, but a high degree of fine tuning is required.Comment: 9 pages, no figures; sign error on equations 20, 36, 37; Added additional reference

    Higher dimensional operators and their effects in (non)supersymmetric models

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    It is shown that a 4D N=1 softly broken supersymmetric theory with higher derivative operators in the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, can be re-formulated as a theory without higher derivatives but with additional (ghost) superfields and modified interactions. The importance of the analytical continuation Minkowski-Euclidean space-time for the UV behaviour of such theories is discussed in detail. In particular it is shown that power counting for divergences in Minkowski space-time does not always work in models with higher derivative operators.Comment: Based on talk presented at "Supersymmetry 2007"; 11 pages, LaTe

    Fixing the EW scale in supersymmetric models after the Higgs discovery

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    TeV-scale supersymmetry was originally introduced to solve the hierarchy problem and therefore fix the electroweak (EW) scale in the presence of quantum corrections. Numerical methods testing the SUSY models often report a good likelihood L (or chi^2=-2ln L) to fit the data {\it including} the EW scale itself (m_Z^0) with a {\it simultaneously} large fine-tuning i.e. a large variation of this scale under a small variation of the SUSY parameters. We argue that this is inconsistent and we identify the origin of this problem. Our claim is that the likelihood (or chi^2) to fit the data that is usually reported in such models does not account for the chi^2 cost of fixing the EW scale. When this constraint is implemented, the likelihood (or chi^2) receives a significant correction (delta_chi^2) that worsens the current data fits of SUSY models. We estimate this correction for the models: constrained MSSM (CMSSM), models with non-universal gaugino masses (NUGM) or higgs soft masses (NUHM1, NUHM2), the NMSSM and the general NMSSM (GNMSSM). For a higgs mass m_h\approx 126 GeV, one finds that in these models (delta_chi^2)/ndf> 1.5 (approx 1 for GNMSSM), which violates the usual condition of a good fit (total chi^2/ndf approx 1) already before fitting observables other than the EW scale itself (ndf=number of degrees of freedom). This has (negative) implications for SUSY models and it is suggested that future data fits properly account for this effect, if one remains true to the original goal of SUSY. Since the expression of delta_chi^2 that emerges from our calculation depends on a familiar measure of fine-tuning, one concludes that EW fine-tuning is an intrinsic part of the likelihood to fit the data that includes the EW scale (m_Z^0).Comment: 18 pages; (v4: added text in Conclusions

    SUSY naturalness without prejudice

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    Unlike the Standard Model (SM), supersymmetric models stabilize the electroweak (EW) scale vv at the quantum level and {\it predict} that vv is a function of the TeV-valued SUSY parameters (γα\gamma_\alpha) of the UV Lagrangian. We show that the (inverse of the) covariance matrix of the model in the basis of these parameters and the usual deviation δχ2\delta\chi^2 (from χmin2\chi^2_{min} of a model) automatically encode information about the "traditional" EW fine-tuning measuring this stability, {\it provided that} the EW scale vmZv\sim m_Z is indeed regarded as a function v=v(γ)v=v(\gamma). It is known that large EW fine-tuning may signal an incomplete theory of soft terms and can be reduced when relations among γα\gamma_\alpha exist (due to GUT symmetries, etc). The global correlation coefficient of this matrix can help one investigate if such relations are present. An upper bound on the usual EW fine-tuning measure ("in quadrature") emerges from the analysis of the δχ2\delta\chi^2 and the s-standard deviation confidence interval by using v=v(γ)v=v(\gamma) and the theoretical approximation (loop order) considered for the calculation of the observables. This upper bound avoids subjective criteria for the "acceptable" level of EW fine-tuning for which the model is still "natural".Comment: 13 pages. LaTeX, (v4: minor corrections

    Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation

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    We study quadratic gravity R2+R[μν]2R^2+R_{[\mu\nu]}^2 in the Palatini formalism where the connection and the metric are independent. This action has a {\it gauged} scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field vμ=(Γ~μΓμ)/2v_\mu= (\tilde\Gamma_\mu-\Gamma_\mu)/2, with Γ~μ\tilde\Gamma_\mu (Γμ\Gamma_\mu) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the R[μν]2R_{[\mu\nu]}^2 term acting as a gauge kinetic term for vμv_\mu. We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field (ϕ\phi) is not added ad-hoc to this purpose but is "extracted" from the R2R^2 term. The gauge field becomes massive by absorbing the derivative term μlnϕ\partial_\mu\ln\phi of the Stueckelberg field ("dilaton"). In the broken phase one finds the Einstein-Proca action of vμv_\mu of mass proportional to the Planck scale MϕM\sim \langle\phi\rangle, and a positive cosmological constant. Below this scale vμv_\mu decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio 0.007r0.010.007\leq r \leq 0.01 for current spectral index nsn_s (at 95%95\%CL) and N=60 efolds. This value of rr is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.Comment: 22 pages, 2 figures, LaTe