349 research outputs found

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

We investigate the decoupling of heavy Kaluza-Klein modes in $\phi^{4}$
theory and scalar QED with space-time topology $\mathbb{R}^{3,1} \times S^{1}$.
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 $M$. With the solutions to the RGE's we find the
$M$-scale dependence of the effective theory due to higher dimensional quantum
effects. We find that the heavy modes decouple in $\phi^{4}$ theory, but do not
decouple in scalar QED. This is due to the zero mode of the 5-th component
$A_{5}$ of the 5-d gauge field. Because $A_{5}$ is a scalar under 4-d Lorentz
transformations, there is no gauge symmetry protecting it from getting mass and
$A_{5}^{4}$ interaction terms after loop corrections. In light of these
unpleasant features, we explore $S^{1}/\mathbb{Z}_{2}$ compactifications, which
eliminate $A_{5}$, 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

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

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

Unlike the Standard Model (SM), supersymmetric models stabilize the
electroweak (EW) scale $v$ at the quantum level and {\it predict} that $v$ is a
function of the TeV-valued SUSY parameters ($\gamma_\alpha$) 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 $\delta\chi^2$ (from
$\chi^2_{min}$ of a model) automatically encode information about the
"traditional" EW fine-tuning measuring this stability, {\it provided that} the
EW scale $v\sim m_Z$ is indeed regarded as a function $v=v(\gamma)$. It is
known that large EW fine-tuning may signal an incomplete theory of soft terms
and can be reduced when relations among $\gamma_\alpha$ 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
$\delta\chi^2$ and the s-standard deviation confidence interval by using
$v=v(\gamma)$ 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

We study quadratic gravity $R^2+R_{[\mu\nu]}^2$ 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
$v_\mu= (\tilde\Gamma_\mu-\Gamma_\mu)/2$, with $\tilde\Gamma_\mu$
($\Gamma_\mu$) the trace of the Palatini (Levi-Civita) connection,
respectively. The underlying geometry is non-metric due to the $R_{[\mu\nu]}^2$
term acting as a gauge kinetic term for $v_\mu$. 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 ($\phi$) is not added
ad-hoc to this purpose but is "extracted" from the $R^2$ term. The gauge field
becomes massive by absorbing the derivative term $\partial_\mu\ln\phi$ of the
Stueckelberg field ("dilaton"). In the broken phase one finds the
Einstein-Proca action of $v_\mu$ of mass proportional to the Planck scale
$M\sim \langle\phi\rangle$, and a positive cosmological constant. Below this
scale $v_\mu$ 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 $0.007\leq r \leq
0.01$ for current spectral index $n_s$ (at $95\%$CL) and N=60 efolds. This
value of $r$ 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

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