Flavor Phenomenology in General 5D Warped Spaces

We have considered a general 5D warped model with SM fields propagating in the bulk and computed explicit expressions for oblique and non-oblique electroweak observables as well as for flavor and CP violating effective four-fermion operators. We have compared the resulting lower bounds on the Kaluza-Klein (KK) scale in the RS model and a recently proposed model with a metric modified towards the IR brane, which is consistent with oblique parameters without the need for a custodial symmetry. We have randomly generated 40,000 sets of O(1) 5D Yukawa couplings and made a fit of the quark masses and CKM matrix elements in both models. This method allows to identify the percentage of points consistent with a given KK mass, which in turn provides us with a measure for the required fine-tuning. Comparison with current experimental data on Rb, FCNC and CP violating operators exhibits an improved behavior of our model with respect to the RS model. In particular, allowing 10% fine-tuning the combined results point towards upper bounds on the KK gauge boson masses around 3.3 TeV in our model as compared with 13 TeV in the RS model. One reason for this improvement is that fermions in our model are shifted, with respect to fermions in the RS model, towards the UV brane thus decreasing the strength of the modifications of electroweak observables.Comment: 28 pages, 7 figures, 4 table

Flavour Physics in the Soft Wall Model

We extend the description of flavour that exists in the Randall-Sundrum (RS) model to the soft wall (SW) model in which the IR brane is removed and the Higgs is free to propagate in the bulk. It is demonstrated that, like the RS model, one can generate the hierarchy of fermion masses by localising the fermions at different locations throughout the space. However, there are two significant differences. Firstly the possible fermion masses scale down, from the electroweak scale, less steeply than in the RS model and secondly there now exists a minimum fermion mass for fermions sitting towards the UV brane. With a quadratic Higgs VEV, this minimum mass is about fifteen orders of magnitude lower than the electroweak scale. We derive the gauge propagator and despite the KK masses scaling as $m_n^2\sim n$, it is demonstrated that the coefficients of four fermion operators are not divergent at tree level. FCNC's amongst kaons and leptons are considered and compared to calculations in the RS model, with a brane localised Higgs and equivalent levels of tuning. It is found that since the gauge fermion couplings are slightly more universal and the SM fermions typically sit slightly further towards the UV brane, the contributions to observables such as $\epsilon_K$ and $\Delta m_K$, from the exchange of KK gauge fields, are significantly reduced.Comment: 33 pages, 15 figures, 5 tables; v2: references added; v3: modifications to figures 4,5 and 6. version to appear in JHE

The Effective Lagrangian for Bulk Fermions in Models with Extra Dimensions

We compute the dimension 6 effective Lagrangian arising from the tree level integration of an arbitrary number of bulk fermions in models with warped extra dimensions. The coefficients of the effective operators are written in terms of simple integrals of the metric and are valid for arbitrary warp factors, with or without an infrared brane, and for a general Higgs profile. All relevant tree level fermion effects in electroweak and flavor observables can be computed using this effective Lagrangian.Comment: 22 pages. V2: typos corrected, matches published versio

Suppressing Electroweak Precision Observables in 5D Warped Models

We elaborate on a recently proposed mechanism to suppress large contributions to the electroweak precision observables in five dimensional (5D) warped models, without the need for an extended 5D gauge sector. The main ingredient is a modification of the AdS metric in the vicinity of the infrared (IR) brane corresponding to a strong deviation from conformality in the IR of the 4D holographic dual. We compute the general low energy effective theory of the 5D warped Standard Model, emphasizing additional IR contributions to the wave function renormalization of the light Higgs mode. We also derive expressions for the S and T parameters as a function of a generic 5D metric and zero-mode wave functions. We give an approximate formula for the mass of the radion that works even for strong deviation from the AdS background. We proceed to work out the details of an explicit model and derive bounds for the first KK masses of the various bulk fields. The radion is the lightest new particle although its mass is already at about 1/3 of the mass of the lightest resonances, the KK states of the gauge bosons. We examine carefully various issues that can arise for extreme choices of parameters such as the possible reintroduction of the hierarchy problem, the onset of nonperturbative physics due to strong IR curvature or the creation of new hierarchies near the Planck scale. We conclude that a KK scale of 1 TeV is compatible with all these constraints.Comment: 44 pages, 11 figures, references adde

Cosmological phase transitions in warped space: gravitational waves and collider signatures

We study the electroweak phase transition within a 5D warped model including a scalar potential with an exponential behavior, and strong back-reaction over the metric, in the infrared. By means of a novel treatment of the superpotential formalism, we explore parameter regions that were previously inaccessible. We nd that for large enough values of the t'Hooft parameter (e.g. N = 25) the holographic phase transition occurs, and it can force the Higgs to undergo a rst order electroweak phase transition, suitable for electroweak baryogenesis. The model exhibits gravitational waves and colliders signatures. It typically predicts a stochastic gravitational wave background observable both at the Laser Interferometer Space Antenna and at the Einstein Telescope. Moreover the radion tends to be heavy enough such that it evades current constraints, but may show up in future LHC runs.The work of EM is supported by the Spanish MINEICO under Grant FPA2015-64041-C2-1-P and FIS2017-85053-C2-1-P, by the Junta de Andaluc a under Grant FQM-225, by the Basque Government under Grant IT979-16, and by the Spanish Consolider Ingenio 2010 Programme CPAN (CSD2007-00042). The research of EM is also supported by the Ram on y Cajal Program of the Spanish MINEICO, and by the Universidad del Pa s Vasco UPV/EHU, Bilbao, Spain, as a Visiting Professor. GN is supported by the Swiss National Science Foundation (SNF) under grant 200020-168988. The work of MQ is partly supported by Spanish MINEICO under Grant CICYT-FEDER-FPA2014- 55613-P and FPA2017-88915-P, by the Severo Ochoa Excellence Program of MINEICO under Grant SEV-2016-0588, and by CNPq PVE fellowship project 405559/2013-5

The Fermion Mass Hierarchy in Models with Warped Extra Dimensions and a Bulk Higgs

The phenomenological implications of allowing the Higgs to propagate in both AdS${}_5$ and a class of asymptotically AdS spaces are considered. Without tuning, the vacuum expectation value (VEV) of the Higgs is peaked towards the IR tip of the space and hence such a scenario still offers a potential resolution to the gauge-hierarchy problem. When the exponent of the Higgs VEV is approximately two and one assumes order one Yukawa couplings, then the fermion Dirac mass term is found to range from $\sim 10^{-5}$ eV to $\sim 200$ GeV in approximate agreement with the observed fermion masses. However, this result is sensitive to the exponent of the Higgs VEV, which is a free parameter. This paper offers a number of phenomenological and theoretical motivations for considering an exponent of two to be the optimal value. In particular, the exponent is bounded from below by the Breitenlohner-Freedman bound and the requirement that the dual theory resolves the gauge hierarchy problem. While, in the model considered, if the exponent is too large, electroweak symmetry may not be broken. In addition, the holographic method is used to demonstrate, in generality, that the flatter the Higgs VEV, the smaller the contribution to the electroweak $T$ parameter. In addition, the constraints from a large class of gauge mediated and scalar mediated flavour changing neutral currents, will be at minimal values for flatter Higgs VEVs. Some initial steps are taken to investigate the physical scalar degrees of freedom that arise from a mixing between the $W_5/Z_5$ components and the Higgs components.Comment: 34 pages, 20 figures, 1 table; v3: matches version to be published in JHE

Universal contributions to scalar masses from five dimensional supergravity

We compute the effective Kahler potential for matter fields in warped compactifications, starting from five dimensional gauged supergravity, as a function of the matter fields localization. We show that truncation to zero modes is inconsistent and the tree-level exchange of the massive gravitational multiplet is needed for consistency of the four-dimensional theory. In addition to the standard Kahler coming from dimensional reduction, we find the quartic correction coming from integrating out the gravity multiplet. We apply our result to the computation of scalar masses, by assuming that the SUSY breaking field is a bulk hypermultiplet. In the limit of extreme opposite localization of the matter and the spurion fields, we find zero scalar masses, consistent with sequestering arguments. Surprisingly enough, for all the other cases the scalar masses are tachyonic. This suggests the holographic interpretation that a CFT sector always generates operators contributing in a tachyonic way to scalar masses. Viability of warped su- persymmetric compactifications necessarily asks then for additional contributions. We discuss the case of additional bulk vector multiplets with mixed boundary conditions, which is a partic- ularly simple and attractive way to generate large positive scalar masses. We show that in this case successful fermion mass matrices implies highly degenerate scalar masses for the first two generations of squarks and sleptons.Comment: 23 pages. v2: References added, new section on effect of additional bulk vector multiplets and phenomenolog

Neutrino Mixing from Wilson Lines in Warped Space

We consider the generation of the hierarchical charged lepton spectrum and anarchic neutrino masses and mixing angles in warped extra dimensional models with Randall-Sundrum metric. We have classified all possible cases giving rise to realistic spectra for both Dirac and Majorana neutrinos. An anarchic neutrino spectrum requires a convenient bulk symmetry broken by boundary conditions on both UV and IR branes. We have in particular considered the case of Majorana neutrinos with a continuous bulk symmetry. To avoid unwanted massless extra gauge bosons the 4D group should be empty. If the 4D coset is not vanishing it can provide a Wilson Line description of the neutrino Majorana mass matrix. We have studied an example based on the bulk gauge group U(3)_{L} \otimes U(3)_{N} \otimes_{i} U(1)_{E^i} with the Wilson Line in SO(3)_{N} satisfying all required conditions. A \chi^2-fit to experimental data exhibits the 95% CL region in the parameter space with no fine-tuning. As a consequence of the symmetries of the theory there is no tree-level induced lepton flavor violation and so one-loop processes are consistent with experimental data for KK-modes about a few TeV. The model is easily generalizable to models with IR deformed metrics with similar conclusions.Comment: 28 pages, 9 eps plots, uses axodraw; v2 Title changed, comments on phenomenology added, version to be published in JHE

Stability of Scalar Fields in Warped Extra Dimensions

This work sets up a general theoretical framework to study stability of models with a warped extra dimension where N scalar fields couple minimally to gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk scalars, and general domain-wall models. We derive the Schrodinger equation governing the spin-0 spectrum of perturbations of such a system. This result is specialized to potentials generated using fake supergravity, and we show that models without branes are free of tachyonic modes. Turning to the existence of zero modes, we prove a criterion which relates the number of normalizable zero modes to the parities of the scalar fields. Constructions with definite parity and only odd scalars are shown to be free of zero modes and are hence perturbatively stable. We give two explicit examples of domain-wall models with a soft wall, one which admits a zero mode and one which does not. The latter is an example of a model that stabilizes a compact extra dimension using only bulk scalars and does not require dynamical branes.Comment: 25 pages, 2 figures; v2: minor changes to text, references added, matches published versio