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

An A4 flavor model for quarks and leptons in warped geometry

We propose a spontaneous A4 flavor symmetry breaking scheme implemented in a warped extra dimensional setup to explain the observed pattern of quark and lepton masses and mixings. The main advantages of this choice are the explanation of fermion mass hierarchies by wave function overlaps, the emergence of tribimaximal neutrino mixing and zero quark mixing at the leading order and the absence of tree-level gauge mediated flavor violations. Quark mixing is induced by the presence of bulk flavons, which allow for cross-brane interactions and a cross-talk between the quark and neutrino sectors, realizing the spontaneous symmetry breaking pattern A4 --> nothing first proposed in [X.G.\,He, Y.Y.\,Keum, R.R.\,Volkas, JHEP{0604}, 039 (2006)]. We show that the observed quark mixing pattern can be explained in a rather economical way, including the CP violating phase, with leading order cross-interactions, while the observed difference between the smallest CKM entries V_{ub} and V_{td} must arise from higher order corrections. We briefly discuss bounds on the Kaluza-Klein scale implied by flavor changing neutral current processes in our model and show that the residual little CP problem is milder than in flavor anarchic models.Comment: 34 pages, 2 figures; version published in JHE

Reliability and validity of a method for the assessment of sport rock climbers' isometric finger strength

Isometric strength of the finger flexors is considered to be one of the main physical determinants of sport rock climbing performance. We set out to determine the test-retest reliability and criterion validity of a low resource maximal isometric finger strength (MIFS) testing protocol that uses a pulley system to add or remove weight to/from a climber's body. To determine test-retest reliability, 15 subjects' MIFS was assessed on 2 occasions, separated by a minimum of 48 hours. Body mass and maximum load were recorded on both occasions. Intra-class correlation coefficients (ICCs) between visits for all variables were very good (ICC > 0.91), with small bias and effect sizes-particularly when expressed as a percentage of body mass (ICC = 0.98, 95% confidence interval 0.93-0.99). To determine the criterion validity of MIFS and climbing ability, data of 229 intermediate to higher elite climbers were compared. Pearson's product moment correlations demonstrated good agreement, again particularly between total load when expressed as a percentage of body mass and climbing performance (r = 0.421-0.503). The results illustrate the sensitivity of a simple test for the determination of MIFS in intermediate to height elite climbers from an ecologically valid, climbing specific test that only requires equipment found at most climbing walls. This low resource test protocol for the assessment of isometric finger strength has wide-reaching utility, for instance when assessing strength before and after a training intervention or when prescribing load intensities for exercises aimed at improving maximal finger strength

Electroweak Constraints on Warped Geometry in Five Dimensions and Beyond

Here we consider the tree level corrections to electroweak (EW) observables from standard model (SM) particles propagating in generic warped extra dimensions. The scale of these corrections is found to be dominated by three parameters, the Kaluza-Klein (KK) mass scale, the relative coupling of the KK gauge fields to the Higgs and the relative coupling of the KK gauge fields to fermion zero modes. It is found that 5D spaces that resolve the hierarchy problem through warping typically have large gauge-Higgs coupling. It is also found in $D>5$ where the additional dimensions are warped the relative gauge-Higgs coupling scales as a function of the warp factor. If the warp factor of the additional spaces is contracting towards the IR brane, both the relative gauge-Higgs coupling and resulting EW corrections will be large. Conversely EW constraints could be reduced by finding a space where the additional dimension's warp factor is increasing towards the IR brane. We demonstrate that the Klebanov Strassler solution belongs to the former of these possibilities.Comment: 18 pages, 3 figures (references added) version to appear in JHE

SUSY Splits, But Then Returns

We study the phenomenon of accidental or "emergent" supersymmetry within gauge theory and connect it to the scenarios of Split Supersymmetry and Higgs compositeness. Combining these elements leads to a significant refinement and extension of the proposal of Partial Supersymmetry, in which supersymmetry is broken at very high energies but with a remnant surviving to the weak scale. The Hierarchy Problem is then solved by a non-trivial partnership between supersymmetry and compositeness, giving a promising approach for reconciling Higgs naturalness with the wealth of precision experimental data. We discuss aspects of this scenario from the AdS/CFT dual viewpoint of higher-dimensional warped compactification. It is argued that string theory constructions with high scale supersymmetry breaking which realize warped/composite solutions to the Hierarchy Problem may well be accompanied by some or all of the features described. The central phenomenological considerations and expectations are discussed, with more detailed modelling within warped effective field theory reserved for future work.Comment: 29 pages. Flavor and CP constraints on left-right symmetric structure briefly discussed. References adde

Charming CP Violation and Dipole Operators from RS Flavor Anarchy

Recently the LHCb collaboration reported evidence for direct CP violation in charm decays. The value is sufficiently large that either substantially enhanced Standard Model contributions or non-Standard Model physics is required to explain it. In the latter case only a limited number of possibilities would be consistent with other existing flavor-changing constraints. We show that warped extra dimensional models that explain the quark spectrum through flavor anarchy can naturally give rise to contributions of the size required to explain the the LHCb result. The D meson asymmetry arises through a sizable CP-violating contribution to a chromomagnetic dipole operator. This happens naturally without introducing inconsistencies with existing constraints in the up quark sector. We discuss some subtleties in the loop calculation that are similar to those in Higgs to \gamma\gamma. Loop-induced dipole operators in warped scenarios and their composite analogs exhibit non-trivial dependence on the Higgs profile, with the contributions monotonically decreasing when the Higgs is pushed away from the IR brane. We show that the size of the dipole operator quickly saturates as the Higgs profile approaches the IR brane, implying small dependence on the precise details of the Higgs profile when it is quasi IR localized. We also explain why the calculation of the coefficient of the lowest dimension 5D operator is guaranteed to be finite. This is true not only in the charm sector but also with other radiative processes such as electric dipole moments, b to s\gamma, \epsilon'/\epsilon_K and \mu\ to e\gamma. We furthermore discuss the interpretation of this contribution within the framework of partial compositeness in four dimensions and highlight some qualitative differences between the generic result of composite models and that obtained for dynamics that reproduces the warped scenario.Comment: 14 page

Ectoplasm with an Edge

The construction of supersymmetric invariant actions on a spacetime manifold with a boundary is carried out using the "ectoplasm" formalism for the construction of closed forms in superspace. Non-trivial actions are obtained from the pull-backs to the bosonic bodies of closed but non-exact forms in superspace; finding supersymmetric invariants thus becomes a cohomology problem. For a spacetime with a boundary, the appropriate mathematical language changes to relative cohomology, which we use to give a general formulation of off-shell supersymmetric invariants in the presence of boundaries. We also relate this construction to the superembedding formalism for the construction of brane actions, and we give examples with bulk spacetimes of dimension 3, 4 and 5. The closed superform in the 5D example needs to be constructed as a Chern-Simons type of invariant, obtained from a closed 6-form displaying Weil triviality.Comment: 25 page

Partially Supersymmetric Composite Higgs Models

We study the idea of the Higgs as a pseudo-Goldstone boson within the framework of partial supersymmetry in Randall-Sundrum scenarios and their CFT duals. The Higgs and third generation of the MSSM are composites arising from a strongly coupled supersymmetric CFT with global symmetry SO(5) spontaneously broken to SO(4), whilst the light generations and gauge fields are elementary degrees of freedom whose couplings to the strong sector explicitly break the global symmetry as well as supersymmetry. The presence of supersymmetry in the strong sector may allow the compositeness scale to be raised to ~10 TeV without fine tuning, consistent with the bounds from precision electro-weak measurements and flavour physics. The supersymmetric flavour problem is also solved. At low energies, this scenario reduces to the "More Minimal Supersymmetric Standard Model" where only stops, Higgsinos and gauginos are light and within reach of the LHC.Comment: 28 pages. v2 minor changes and Refs. adde

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

The Spectrum of Goldstini and Modulini

When supersymmetry is broken in multiple sectors via independent dynamics, the theory furnishes a corresponding multiplicity of "goldstini" degrees of freedom which may play a substantial role in collider phenomenology and cosmology. In this paper, we explore the tree-level mass spectrum of goldstini arising from a general admixture of F-term, D-term, and almost no-scale supersymmetry breaking, employing non-linear superfields and a novel gauge fixing for supergravity discussed in a companion paper. In theories of F-term and D-term breaking, goldstini acquire a mass which is precisely twice the gravitino mass, while the inclusion of no-scale breaking renders one of these modes, the modulino, massless. We argue that the vanishing modulino mass can be explained in terms of an accidental and spontaneously broken "global" supersymmetry.Comment: 10 pages, 2 figures; v2: typo corrected, references updated; v3: version to appear in JHE