Impact of Warped Extra Dimensions on the Dipole Coefficients in b→sγ\boldsymbol{b\to s\gamma} Transitions

We calculate the electro- and chromomagnetic dipole coefficients $C_{7\gamma,8g}$ and $\tilde C_{7\gamma,8g}$ in the context of the minimal Randall-Sundrum (RS) model with a Higgs sector localized on the IR brane using the five-dimensional (5D) approach, where the coefficients are expressed in terms of integrals over 5D propagators. Since we keep the full dependence on the Yukawa matrices, the integral expressions are formally valid to all orders in $v^2/M_{\rm KK}^2$. In addition we relate our results to the expressions obtained in the Kaluza-Klein (KK) decomposed theory and show the consistency in both pictures analytically and numerically, which presents a non-trivial cross-check. In Feynman-'t Hooft gauge, the dominant corrections from virtual KK modes arise from the scalar parts of the $W^\pm$-boson penguin diagrams, including the contributions from the scalar component of the 5D gauge-boson field and from the charged Goldstone bosons in the Higgs sector. The size of the KK corrections depends on the parameter $y_\ast$, which sets the upper bound for the anarchic 5D Yukawa matrices. We find that for $y_\ast\gtrsim1$ the dominant KK corrections are proportional to $y_\ast^2$. We discuss the phenomenological implications of our results for the branching ratio ${\rm Br}(\bar B\to X_s\gamma)$, the time-dependent CP asymmetry $S_{K^*\gamma}$, the direct CP asymmetry $A_{\rm CP}^{b\to s\gamma}$ and the CP asymmetry difference $\Delta A_{\rm CP}^{b\to s\gamma}$. We can derive a lower bound on the first KK gluon resonance of $3.8\,$TeV for $y_\ast=3$, requiring that at least $10\%$ of the RS parameter space covers the experimental $2\sigma$ error margins. We further discuss the branching ratio ${\rm Br}(\bar B\to X_sl^+l^-)$ and compare our predictions for $C_{7\gamma,9,10}$ and $\tilde C_{7\gamma,9,10}$ with phenomenological results derived from model-independent analyses.Comment: 44 pages plus appendix, 10 figures, added equations (58) and (61

Higgs Couplings and Phenomenology in a Warped Extra Dimension

We present a comprehensive description of the Higgs-boson couplings to Standard Model fermions and bosons in Randall-Sundrum (RS) models with a Higgs sector localized on or near the infra-red brane. The analytic results for all relevant Higgs couplings including the loop-induced couplings to gluons and photons are summarized for both the minimal and the custodial RS model. The RS predictions for all relevant Higgs decays are compared with current LHC data, which already exclude significant portions of the parameter space. We show that the latest measurements are sensitive to KK gluon masses up to $20\, \rm{TeV} \times (y_*/3)$ at $95\%$ confidence level for anarchic 5D Yukawa couplings bounded from above by $|(Y_f)_{ij}| < y_*$. We also derive the sensitivity levels attainable in the high-luminosity run of the LHC and at a future linear collider.Comment: 28 pages plus appendix, 9 figures; equation (52) corrected, references update

5D Perspective on Higgs Production at the Boundary of a Warped Extra Dimension

A comprehensive, five-dimensional calculation of Higgs-boson production in gluon fusion is performed for both the minimal and the custodially protected Randall-Sundrum (RS) model, with Standard Model fields propagating in the bulk and the scalar sector confined on or near the IR brane. For the first time, an exact expression for the gg->h amplitude in terms of the five-dimensional fermion propagator is derived, which includes the full dependence on the Higgs-boson mass. Various results in the literature are reconciled and shown to correspond to different incarnations of the RS model, in which the Higgs field is either localized on the IR brane or is described in terms of a narrow bulk state. The results in the two scenarios differ in a qualitative way: the gg->h amplitude is suppressed in models where the scalar sector is localized on the IR brane, while it tends to be enhanced in bulk Higgs models. In both cases, effects of higher-dimensional operators contributing to the gg->h amplitude at tree level are shown to be numerically suppressed under reasonable assumptions. There is no smooth cross-over between the two scenarios, since the effective field-theory description breaks down in the transition region. A detailed phenomenological analysis of Higgs production in various RS scenarios is presented, and for each scenario the regions of parameter space already excluded by LHC data are derived.Comment: 44 pages (plus appendices), 6 figures; several improvements of the discussion, new section estimating the effects of brane-localized higher-dimensional operator

Higgs Decay into Two Photons at the Boundary of a Warped Extra Dimension

A detailed five-dimensional calculation of the Higgs-boson decay into two photons is performed in both the minimal and the custodially protected Randall-Sundrum (RS) model, where the Standard Model (SM) fields propagate in the bulk and the scalar sector lives on or near the IR brane. It is explicitly shown that the $R_\xi$ gauge invariance of the sum of diagrams involving bosonic fields in the SM also applies to the case of these RS scenarios. An exact expression for the $h\to\gamma\gamma$ amplitude in terms of the five-dimensional (5D) gauge-boson and fermion propagators is presented, which includes the full dependence on the Higgs-boson mass. Closed expressions for the 5D $W$-boson propagators in the minimal and the custodial RS model are derived, which are valid to all orders in $v^2/M_\textrm{KK}^2$. In contrast to the fermion case, the result for the bosonic contributions to the $h\to\gamma\gamma$ amplitude is insensitive to the details of the localization of the Higgs profile on or near the IR brane. The various RS predictions for the rate of the $pp\to h\to\gamma\gamma$ process are compared with the latest LHC data, and exclusion regions for the RS model parameters are derived.Comment: 30 pages (plus appendices), 4 figures (V2: several improvements of the discussion, discussion of the lepton sector added, typos corrected, references added

Hunting for warped extra dimensions via loop-induced processes

This thesis is on loop-induced processes in theories with warped extra dimensions where the fermions and gauge bosons are allowed to propagate in the bulk, while the Higgs sector is localized on or near the infra-red brane. These so-called Randall-Sundrum (RS) models have the potential to simultaneously explain the hierarchy problem and address the question of what causes the large hierarchies in the fermion sector of the Standard Model (SM). The Kaluza-Klein (KK) excitations of the bulk fields can significantly affect the loop-level processes considered in this thesis and, hence, could indirectly indicate the existence of warped extra dimensions. The analytical part of this thesis deals with the detailed calculation of three loop-induced processes in the RS models in question: the Higgs production process via gluon fusion, the Higgs decay into two photons, and the flavor-changing neutral current b → sγ. A comprehensive, five-dimensional (5D) analysis will show that the amplitudes of the Higgs processes can be expressed in terms of integrals over 5D propagators with the Higgs-boson profile along the extra dimension, which can be used for arbitrary models with a compact extra dimension. To this end, both the boson and fermion propagators in a warped 5D background are derived. It will be shown that the seemingly contradictory results for the gluon fusion amplitude in the literature can be traced back to two distinguishable, not smoothly-connected incarnations of the RS model. The investigation of the b → sγ transition is performed in the KK decomposed theory. It will be argued that summing up the entire KK tower leads to a finite result, which can be well approximated by a closed, analytical expression.rnIn the phenomenological part of this thesis, the analytic results of all relevant Higgs couplings in the RS models in question are compared with current and in particular future sensitivities of the Large Hadron Collider (LHC) and the planned International Linear Collider. The latest LHC Higgs data is then used to exclude significant portions of the parameter space of each RS scenario. The analysis will demonstrate that especially the loop-induced Higgs couplings are sensitive to KK particles of the custodial RS model with masses in the multi tera-electronvolt range. Finally, the effect of the RS model on three flavor observables associated with the b → sγ transition are examined. In particular, we study the branching ratio of the inclusive decay B → X_s γthe time-dependent CP asymmetry S_{K^{*}γ} in the decay B → K^{*} γ, and the photon polarization parameter in the decay B → K_1 γ. It will be shown that the latter two processes are especially sensitive to the RS corrections considered in this work, which could be probed at future precision experiments.Gegenstand dieser Arbeit ist die Behandlung Schleifen-induzierter Prozesse in Theorien mit gekrümmten Extradimensionen. Diese sogenannten Randall-Sundrum (RS)-Modelle sind besonders attraktive Erweiterungen des Standardmodells (SM), da sie sowohl für das Hierarchieproblem im Eichsektor als auch für die Hierarchien im Flavorsektor Erklärungen liefern können. Die Arbeit fokussiert sich auf RS-Modelle mit Fermionen und Bosonen im Bulk und einem Higgs-Sektor auf bzw. nahe der Infrarot-Brane. Die Kaluza-Klein (KK)-Anregungen der Bulkfelder können signifikant zu den in dieser Arbeit behandelten Schleifen-induzierten Prozessen beitragen und daher indirekt auf die Existenz von gekrümmten Extradimensionen schließen lassen. Der analytische Teil dieser Arbeit befasst sich mit der detaillierten Berechnung von drei Schleifen-induzierten Prozessen in o.g. RS-Modellen: dem Higgs-Produktionsprozess über Gluonfusion, dem Higgszerfall in zwei Photonen und dem Flavor ändernden neutralen Strom b → sγ. Eine ausführliche, fünfdimensionale (5D) Analyse wird zeigen, dass die Amplituden der Higgsprozesse als Integrale über 5D Propagatoren mit dem Higgsprofil entlang der kompakten Extradimension ausgedrückt werden können. Zu diesem Zweck werden die 5D Boson- und Fermionpropagatoren in einem gekrümmten 5D Hintergrund hergeleitet, wobei der Fermionpropagator erstmals mit der exakten Abhängigkeit von den Yukawa-Matrizen und der vollen drei-Generationen-Flavorstruktur berechnet wird. Ein wichtiges Ergebnis dieser Arbeit ist, dass die sich widersprechenden Resultate in der Literatur durch zwei sich unterscheidende, nicht stetig ineinander überführbare Versionen des RS-Modells erklärt werden können. Der b → sγ Übergang enthält zwei unendliche KK-Summen und wird deshalb gesondert behandelt. Es wird argumentiert, dass die Summation über alle KK-Moden zu einem endlichen Ergebnis führt, für das ein approximativer Ausdruck hergeleitet wird. Im phänomenologischen Teil der Arbeit werden die Voraussagen für alle wichtigen Higgskopplungen sowohl mit den gegenwärtigen als auch den zukünftigen Sensitivitäten des Large Hadron Collider (LHC) und dem geplanten International Linear Collider verglichen. Die neuesten Higgs-Daten des LHC werden dazu verwendet um signifikante Regionen des Parameterraums jedes RS-Szenarios auszuschließen. Die Analyse wird zeigen, dass die Higgskopplungen sensitiv auf KK-Teilchen sind, deren Massen bis in den multi-Teraelektronenvolt-Bereich reichen. Abschließend werden die Auswirkungen des RS-Modells auf drei auf b → sγ basierenden Flavor-Observablen untersucht. Speziell wird auf das Verzweigungsverhältnis des inklusiven Zerfalls B → X_s γ, die zeitabhängige CP-Asymmetrie S_{K^{*}γ} im Zerfall B → K^{*} γ und auf die Polarisation des Photons im Zerfall B → K_1 γ eingegangen. Es wird gezeigt, dass die letzteren beiden Prozesse sensitiv auf die in der Arbeit gefundenen RS Korrekturen sind, was durch zukünftige, sehr genaue Messungen einen Hinweis auf die Existenz von gekrümmten Extradimensionen geben könnte