Alexander Knochel

The Higgs mass from a string-theoretic perspective

Abstract The Higgs quartic coupling λ has now been indirectly measured at the electroweak scale. Assuming no new low-scale physics, its running is known and, together with gauge and Yukawa couplings, it is a crucial new piece of information constraining UV completions of the Standard Model. In particular, supersymmetry broken at an intermediate or high energy scale with tan β = 1 (i.e. λ = 0 ) is consistent with present data and has an independent theoretical appeal. We analyze the possible string-theoretic motivations for tan β = 1 (including both the shift-symmetry and the more economical variant of a Z 2 symmetry) in a Higgs sector realized on either 6- or 7-branes. We identify specific geometries where λ ≃ 0 may arise naturally and specify the geometrical problems which need to be solved to determine its precise value in the generic case. We then analyze the radiative corrections to λ. Finally we show that, in contrast to naive expectations, λ 0 at the SUSY breaking scale is also possible. Specifically, string theory may produce an MSSM plus chiral singlet at a very high scale, which immediately breaks to a non-SUSY Standard Model with λ 0 . This classically unstable theory then becomes metastable through running towards the IR.

Discriminating 4D supersymmetry from its 5D warped version

In the scenario where only superpartners were produced at the Large Hadron Collider, how one could determine whether the supersymmetric model pointed out is 4-dimensional or higher-dimensional ? We propose and develop a series of tests for discriminating between a pure supersymmetry (SUSY) and a SUSY realized within the well-motivated warped geometry a la Randall-Sundrum (RS). Two of these tests make use of some different patterns arising in the squark/slepton mass spectrum. The other distinctive RS SUSY feature is the possibly larger (even dominant) Higgs boson decay branching ratios into sleptons, compared to pure SUSY. Techniques for pinning up the presence of soft SUSY breaking terms on the TeV-brane are also suggested, based on the analysis of stop pair production at the International Linear Collider. For all these phenomenological studies, we had first to derive the 4-dimensional (4D) effective couplings and mass matrices of the sfermions and Higgs bosons in RS SUSY. The localization of Higgs bosons, characteristic of RS, leads to singularities in their couplings which are regularized by the exchange contribution of infinite towers of Kaluza-Klein (KK) scalar modes with Dirichlet-Dirichlet boundary conditions. A general method is provided for this regularization, based on the completeness relation. The sfermion masses are obtained either from integrating out those specific KK towers or by treating their mixing effects. Finally, we show at the one-loop level how all quadratic divergences in the Higgs mass cancel out for any cut-off, due to 5D SUSY and to 5D anomaly cancellation; the analytical way followed here also allows a justification of the infinite KK summation required for the so-called KK regularization in 5D SUSY, which has motivated a rich literature.

The Price of Neutrino Superluminality Continues to Rise

Abstract We revisit the model building challenges that one faces when trying to reconcile the OPERA claim of neutrino superluminality with other observational constraints. The severity of the supernova bound and of the kinematical constraints of Cohen–Glashow type lead us to focus on scenarios where all types of particles are superluminal inside matter. In contrast to the Dvali–Vikman proposal, this matter effect needs to be very short-ranged to avoid constraints from experiments on the Earthʼs surface in low-density environments. Due to this short range, the interaction underlying such a matter effect would have to be far stronger than permitted by fifth-force bounds. As a conceivable way out we suggest to make the matter effect “binary”, i.e., dense matter does not directly trigger superluminality, but merely induces the transition to a different phase of some weakly coupled hidden sector. This phase exhibits spontaneous Lorentz violation or at least a stronger than usual mediation of some residual Lorentz violation to all matter. The effect has not been observed before since we have never before been able to measure the velocity of high-energy particles in dense matter with sufficient precision.

Supersymmetric extensions and dark matter in models of warped Higgsless electroweak symmetry breaking

We introduce a minimal supersymmetric extension of a Higgsless model for electroweak symmetry breaking in a warped extra dimension. In contrast to the nonsupersymmetric version, our model naturally contains a candidate for cold dark matter. No Kaluza-Klein parity is required, because its stability is guaranteed by an R-parity. We discuss the regions in parameter space that are compatible with the observed dark matter content of our Universe and are allowed by electroweak precision measurements as well as direct searches.

Theoretical constraints on new generations with and without quarks or neutrinos

Abstract We consider large classes of chiral extensions of the Standard Model, including new quark generations that do not involve additional neutrinos as well as lepton generations without quarks. An analysis of renormalization flows of Yukawa and quartic scalar couplings reveals that additional quarks are not compatible with a scenario of grand unification without violating the strong bounds from direct and Higgs searches at colliders. Constraints from direct searches, electroweak precision observables, and Higgs physics, together with the assumption that additional new physics beyond the extended chiral field content should enter significantly above the TeV scale, allows us to make predictions for searches at the LHC.

Pfadintegrale für Skalarfelder

Wir werden jetzt eine zweite, auf Feynman zuruck gehende Quantisierungsvorschrift kennenlernen, die direkt mit der Lagrange-Dichte arbeitet und vollstandig kovariant ist: die Quantisierung mit Pfadintegralen. Zunachst werden wir ausgehend von der kanonisch quantisierten Theorie einen Ausdruck fur Green’sche Funktionen durch Pfadintegrale herleiten. Basierend auf diesem Ergebnis fuhren wir dann verschiedene erzeugende Funktionale ein und verwenden diese, um Feynman-Graphen aufzustellen und storungstheoretische Streuamplituden zu berechnen.

Regularisierung und Renormierung der QED

Wie schon in der skalaren Feldtheorie treten in der Quantenelektrodynamik divergente Schleifengraphen auf, sobald man uber die fuhrende Ordnung der Storungstheorie hinaus will. In diesem Kapitel lernen wir die notigen Methoden kennen, um Ein-Schleifen-Integrale mit Fermionen und Photonen auszuwerten und die auftretenden Divergenzen wieder systematisch durch Regularisierung und Renormierung zu eliminieren. Wir leiten dann die Renormierungsgruppengleichung fur die elektromagnetische Kopplungskonstante her und wenden sie in einem einfachen Beispiel an. Zum Abschluss diskutieren wir skizzenhaft den Umgang mit infraroten und kollinearen Divergenzen und die dafur relevanten Theoreme, und besprechen anhand eines konkreten Beispiels, zwischen welchen Beitragen sich infrarote Divergenzen in Streuquerschnitten wegheben und welche konzeptionellen Probleme dabei auftreten konnen.

Eichsymmetrien und Ward-Identitäten

In diesem Kapitel werden wir am Beispiel der Quantenelektrodynamik einige Konsequenzen von Eichsymmetrien in quantisierten Feldtheorien ausarbeiten. Dazu leiten wir erst mithilfe der zuvor entwickelten Pfadintegralmethoden die allgemeinen Ward-Identitaten her und untersuchen dann anhand einiger Spezialfalle, was diese Identitaten uns uber die Eigenschaften von Streuamplituden und Propagatoren verraten. Dabei werden wir den Umgang mit Green’schen Funktionen und erzeugenden Funktionalen weiter vertiefen.

Das Dirac-Feld

Dieses Kapitel ist Fermionen mit Spin 1/2 gewidmet. Wir konstruieren zunachst die entsprechenden Darstellungen der Poincare-Gruppe und uben den Umgang mit der Dirac-Algebra. Wir schreiben dann die Dirac-Lagrangedichte auf und untersuchen die Losungen der resultierenden Dirac-Gleichung. All diese Vorarbeiten erlauben es uns dann, das Dirac-Feld kanonisch und mit Pfadintegralen zu quantisieren und die in den vergangenen Kapiteln fur Skalarfelder hergeleiteten Ergebnisse und Methoden zu verallgemeinern. Anhand der Yukawa-Theorie eines Fermions und eines Skalars werden wir uben, Feynman-Graphen mit Fermionen aufzustellen und auszuwerten.

Das klassische Skalarfeld

Die Theorie eines einzelnen Skalarfeldes ohne Wechselwirkungen ist die einfachste nicht-triviale Feldtheorie. Trotzdem konnen wir an diesem Beispiel viele grundlegende Prinzipien und Ideen besprechen, die auch fur die komplizierteren (und realistischeren) Modelle von Feldern mit Spin noch gultig sein werden oder zumindest nur einer Erganzung bedurfen. Auch fur die Behandlung wechselwirkender Theorien werden unsere Erkenntnisse aus diesem Kapitel noch relevant sein, da wir einen storungstheoretischen Ansatz verfolgen, dem stets die wechselwirkungs- freie Theorie als Ausgangspunkt dient. Auf geht’s also zu der Konstruktion unserer ersten Quantenfeldtheorie!