Intertwinors on Functions over the Product of Spheres

We give explicit formulas for the intertwinors on the scalar functions over the product of spheres with the natural pseudo-Riemannian product metric using the spectrum generating technique. As a consequence, this provides another proof of the even order conformally invariant differential operator formulas obtained earlier by T. Branson and the present author

Translation to Bundle Operators

We give explicit formulas for conformally invariant operators with leading term an $m$-th power of Laplacian on the product of spheres with the natural pseudo-Riemannian product metric for all $m$.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

LHC Signals from Cascade Decays of Warped Vector Resonances

Recently (arXiv:1608.00526), a new framework for warped higher-dimensional compactifications with "bulk" standard model (SM) was proposed: in addition to the UV (Planck scale) and IR (a couple of TeV) branes, there is an intermediate brane, taken to be around 10 TeV. The SM matter and Higgs fields propagate from the UV brane down to this intermediate brane only, while gauge and gravity fields propagate in the entire bulk. Such a configuration renders the lightest gauge Kaluza-Klein (KK) states within LHC reach, simultaneously satisfying flavor and CP constraints. In addition, the usual leading decay modes of the lightest KK gauge bosons into top and Higgs bosons are suppressed. This effect permits erstwhile subdominant channels to become significant. These include flavor-universal decays to SM fermions and Higgs bosons, and a novel channel - decay to a radion and a SM gauge boson, followed by radion decay to a pair of SM gauge bosons. In this work, we first delineate the parameter space where the above mentioned cascade decay of gauge KK particles dominates, and thereby can be the discovery mode at the LHC. We then perform a detailed analysis of the LHC signals from this model, finding that 300/fb suffices for evidence of KK-gluon in tri-jet, jet + di-photon and jet + di-boson channels. However, KK photon in photon + di-jet, and KK-W in leptonic W + di-jet require 3000/fb. The crucial feature of this decay chain is a "double" resonance, i.e. 3-particle and 2-particle invariant mass peaks, corresponding to the KK gauge boson and the radion respectively.Comment: 50 page

Detecting a Boosted Diboson Resonance

New light scalar particles in the mass range of hundreds of GeV, decaying into a pair of $W/Z$ bosons can appear in several extensions of the SM. The focus of collider studies for such a scalar is often on its direct production, where the scalar is typically only mildly boosted. The observed $W/Z$ are therefore well-separated, allowing analyses for the scalar resonance in a standard fashion as a low-mass diboson resonance. In this work we instead focus on the scenario where the direct production of the scalar is suppressed, and it is rather produced via the decay of a significantly heavier (a few TeV mass) new particle, in conjunction with SM particles. Such a process results in the scalar being highly boosted, rendering the $W/Z$'s from its decay merged. The final state in such a decay is a "fat" jet, which can be either four-pronged (for fully hadronic $W/Z$ decays), or may be like a $W/Z$ jet, but with leptons buried inside (if one of the $W/Z$ decays leptonically). In addition, this fat jet has a jet mass that can be quite different from that of the $W/Z$/Higgs/top quark-induced jet, and may be missed by existing searches. In this work, we develop dedicated algorithms for tagging such multi-layered "boosted dibosons" at the LHC. As a concrete application, we discuss an extension of the standard warped extra-dimensional framework where such a light scalar can arise. We demonstrate that the use of these algorithms gives sensitivity in mass ranges that are otherwise poorly constrained.Comment: 33 pages, 13 figure

Dedicated Strategies for Triboson Signals from Cascade Decays of Vector Resonances

New colorless electroweak (EW) charged spin-1 particles with mass of a few TeV arise in numerous extensions of the Standard Model (SM). Decays of such a vector into a pair of SM particles, either fermions or EW bosons, are well studied. Many of these models have an additional scalar, which can lead to (and even dominate in certain parameter regions) a novel decay channel for the heavy vector particles instead - into a SM EW boson and the scalar, which subsequently decays into a SM EW boson pair. In this work, we focus on the scalar being relatively heavy, roughly factor of two lighter than the vector particles, rendering its decay products well separated. Such a cascade decay results in a final state with three isolated bosons. We argue that for this "triboson" signal the existing diboson searches are not quite optimal due to combinatorial ambiguity for three identical bosons, and in addition, due to a relatively small signal cross-section determined by the heaviness of the decaying vector particle. In order to isolate the signal, we demonstrate that tagging all three bosons, followed by use of the full triboson invariant mass distribution as well as that of appropriate subsets of dibosons, is well motivated. We develop these general strategies in detail within the context of a specific class of models that are based on extensions of the standard warped extra-dimensional scenario. We also point out that a similar analysis would apply to models with an enlarged EW gauge sector in four dimensions, even if they involve a different Lorentz structure for the relevant couplings

Spectrum generating on twistor bundle

summary:Spectrum generating technique introduced by Ólafsson, Ørsted, and one of the authors in the paper (Branson, T., Ólafsson, G. and Ørsted, B., Spectrum generating operators, and intertwining operators for representations induced from a maximal parabolic subgroups, J. Funct. Anal. 135 (1996), 163–205.) provides an efficient way to construct certain intertwinors when $K$-types are of multiplicity at most one. Intertwinors on the twistor bundle over $S^1\times S^{n-1}$ have some $K$-types of multiplicity 2. With some additional calculation along with the spectrum generating technique, we give explicit formulas for these intertwinors of all orders