Rare FCNC top, beauty and charm decays

Rare flavour changing neutral current (FCNC) decays of top, beauty and charm quarks can provide a powerful probe for as yet unobserved particles. Recent results on FCNC $b \to s$, $c \to u$ and $t$ transitions from the LHC experiments are reviewed. Particular attention is paid to the angular distribution of the $B^{0} \to K^{*0} \mu^{+} \mu^{-}$ decay, where a measurement performed by LHCb shows a local discrepancy of 3.7 standard deviations with respect to the SM prediction. Using the decay $B^{+} \to K^{+}\pi^{-}\pi^{+}\gamma$, LHCb have also been able to demonstrate the polarisation of photons produced in $b \to s\gamma$ transitions. More work is needed both experimentally and theoretically to understand if the Standard Model description of these rare FCNC processes is correct.Comment: Proceedings for LHCP 2014 conferenc

Electroweak penguin decays at LHCb

Promising ways to search for New Physics effects in radiative penguin decays are in the angular analysis of $B_{d} \rightarrow K^{*0} \mu^{+}\mu^{-}$, in the measurement of direct CP violation in \B_{d} \rightarrow K^{*0}\mu^{+}\mu^{-} and a time dependent analysis of $B_{s} \rightarrow \phi \gamma$. All of these studies are being pursued at LHCb. First results will be shown from the 2010 and early 2011 data, with particular emphasis on $B_{d} \rightarrow K^{*0} \mu^{+}\mu^{-}$.Comment: Proceedings of the DPF-2011 Conferenc

Chord Diagrams and Gauss Codes for Graphs

Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study of spatial graphs. We will define chord diagrams for planar embeddings of planar graphs and their intersection graphs, and prove some basic results. Then, as an application, we will introduce Gauss codes for immersions of graphs in the plane and give algorithms to determine whether a particular crossing sequence is realizable as the Gauss code of an immersed graph.Comment: 20 pages, many figures. This version has been substantially rewritten, and the results are stronge

Performance Analysis of Spectral Clustering on Compressed, Incomplete and Inaccurate Measurements

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and partially observed signals respectively. We combine the distance preserving measurements of compressed sensing and matrix completion with the power of robust spectral clustering. Our analysis provides rigorous bounds on how small errors in the affinity matrix can affect the spectral coordinates and clusterability. This work generalizes the current perturbation results of two-class spectral clustering to incorporate multi-class clustering with k eigenvectors. We thoroughly track how small perturbation from using compressed sensing and matrix completion affect the affinity matrix and in succession the spectral coordinates. These perturbation results for multi-class clustering require an eigengap between the kth and (k+1)th eigenvalues of the affinity matrix, which naturally occurs in data with k well-defined clusters. Our theoretical guarantees are complemented with numerical results along with a number of examples of the unsupervised organization and clustering of image data

An Introduction to Virtual Spatial Graph Theory

Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results. We state the definitions, provide some examples, and survey the known results. We hope that this paper will help lead to rapid development of the area.Comment: 9 pages, 7 figures, presented at the International Workshop on Knot Theory for Scientific Objects at Osaka City University, March 200

Angular distribution of polarised Λb\Lambda_b baryons decaying to Λℓ+ℓ−\Lambda \ell^+\ell^-

Rare $b \to s\ell^+\ell^-$ flavour-changing-neutral-current processes provide important tests of the Standard Model of particle physics. Angular observables in exclusive $b \to s\ell^+\ell^-$ processes can be particularly powerful as they allow hadronic uncertainties to be controlled. Amongst the exclusive processes that have been studied by experiments, the decay $\Lambda_b\to \Lambda\ell^+\ell^-$ is unique in that the $\Lambda_b$ baryon can be produced polarised. In this paper, we derive an expression for the angular distribution of the $\Lambda_b\to \Lambda\ell^+\ell^-$ decay for the case where the $\Lambda_b$ baryon is produced polarised. This extends the number of angular observables in this decay from 10 to 34. Standard Model expectations for the new observables are provided and the sensitivity of the observables is explored under a variety of new physics models. At low-hadronic recoil, four of the new observables have a new short distance dependence that is absent in the unpolarised case. The remaining observables depend on the same short distance contributions as the unpolarised observables, but with different dependence on hadronic form-factors. These relations provide possibilities for novel tests of the SM that could be carried out with the data that will become available at the LHC or a future $e^+e^-$ collider

A tidally interacting disk in the young triple system WL 20?

We present high-resolution λ = 2.7 mm imaging of the close triple pre-main-sequence system WL 20. Compact dust emission with integrated flux density of 12.9 ± 1.3 mJy is associated with two components of the triple system, WL 20W and WL 20S. No emission above a 3 σ level of 3.9 mJy is detected toward the third component, WL 20E, which lies 3."17 (400 AU) due east in projection from its neighbors. A possibly warped structure of ~0.1 M_☉ and ≤3."2 extent encompasses WL 20W and WL 20S, which have a projected separation of 2."25 (~280 AU) along a north-south axis. This structure is most likely a tidally disrupted disk surrounding WL 20S. New near-infrared spectra of the individual components show a remarkable similarity between the two T Tauri stars of the system: WL 20E has a K7 spectral type (T_eff = 4040 K) with r_K = 0.2, and WL 20W has an M0 spectral type (T_eff = 3800 K) with r_K = 0.2. The spectrum of WL 20S is consistent with that of a source intrinsically similar to WL 20W, with r_K < 0.9, but seen through an A_V = 25 in addition to the A_V = 16.3 to the system as a whole. Taken together, these millimeter and infrared data help explain the peculiar nature of the infrared companion, WL 20S, as resulting from a large enhancement in its dusty, circumstellar environment in relation to its companions

Intrinsic Linking and Knotting in Virtual Spatial Graphs

We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that these filtrations are descending and non-terminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, we introduce the {\it virtual unknotting number} of a knot, and show that any knot with non-trivial Jones polynomial has virtual unknotting number at least 2.Comment: 13 pages, 13 figure