Kaon decays and the flavour problem

After a brief introduction to the so-called flavour problem, we discuss the role of rare K decays in probing the mechanism of quark-flavour mixing. Particular attention is devoted to the formulation of the Minimal Flavour Violation hypothesis, as a general and natural solution to the flavour problem, and to the fundamental role of K -> pi nu nu-bar decays in testing this scenario.Comment: 10 pages, 6 figures, contribution to TH 2002 (Paris, July 2002

Long-distance contribution to the forward-backward asymmetry in decays K+ --> pi+ l+ l-

The long-distance contribution via the two-photon intermediate state to the forward-backward asymmetries in decays K+ --> pi+ l+ l- (l=e and mu) has been studied within the standard model. In order to evaluate the dispersive part of the K+ --> pi+ gamma* gamma* --> pi+ l+ l- amplitude, we employ a phenomenological form factor to soften the ultraviolet behavior of the transition. It is found that, this long-distance transition, although subject to some theoretical uncertainties, can lead to significant contributions to the forward-backward asymmetries, which could be tested in the future high-precise experiments.Comment: 13 pages, 5 figure

K^+ -> pi^+pi^0e^+e^-: a novel short-distance probe

We study the decay K^+ -> pi^+ pi^0 e^+ e^-, currently under analysis by the NA62 Collaboration at CERN. In particular, we provide a detailed analysis of the Dalitz plot for the long-distance, gamma^*-mediated, contributions (Bremsstrahlung, direct emission and its interference). We also examine a set of asymmetries to isolate genuine short-distance effects. While we show that charge asymmetries are not required to test short distances, they provide the best environment for its detection. This constitutes by itself a strong motivation for NA62 to study K^- decays in the future. We therefore provide a detailed study of different charge asymmetries and the corresponding estimated signals. Whenever possible, we make contact with the related processes K^+ -> pi^+ pi^0 gamma and K_L -> pi^+ pi^- e^+ e^- and discuss the advantages of K^+ -> pi^+ pi^0 e^+ e^- over them.Comment: 25 pages, 6 figure

FROM THE DIGITAL TWIN OF ARCHITECTURAL HERITAGE TO THE DEFINITION OF THE CONSTRAINT MAPS. THE CASE STUDY OF THE CASTELLO SFORZESCO IN MILAN

The work presented here is part of the widespread digitisation process that is affecting the world of architecture and cultural heritage. The text reports part of the activities carried out on the Castello Sforzesco in Milan, in collaboration with its Superintendence bodies. This work proposes an innovative way to draft, in a digital environment, 3D constraint maps, capable of describing and protecting the complex system of structures in that area, especially in the subsoil. The activity began with the creation of a georeferenced 3D model of all the existing architectural elements in the analyzed area of the Castle. The work was carried out on the northwest corner of the fortress, the area between the Torre della Colubrina and the Porta del Soccorso. The modeling activity was based both on data obtained from surveys and historical documentation describing structures that are no longer visible. From the 3D model, it was then possible to obtain all useful data to draw up constraint maps in GIS (Geographic Information System) environment. This latter allows multiple interactions both with the normal surface cartographic information (Topographic Database and others) and with the multitude of datasets available for managing the territory and its subsystems. The constraints consider a ‘safety’ offset, applied in all three directions. These maps describe the various three-dimensional areas, referring to the different structures present in the subsoil, within which it is recommended to operate with extreme caution, in relation to the position and conformation of the same identified assets

Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group

We prove geometric $L^p$ versions of Hardy's inequality for the sub-elliptic Laplacian on convex domains $\Omega$ in the Heisenberg group $\mathbb{H}^n$, where convex is meant in the Euclidean sense. When $p=2$ and $\Omega$ is the half-space given by $\langle \xi, \nu\rangle > d$ this generalizes an inequality previously obtained by Luan and Yang. For such $p$ and $\Omega$ the inequality is sharp and takes the form \begin{equation} \int_\Omega |\nabla_{\mathbb{H}^n}u|^2 \, d\xi \geq \frac{1}{4}\int_{\Omega} \sum_{i=1}^n\frac{\langle X_i(\xi), \nu\rangle^2+\langle Y_i(\xi), \nu\rangle^2}{\textrm{dist}(\xi, \partial \Omega)^2}|u|^2\, d\xi, \end{equation} where $\textrm{dist}(\, \cdot\,, \partial \Omega)$ denotes the Euclidean distance from $\partial \Omega$.Comment: 14 page

A holographic approach to low-energy weak interactions of hadrons

We apply the double-trace formalism to incorporate nonleptonic weak interactions of hadrons into holographic models of the strong interactions. We focus our attention upon $\Delta S=1$ nonleptonic kaon decays. By working with a Yang-Mills--Chern-Simons 5-dimensional action, we explicitly show how, at low energies, one recovers the $\Delta S=1$ weak chiral Lagrangian for both the anomalous and nonanomalous sectors. We provide definite predictions for the low energy coefficients in terms of the AdS metric and argue that the double-trace formalism is a 5-dimensional avatar of the Weak Deformation Model introduced long ago by Ecker et al. As a significant phenomenological application, we reassess the $K\to 3\pi$ decays in the light of the holographic model. Previous models found a fine-tuned cancellation of resonance exchange in these decays, which was both conceptually puzzling and quantitatively in disagreement with experimental results. The holographic model we build is an illustrative counterexample showing that the cancellation encountered in the literature is not generic but a model-dependent statement and that agreement with experiment can be obtained.Comment: 20 page

Dynamics of Post-Injection Fuel Flow in Mini-Sac Diesel Injectors Part 1: Admission of 1 External Gases and Implications for Deposit Formation

Samples of unadditized, middle distillate diesel fuel were injected through real-size optically accessible mini-sac diesel injectors into ambient air at common rail pressures of 250 bar and 350 bar respectively. High-resolution images of white light scattered from the internal mini-sac and nozzle flow were captured on a high-speed monochrome video camera. Following the end of each injection, the momentum-driven evacuation of fuel liquid from the mini-sac and nozzle holes resulted in the formation of a vapour cloud and bubbles in the mini-sac, and vapour capsules in the nozzle holes. This permitted external gas to gain entrance to the nozzle holes. The diesel fuel in the mini-sac was observed to rotate with large initial vorticity, which decayed until the fuel became stationary. The diesel fuel remaining in the nozzle holes was observed to move inwards towards the mini-sac or outwards towards the nozzle exit in concert with the rotational flow in the mini-sac. The mini-sac bubbles’ internal pressure differences revealed that the bubbles must have contained previously dissolved oxygen and nitrogen. Under diesel engine operating conditions, this multi-phase mixture would be highly reactive and could initiate local pyrolysis and/or oxidation reactions. Finally, the dynamical behaviour of the diesel fuel in the nozzle holes would support the admission of external hot combustion gases into the nozzle holes, establishing the conditions for oxidation/pyrolysis reactions with surrounding liquid fuel films

TORCH: A Cherenkov Based Time-of-Flight Detector

TORCH is a novel high-precision time-of-flight detector suitable for large area applications and covering the momentum range up to 10 GeV/c. The concept uses Cherenkov photons produced in a fused silica radiator which are propagated to focussing optics coupled to fast photodetectors. For this purpose, custom MCP-PMTs are being produced in collaboration with industrial partners. The development is divided into three phases. Phase 1 addresses the lifetime requirements for TORCH, Phase 2 will customize the MCP-PMT granularity and Phase 3 will deliver prototypes that meet the TORCH requirements. Phase 1 devices have been successfully delivered and initial tests show stable gain performance for integrated anode current >5 C/cm2 and a single photon time resolution of ≤ 30 ps. Initial simulations indicate the single photon timing resolution of the TORCH detector will be ∼70 ps

The s ---> d gamma decay in and beyond the Standard Model

The New Physics sensitivity of the s ---> d gamma transition and its accessibility through hadronic processes are thoroughly investigated. Firstly, the Standard Model predictions for the direct CP-violating observables in radiative K decays are systematically improved. Besides, the magnetic contribution to epsilon prime is estimated and found subleading, even in the presence of New Physics, and a new strategy to resolve its electroweak versus QCD penguin fraction is identified. Secondly, the signatures of a series of New Physics scenarios, characterized as model-independently as possible in terms of their underlying dynamics, are investigated by combining the information from all the FCNC transitions in the s ---> d sector.Comment: 54 pages, 14 eps figure