Transience of continuous-time conservative random walks

We consider two continuous-time generalizations of conservative random walks introduced in [J.Englander and S.Volkov (2022)], an orthogonal and a spherically-symmetrical one; the latter model is known as {\em random flights}. For both models, we show the transience of the walks when $d\ge 2$ and the rate of changing of direction follows power law $t^{-\alpha}$, $0<\alpha\le 1$, or the law $(\ln t)^{-\beta}$ where $\beta>2$

Search for Excited Quarks in qqˉ→γγq\bar{q} \to \gamma\gamma at the LHC

If quarks are composite particles, then excited states are expected to play a r\^ole in the Large Hadron Collider phenomena. Concentrating on virtual effects, and using a large part of the CMS detection criteria, we present here a realistic examination of their effect in diphoton production at the LHC. For various luminosities, we present the 99 % confidence limit (CL) achievable in $\Lambda-M_{q*}$ parameter space where $\Lambda$ is the compositeness scale and M_{q^*} the mass of the state. For a q^* of mass 0.5 TeV, $\Lambda \leq 1.55 (2.95)$ can be excluded at 99% CL with 30 (200)${\rm fb}^{-1}$ integrated luminosity.Comment: 11 pages, 11 figure

A New Spatio-Temporal Model Exploiting Hamiltonian Equations

The solutions of Hamiltonian equations are known to describe the underlying phase space of the mechanical system. In Bayesian Statistics, the only place, where the properties of solutions to the Hamiltonian equations are successfully applied, is Hamiltonian Monte Carlo. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations, incorporating appropriate stochasticity via Gaussian processes. The resultant sptaio-temporal process, continuously varying with time, turns out to be nonparametric, nonstationary, nonseparable and no-Gaussian. Besides, the lagged correlations tend to zero as the spatio-temporal lag tends to infinity. We investigate the theoretical properties of the new spatio-temporal process, along with its continuity and smoothness properties. Considering the Bayesian paradigm, we derive methods for complete Bayesian inference using MCMC techniques. Applications of our new model and methods to two simulation experiments and two real data sets revealed encouraging performance

Probing the light radion through diphotons at the Large Hadron Collider

A radion in a scenario with a warped extra dimension can be lighter than the Higgs boson, even if the Kaluza-Klein excitation modes of the graviton turn out to be in the multi-TeV region. The discovery of such a light radion would be gateway to new physics. We show how the two-photon mode of decay can enable us to probe a radion in the mass range 60 - 110 GeV. We take into account the diphoton background, including fragmentation effects, and include cuts designed to suppress the background to the maximum possible extent. Our conclusion is that, with an integrated luminosity of 3000 $\rm fb^{-1}$ or less, the next run of the Large Hadron Collider should be able to detect a radion in this mass range, with a significance of 5 standard deviations or more.Comment: 24 pages, 4 figures, Version published in Phys. Rev.

Pulse Shape Simulation and Discrimination using Machine-Learning Techniques

An essential metric for the quality of a particle-identification experiment is its statistical power to discriminate between signal and background. Pulse shape discrimination (PSD) is a basic method for this purpose in many nuclear, high-energy and rare-event search experiments where scintillation detectors are used. Conventional techniques exploit the difference between decay-times of the pulses from signal and background events or pulse signals caused by different types of radiation quanta to achieve good discrimination. However, such techniques are efficient only when the total light-emission is sufficient to get a proper pulse profile. This is only possible when adequate amount of energy is deposited from recoil of the electrons or the nuclei of the scintillator materials caused by the incident particle on the detector. But, rare-event search experiments like direct search for dark matter do not always satisfy these conditions. Hence, it becomes imperative to have a method that can deliver a very efficient discrimination in these scenarios. Neural network based machine-learning algorithms have been used for classification problems in many areas of physics especially in high-energy experiments and have given better results compared to conventional techniques. We present the results of our investigations of two network based methods \viz Dense Neural Network and Recurrent Neural Network, for pulse shape discrimination and compare the same with conventional methods.Comment: 18 pages, 39 figure

The Discrete Voronoi game in &Ropf;\u3csup\u3e2\u3c/sup\u3e

In this paper we study the last round of the discrete Voronoi game in ℝ2, a problem which is also of independent interest in competitive facility location. The game consists of two players P1 and P2, and a finite set U of users in the plane. The players have already placed two disjoint sets of facilities F and S, respectively, in the plane. The game begins with P1 placing a new facility followed by P2 placing another facility, and the objective of both the players is to maximize their own total payoffs. In this paper we propose polynomial time algorithms for determining the optimal strategies of both the players for arbitrarily located existing facilities F and S. We show that in the L1 and the L∞ metrics, the optimal strategy of P2, given any placement of P1, can be found in O(n log n) time, and the optimal strategy of P1 can be found in O(n5 log n) time. In the L2 metric, the optimal strategies of P2 and P1 can be obtained in O(n2) and O(n2) and O(n8) times, respectively

Quark Excitations Through the Prism of Direct Photon Plus Jet at the LHC

The quest to know the structure of matter has resulted in various theoretical speculations wherein additional colored fermions are postulated. Arising either as Kaluza-Klein excitations of ordinary quarks, or as excited states in scenarios wherein the quarks themselves are composites, or even in theories with extended gauge symmetry, the presence of such fermions ($q^*$) can potentially be manifested in $\gamma + jet$ final states at the LHC. Using unitarized amplitudes and the CMS setup, we demonstrate that in the initial phase of LHC operation (with an integrated luminosity of 200 \pb^{-1}) one can discover such states for a mass upto 2.0 TeV. The discovery of a $q^*$ with a mass as large as $\sim$5 TeV can be acheived for an integrated luminosity of \sim 140 \fb^{-1}. We also comment on the feasibility of mass determination.Comment: 21 pages, 19 figure