A Passive Hopper With Lossless Collisions

A passive vertical hopping robot is here highly idealised as two vertically arranged masses acted on by gravity and coupled by a linear spring. The lower mass makes dead (e = 0) collisions with the rigid ground. The equations of motion can be reduced to a one dimensional map. Fixed points of the map are found in which case the robot hops incessantly. For these conservative solutions the lower mass collides with the ground with zero impact velocity. The interval of attraction for these conservative fixed points depends on system parameters.

Flux tube model signals for baryon correlations in heavy ion collisions

The flux tube model offers a pictorial description of what happens during the deconfinement phase transition in QCD. The three-point vertices of a flux tube network lead to formation of baryons upon hadronization. Therefore, correlations in the baryon number distribution at the last scattering surface are related to the preceding pattern of the flux tube vertices in the quark-gluon plasma, and provide a signature of the nearby deconfinement phase transition. I discuss the nature of the expected signal, and how to extract it from the experimental data for heavy ion collisions at RHIC and LHC.

Generalized top-spin analysis and new physics in e(+)e(-) collisions with beam polarization

A generalized top-spin analysis proposed some time ago in the context of the standard model and subsequently studied in varying contexts is now applied primarily to the case of e(+)e(-) -> t (tww) over bar with transversely polarized beams. This extends our recent work with new physics couplings of scalar (S) and tensor (T) types. We carry out a comprehensive analysis assuming only the electron beam to be transversely polarized, which is sufficient to probe these interactions, and also eliminates any azimuthal angular dependence due to the standard model or new physics of the vector (V) and axial-vector (A) type interactions. We then consider new physics of the general four-Fermi type of V and A type with both beams transversely polarized and discuss implications with longitudinal polarization as well. The generalized spin bases are all investigated in the presence of either longitudinal or transverse beam polarization to look for appreciable deviation from the SM prediction in case of the new physics. 90% confidence level limits are obtained on the interactions for the generalized spin bases with realistic integrated luminosity. In order to achieve this we present a general discussion based on helicity amplitudes and derive a general transformation matrix that enables us to treat the spin basis. We find that beamline basis combined with transverse polarization provides an excellent window of opportunity both for S, T and V, A new physics, followed by the off-diagonal basis. The helicity basis is shown to be the best in case of longitudinal polarization to look for new physics effects due to V and A. DOI: 10.1103/PhysRevD.86.114019

Top-spin analysis of new scalar and tensor interactions in e(+) e (-) collisions with transverse beam polarization

The top polarization at the International Linear Collider (ILC) with transverse beam polarization is utilized in the process to probe interactions of the scalar and tensor type beyond the Standard Model and to disentangle their individual contributions. Confidence level limits of 90% are presented on the interactions with realistic integrated luminosity and are found to improve by an order of magnitude compared to the case when the spin of the top quark is not measured. Sensitivities of the order of a few times 10 (-aEuro parts per thousand 3) TeV (-aEuro parts per thousand 2) for real and imaginary parts of both scalar and tensor couplings at and 800 GeV with an integrated luminosity of 500 fb (-aEuro parts per thousand 1) and completely polarized beams are shown to be possible.

Beam polarization effects in the radiative production of lightest neutralinos in e(+)e(-) collisions in supersymmetric grand unified models

We study the production of the lightest neutralinos in the process e(+)e(-) -> chi(0)(1)chi(0)(1)gamma in supersymmetric grand unified models for the International Linear Collider energies with longitudinally polarized beams. We consider cases where the standard model gauge group is unified into the grand unified gauge groups SU(5), or SO(10). We have carried out a comprehensive study of this process in the SU(5) and SO(10) grand unified theories which includes the QED radiative corrections. We compare and contrast the dependence of the signal cross section on the grand unified gauge group, and on the different representations of the grand unified gauge group, when the electron and positron beams are longitudinally polarized. To assess the feasibility of experimentally observing the radiative production process, we have also considered in detail the background to this process coming from the radiative neutrino production process e(+)e(-)-> nu(nu) over bar gamma with longitudinally polarized electron and positron beams. In addition we have also considered the supersymmetric background coming from the radiative production of scalar neutrinos in the process e(+)e(-) -> (nu) over tilde(nu) over tilde*gamma with longitudinally polarized beams. The process can be a major background to the radiative production of neutralinos when the scalar neutrinos decay invisibly.

A model for probing large distance behaviour in high energy collisions

We apply to total cross-sections our model for soft gluon resummation in the infrared region. The model aims to probe large distance interactions in QCD. Our ansatz for an effective coupling for gluons and quarks in the infrared region follows an inverse power law which is singular but integrable. In the context of an eikonal formalism with QCD mini-jets, we study total hadronic cross-sections for protons, pions, photons. We estimate the total inelastic cross-section at LHC comparing with recent measurements and update previous results for survival probability.

EXPERIMENTAL AND THEORETICAL STUDY OF BINARY DROPLET HEAD-ON COLLISIONS IN MEMS

The experimental and theoretical investigations into the head-on collision between a landing droplet with another one resting on the PDMS substrate were addressed in this talk. The colliding process of the two droplets was recorded with highspeed camera. Four different responses after collision were observed in our experiments: complete rebound, coalescence, partial rebound with conglutination, and coalescence accompanied by conglutination. The contact time between the two colliding droplets was found to be in the range of 10-20 milliseconds. For the complete bouncing case, Hertz contact model was applied to estimate the contact time of the binary head-on colliding droplets with both the droplets considered as elastic bodies. The estimated contact time was in good agreement with the experimental result.

Searches for new symmetries in pp collisions with the razor kinematic variables at √s = 7 TeV

The construction and LHC phenomenology of the razor variables M_R, an event-by-event indicator of the heavy particle mass scale, and R, a dimensionless variable related to the transverse momentum imbalance of events and missing transverse energy, are presented.  The variables are used  in the analysis of the first proton-proton collisions dataset at CMS  (35 pb^-1) in a search for superpartners of the quarks and gluons, targeting indirect hints of dark matter candidates in the context of supersymmetric theoretical frameworks. The analysis produced the highest sensitivity results for SUSY to date and extended the LHC reach far beyond the previous Tevatron results.  A generalized inclusive search is subsequently presented for new heavy particle pairs produced in √s = 7 TeV proton-proton collisions at the LHC using 4.7±0.1 fb^-1 of integrated luminosity from the second LHC run of 2011.  The selected events are analyzed in the 2D razor-space of M_R and R and the analysis is performed in 12 tiers of all-hadronic, single and double leptons final states in the presence and absence of b-quarks, probing the third generation sector using the event heavy-flavor content.   The search is sensitive to generic supersymmetry models with minimal assumptions about the superpartner decay chains. No excess is observed in the number or shape of event yields relative to Standard Model predictions. Exclusion limits are derived in the CMSSM framework with  gluino masses up to 800 GeV and squark masses up to 1.35 TeV excluded at 95% confidence level, depending on the model parameters. The results are also interpreted for a collection of simplified models, in which gluinos are excluded with masses as large as 1.1 TeV, for small neutralino masses, and the first-two generation squarks, stops and sbottoms are excluded for masses up to about 800, 425 and 400 GeV, respectively.

With the discovery of a new boson by the CMS and ATLAS experiments in the γ-γ and 4 lepton final states, the identity of the putative Higgs candidate must be established through the measurements of its properties. The spin and quantum numbers are of particular importance, and we describe a method for measuring the J^PC of this particle using the observed signal events in the H to ZZ^* to 4 lepton channel developed before the discovery. Adaptations of the razor kinematic variables are introduced for the H to WW^* to 2 lepton/2 neutrino channel, improving the resonance mass resolution and increasing the discovery significance. The prospects for incorporating this channel in an examination of the new boson J^PC is discussed, with indications that this it could provide complementary information to the H to ZZ^* to 4 lepton final state, particularly for measuring CP-violation in these decays.

Application of the Schwinger multichannel method to multichannel studies of electronically inelastic electron-molecule collisions

We have applied the Schwinger Multichannel Method(SMC) to the study of electronically inelastic, low energy electron-molecule collisions. The focus of these studies has been the assessment of the importance of multichannel coupling to the dynamics of these excitation processes. It has transpired that the promising quality of results realized in early SMC work on such inelastic scattering processes has been far more difficult to obtain in these more sophisticated studies.

We have attempted to understand the sources of instability of the SMC method which are evident in these multichannel studies. Particular instances of such instability have been considered in detail, which indicate that linear dependence, failure of the separable potential approximation, and difficulties in converging matrix elements involving recorrelation or Q-space terms all conspire to complicate application of the SMC method to these studies. A method involving singular value decomposition(SVD) has been developed to, if not resolve these problems, at least mitigate their deleterious effects on the computation of electronically inelastic cross sections.

In conjunction with this SVD procedure, the SMC method has been applied to the study of the H_2 , H_2O, and N_2 molecules. Rydberg excitations of the first two molecules were found to be most sensitive to multichannel coupling near threshold. The (3σ_g → 1π_g ) and (1π_u → 1π_g) valence excitations of the N_2 molecule were found to be strongly influenced by the choice of channel coupling scheme at all collision energies considered in these studies.

Studies of Zγ production and constraints on anomalous triple gauge couplings in pp collisions at √s = 7 TeV

In this thesis, we test the electroweak sector of the Standard Model of particle physics through the measurements of the cross section of the simultaneous production of the neutral weak boson Z and photon γ, and the limits on the anomalous Zγγ and ZZγ triple gauge couplings h3 and h4 with the Z decaying to leptons (electrons and muons). We analyze events collected in proton-proton collisions at center of mass energy of sqrt(s) = 7 TeV corresponding to an integrated luminosity of 5.0 inverse femtobarn. The analyzed events were recorded by the Compact Muon Solenoid detector at the Large Hadron Collider in 2011.

The production cross section has been measured for hard photons with transverse momentum greater than 15 GeV that are separated from the the final state leptons in the eta-phi plane by Delta R greater than 0.7, whose sum of the transverse energy of hadrons over the transverse energy of the photon in a cone around the photon with Delta R less than 0.3 is less than 0.5, and with the invariant mass of the dilepton system greater than 50 GeV. The measured cross section value is 5.33 +/- 0.08 (stat.) +/- 0.25 (syst.) +/- 0.12 (lumi.) picobarn. This is compatible with the Standard Model prediction that includes next-to-leading-order QCD contributions: 5.45 +/- 0.27 picobarn.

The measured 95 % confidence-level upper limits on the absolute values of the anomalous couplings h3 and h4 are 0.01 and 8.8E-5 for the Zγγ interactions, and, 8.6E-3 and 8.0E-5 for the ZZγ interactions. These values are also compatible with the Standard Model where they vanish in the tree-level approximation. They extend the sensitivity of the 2012 results from the ATLAS collaboration based on 1.02 inverse femtobarn of data by a factor of 2.4 to 3.1.

Singularities and horizons in the collisions of gravitational waves

This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. It is focused mainly on two fundamental questions: First, what is the general structure of the singularities and Killing-Cauchy horizons produced in the collisions of exactly plane-symmetric gravitational waves? Second, under what conditions will the collisions of almost-plane gravitational waves (waves with large but finite transverse sizes) produce singularities?

In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and that generic initial data for the colliding plane waves always produce "pure" spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction.

In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wavefronts; i.e., it must leave behind tails in the spacetime region through which it passes. Next, the occurrence of spacetime singularities in the collisions of almost-plane waves is investigated. It is proved that if two colliding, almost-plane gravitational waves are initially exactly plane-symmetric across a central region of sufficiently large but finite transverse dimensions, then their collision produces a spacetime singularity with the same local structure as in the exact-plane-wave collision. Finally, it is shown that a singularity still forms when the central regions are only approximately plane-symmetric initially. Stated more precisely, it is proved that if the colliding almost-plane waves are initially sufficiently close to being exactly plane-symmetric across a bounded central region of sufficiently large transverse dimensions, then their collision necessarily produces spacetime singularities. In this case, nothing is now known about the local and global structures of the singularities.

Extraction of CP Properties of the H(125) Boson Discovered in Proton-Proton Collisions at sqrt(s) = 7 and 8 TeV with the CMS Detector at the LHC

In this thesis we build a novel analysis framework to perform the direct extraction of all possible effective Higgs boson couplings to the neutral electroweak gauge bosons in the H → ZZ^(*) → 4l channel also referred to as the golden channel. We use analytic expressions of the full decay differential cross sections for the H → VV' → 4l process, and the dominant irreducible standard model qq ̄ → 4l background where 4l = 2e2μ,4e,4μ. Detector effects are included through an explicit convolution of these analytic expressions with transfer functions that model the detector responses as well as acceptance and efficiency effects. Using the full set of decay observables, we construct an unbinned 8-dimensional detector level likelihood function which is con- tinuous in the effective couplings, and includes systematics. All potential anomalous couplings of HVV' where V = Z,γ are considered, allowing for general CP even/odd admixtures and any possible phases. We measure the CP-odd mixing between the tree-level HZZ coupling and higher order CP-odd couplings to be compatible with zero, and in the range [−0.40, 0.43], and the mixing between HZZ tree-level coupling and higher order CP -even coupling to be in the ranges [−0.66, −0.57] ∪ [−0.15, 1.00]; namely compatible with a standard model Higgs. We discuss the expected precision in determining the various HVV' couplings in future LHC runs. A powerful and at first glance surprising prediction of the analysis is that with 100-400 fb^-1, the golden channel will be able to start probing the couplings of the Higgs boson to diphotons in the 4l channel. We discuss the implications and further optimization of the methods for the next LHC runs.

The complex angular momentum theory of the production of three particles in collisions of two strongly interacting particles at high energy

The problem of the continuation to complex values of the angular momentum of the partial wave amplitude is examined for the simplest production process, that of two particles → three particles. The presence of so-called "anomalous singularities" complicates the procedure followed relative to that used for quasi two-body scattering amplitudes. The anomalous singularities are shown to lead to exchange degenerate amplitudes with possible poles in much the same way as "normal" singularities lead to the usual signatured amplitudes. The resulting exchange-degenerate trajectories would also be expected to occur in two-body amplitudes.

The representation of the production amplitude in terms of the singularities of the partial wave amplitude is then developed and applied to the high energy region, with attention being paid to the emergence of "double Regge" terms. Certain new results are obtained for the behavior of the amplitude at zero momentum transfer, and some predictions of polarization and minima in momentum transfer distributions are made. A calculation of the polarization of the ρ^o meson in the reaction π ^- p → π ^- ρ^op at high energy with small momentum transfer to the proton is compared with data taken at 25 Gev by W. D. Walker and collaborators. The result is favorable, although limited by the statistics of the available data.

I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.