Narrow Results

The study of transverse momentum dependent parton distributions (TMDs) features prominently among the goals of the EIC program. During Week 2, several topics related to TMDs have been discussed, offering complementary information with respect to the original EIC white paper. In this introduction to Week 2, we mention the main ideas and include some developments that occurred even after the conclusion of the program.

The LHCspin project aims to bring polarized physics at the LHC through the installation of a gaseous fixed target at the upstream end of the LHCb detector. The forward geometry of the LHCb spectrometer (2 < η < 5) is perfectly suited for the reconstruction of particles produced in fixed-target collisions. The fixed-target configuration, with center-of-mass energy at $\sqrt{s}=115\text{GeV}$, allows to cover a wide backward center-of-mass rapidity region, corresponding to the poorly explored high x-Bjorken and high x-Feynman regimes. The project has several ambitious goals, in particular regarding nucleon’s internal dynamics in terms of both quarks and gluons degrees of freedom. The use of transversely polarized H and D targets will allow to study the quarks TMDs in pp collisions at unique kinematic conditions.

It is known that a particle shows two different characters, particle-wave duality in the quantum mechanical world. Photons show the character of wave, such as diffraction and interference, but the photo-electric effect and the black-body radiation can be explained only by the particle character of light. In the microscopic world, duality is a property not only inherent in photons but also common in all particles including electrons, protons and neutrons. From this peculiar character of particles, the motion in the microscopic world can be understood only in the probability interpretation, i.e., the particles are described by the wave function ψ with a wave character and the measurements give the probabilities of finding particles in space-time. This is the concept called the Copenhagen interpretation of quantum mechanics, developed by Niels Bohr and his group. In this chapter, we summarize the basic ideas, principles and concepts of quantum mechanics.

With the gas ionization experiments (Section 1.7) we know that atoms and molecules are made of nuclei and electrons that revolve around them. In this chapter we give representations of these microscopic objects and show how certain atoms or molecular fragments form bonds between them. From the description of the hydrogen atom, the lightest atom in Nature since it contains only one proton and one electron, we will develop a simple model for the bonds between atoms in molecules stable at 25°C. Without making complicated calculations we will be able to predict which bonds between atoms are possible a priori and which structures the molecules containing them have. Atoms are the parts of a Lego® set that can be assembled to make a large number of constructions, but not just any construction (three-dimensional objects with predefined geometries). In Chapter 7, we will develop a slightly more advanced model of the chemical bond. We will examine why some bonds are weaker than others, i.e. which bonds are more or less easily broken by heating…

Standard model has to be generalized to a “New Physics” beyond the Standard Model. Main problem is the lack of consistency SM with gravity. We analyse Kerr-Newman spinning particle which is consistent with gravity by nature and, contrary to opinion that gravity conflicts with quantum theory, we obtain that spinning Kerr’s gravity collaborates with quantum theory in the process of formation of spinning particle. The most dramatic is the shift of the fundamental scale from Planck to Compton distances.

A unified approach to the study of classical and quantum spin in external fields is developed. Understanding the dynamics of particles with spin and dipole moments in arbitrary gravitational, inertial and electromagnetic fields is important in astrophysics and high-energy and heavy-ion experimental physics.

We discuss the interaction of gravitational waves with spinning particle. To obtain physically measurable quantities, we make use of Fermi coordinates and we show that, using these coordinates, the magnetic-like (or gravitomagnetic) part of the gravitational field of the wave is emphasized. Eventually, we evaluate the magnitude of the effects induced by the waves on spinning particles, and discuss some measurement possibilities.

Deployment of quantum technology in space provides opportunities for new types of precision tests of gravity. On the other hand, the operational demands of such technology can make previously unimportant effects practically relevant. We describe a novel optical interferometric red-shift measurement and a measurement scheme designed to witness the possible spin-gravity coupling effects.

It has been shown that when electrons are transferred through chiral molecules, the efficiency of the transfer depends on the electron’s spin and on the handedness of the chiral potential. Hence, chiral molecules serve as spin filters. This effect is termed chiral-induced spin selectivity (CISS). The dependence of the CISS effect on the molecular properties is discussed here as well as some implications of the effect such as in bio-recognition and in the interaction of chiral molecules with ferromagnetic substrates. The role of the CISS effect in various fields is also reviewed.

Shortly after his escape, in 1968, from the DDR to the Western world, Harald Fritzsch made a fast career in physics while investigating the strong force in elementary particles. Inspired by Gell-Mann, Yang and Mills and many others, he contributed to the rise of the Standard Model, and in particular the developments of theories for the color confinement mechanism.

We discuss the invariance of the spinning free particle Lagrangian under the global coordinate transformations for the classical model of the electron with internal degrees of freedom and obtain the conservation of the energy-momentum, total angular momentum and electric charge. The local transformations give the minimal and non-minimal gravitational and minimal electromagnetic interactions of the spinning particle in the Riemann-Cartan space from the generalized spin connections.

The measurement of a spin-½ is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement, regarded as a process of quantum statistical mechanics. Schrödinger cat terms involving both the system and the apparatus, die out very quickly, while the registration is a process taking the apparatus from its initially metastable state to one of its stable final states. The occurrence of Born probabilities can be inferred at the macroscopic level, by looking at the pointer alone. Apparent non-unitary behavior of the measurement process is explained by the arisal of small many particle correlations, that characterize relaxation.

The Kerr-Newman (KN) solution to Einstein's equation shows a gyromagnetic factor g = 2, typical of a Dirac spinor. This fact has prompted many attempts to consider this solution as the exterior metric for a fundamental spin 1/2 particle. In the present work, the KN solution is proposed as the exterior and interior solution for a fundamental particle, leading to a redefinition of the particle concept. By considering the extended interpretation of Hawking and Ellis, other properties like the spacetime spinorial structure, mass and charge follow from its non- trivial geometry. A crucial point of the model is the excision of the ring singularity present in the original KN solution. This excision removes non-causal regions of the solution, and is consistent with its metric structure. Although the spacetime dimension of the singularity is of the order of the particles's Compton wavelength, which for the electron is λ = 10⁻¹¹cm, the space dimension of the ring is found to vanish. In the three-dimensional space, therefore, it is a point-like object, a property that validates the concept of “fundamental particle” of the model.

In classical electrodynamics, extended with gradients of the electric and magnetic fields, a linear soliton is presented which bears features of the Kerr-Newman electron of electro-gravity. This is considered as a model for the electron, having a ring shape, with diameter equal to the Compton length ħ/mc and thickness smaller by the fine structure constant. The soliton has a finite mass, a spin-½, a g = 2 factor, and an electric quadrupole moment that is also “twice too large”. From this setup, all relativistic corrections to the classical version of the Pauli Hamiltonian are derived. There appears an additional, spin-dependent quadrupolar force that may vanish on the average. Particle-antiparticle annihilation may become explained on the basis of electromagnetic attraction.

The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s = 1/2 interacting with one of spin s = 0. Non-trivial superintegrable systems with 8- and 9-dimensional Lie algebras of first-order integrals of motion are constructed in two- and three-dimensional spaces, respectively.

The nucleon spin structure has been an active, exciting and intriguing subject of interest for the last three decades. Recent experimental data on nucleon spin structure at low to intermediate momentum transfers provide new information in the confinement regime and the transition region from the confinement regime to the asymptotic freedom regime. New insight is gained by exploring moments of spin structure functions and their corresponding sum rules (i.e. the generalized Gerasimov-Drell-Hearn, Burkhardt-Cottingham and Bjorken). The Burkhardt-Cottingham sum rule is verified to good accuracy. The spin structure moments data are compared with Chiral Perturbation Theory calculations at low momentum transfers. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g₁ at momentum transfer of 0.05 to 0.1 GeV² but fail to reproduce the neutron data in the case of the generalized polarizability δ_LT (the δ_LT puzzle). New data have been taken on the neutron (³He), the proton and the deuteron at very low Q² down to 0.02 GeV². They will provide benchmark tests of Chiral dynamics in the kinematic region where the Chiral Perturbation theory is expected to work.

Preliminary measurements of the Transverse Target Spin Asymmetry, A_UT(φ), for hard exclusive electro-production of ρ⁰ mesons at HERMES are presented. Information about the poorly known GPD E can be obtained through measurement of the transverse target spin asymmetry in the longitudinal cross section . Using the self-analyzing character of ρ⁰ meson decay, both and were extracted from HERMES data. The TTSA was compared with GPD model predictions.

Leopold Ernst Halpern, who was a close associate of both Erwin Schrödinger and Paul Dirac before making his own mark as a theoretical physicist of the first rank, died in Tallahassee, Florida on 3 June 2006 after a valiant struggle with cancer. We give an outline of his life and work, including his progress towards a unified gauge theory of gravitation and spin.

We derive the rate of change of the mean motion up to the second post-Newtonian order for inspiralling compact binaries with spin, mass quadrupole and magnetic dipole moments on eccentric orbits. We give this result in terms of orbital elements. We also present the related orbital phase for circular orbits.

The radial component of the motion of compact binary systems composed of neutron stars and/or black holes on eccentric orbit is integrated. We consider all type of perturbations that emerge up to second post-Newtonian order. These perturbations are either of relativistic origin or are related to the spin, mass quadrupole and magnetic dipole moments of the binary components. We derive a generalized Kepler equation and investigate its domain of validity, in which it properly describes the radial motion.