General relativity effects in precision spin experimental tests of fundamental symmetries

Abstract

A search for the P -and CP (T )-violating electric dipole moments (EDM) of atoms, particles and nuclei with sensitivity up to 10 −15 in units of the magnetic dipole moments, allowed by all discrete symmetries, is one of the topical problems of modern physics. According to Sakharov, CP -violation is one of the three key criteria of the baryogenesis in the generally accepted paradigm of the Big Bang cosmology. All three criteria are supported by the Standard Model, but it fails to describe quantitatively the observed baryon asymmetry of the Universe. This is regarded a strong argument in favor of the existence of CP -symmetry breaking mechanisms beyond the minimal Standard Model, which can lead to a measurable EDMs of atoms, particles and nuclei. Searches for the EDM via the spin rotation in electric fields are currently underway in dozens of laboratories worldwide. Direct searches for EDM of charged particles and nuclei are possible only in storage rings (COSY, NICA). After successful studies by the JEDI collaboration at the COSY synchrotron, at the forefront in the field is a search for the proton EDM in an electrostatic storage ring with the proton spin frozen at the magic energy with the projected sensitivity dp ∼ 10 −29 e•cm. The prototype storage ring PTR is proposed as a precursor to such a dedicated storage ring, with the prospect of the frozen proton spin ring becoming a part of the physics at CERN beyond the Large Hadron Collider program. Following a brief introduction to the CP -violation physics and the baryogenesis, the review presents a detailed discussion of significant contributions to the spin dynamics from the terrestrial gravity along with the new effects of Earth's rotation in ultrasensitive searches for the EDM of charged particles and neutrons. Quite remarkably, for the projected sensitivity to the proton EDM, these false EDM effects can by one to two orders of magnitude exceed the signal of the proton EDM, and become comparable to an EDM contribution in experiments with ultracold neutrons. We also discuss the role of a precessing spin as a detector of the axion-like dark matter, and consider applications of the quantum gravitational anomalies to the dense matter hydrodynamics and the spin phenomena in the non-central nuclear collisions.

Basic Notions of Poisson and Symplectic Geometry in Local Coordinates, with Applications to Hamiltonian Systems

“…of covariant tensor fields, see (35). Let M n = {z k , ωij (z k )} is a symplectic manifold and N k is a submanifold determined by the functions Φ α (z k ) = 0 (see (22)), n and k are even numbers.…”

Spin of protons in NICA and PTR storage rings as an axion antenna

“…A comprehensive introduction into the physics of axions is found in reviews [4,[10][11][12], here we only mention the principal points of importance to our discussion, alongside the basics of the spin precession in storage rings * nikolaev@itp.ac.ru [10][11][12][13][14][15]. When the angular frequency of the axion field is about three times the expansion rate of the Universe, coherent oscillations of the cold cosmological axion field do establish [16][17][18].…”