symmetry S S Review Siberian Snakes, Figure-8 and Spin Transparency Techniques for High Precision Experiments with Polarized Hadron Beams in Colliders Yaroslav S. Derbenev 1 , Yury N. Filatov 2 , Anatoliy M. Kondratenko 2,3 and Mikhail A. Kondratenko 2,3 and Vasiliy S. Morozov 1, *   Citation: Derbenev, Y.S.; Filatov, Y.N.; Kondratenko, A.M.; Kondratenko, M.A.; Morozov, V.S. Siberian Snakes, Figure-8 and Spin Transparency Techniques for High Precision Experiments with Polarized Hadron Beams in Colliders. Symmetry 2021, 13, 398. https://doi.org/10.3390/ sym13030398 Academic Editor: Sergey Troshin Received: 30 January 2021 Accepted: 20 February 2021 Published: 28 February 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA; derbenev@jlab.org 2 Moscow Institute of Physics and Technology, 141701 Dolgoprudny, Russia; filatov.iun@mipt.ru (Y.N.F.); kondratenkom@mail.ru (A.M.K.); ma_kondratenko@mail.ru (M.A.K.) 3 Science and Technique Laboratory “Zaryad”, 630090 Novosibirsk, Russia * Correspondence: morozov@jlab.org Abstract: We present a review of the possibilities to conduct experiments of high efficiency in the nuclear and high energy physics with spin-polarized beams in a collider complex, configuration of which includes Siberian snakes or figure-8 collider ring. Special attention is given to the recently elicited advantageous possibility to conduct high precision experiments in a regime of the spin transparency (ST) when the design global spin tune is close to zero. In this regime, the polarization control is realized by use of spin navigators (SN), which are compact special insertions of magnets dedicated to a high flexibility spin manipulation including frequent spin flips. Keywords: spin-polarized beams; Siberian snakes; figure-8 collider ring; spin transparency; spin navigator 1. Introduction Experiments with polarized beams have been and remain a crucial tool in understand- ing particle and nuclear structure and reactions from the first principles [1]. The necessity of fundamental studies of the matter microstructure with polarized beams in accelerators can be justified in general by an irrefutable argument that one needs to characterize the state of the incident colliding particles by a complete set of the involved dynamical parameters, and the particle spin orientation (longitudinal and transverse) is one of them. The search for new physics beyond the Standard model necessitates high-precision experiment with po- larized beams. The search for CP- and T-violations in semi-strong hadron interactions [2–4] belongs to this category. In particular, the extension of the Standard model including CP- and T-violations may explain the anomalously large baryonic asymmetry of the Universe where the Standard model of the elementary particle physics disagrees with the experi- mental results by many orders of magnitude [5]. The study of the nucleon spin structure is one of the main goals of the Electron-Ion Collider EIC (BNL, Brookhaven, NY, USA) [6] and the NICA collider (JINR, Dubna, Russia) [7]. Recent advances in spin physics have led to a proposal of using storage rings for the search of axion-like particles, which are one of the candidates for explaining the dark matter in the Universe [8]. The aforementioned projects require precise control of the longitudinal and transverse polarizations in colliders and storage rings [6,7,9]. The presented article is a review of the related accelerator aspects of the polarized beam instrumentation, namely acceleration, maintenance, control and spin manipulation of the polarized beams. Based on earlier established methods and concepts of the coherent spin preservation and control such as Siberian Snakes (SibS) [10] and Figure-8 synchrotrons (F8S) [11,12], here we mainly focus on the newly discovered possibilities of further enhanc- ing the flexibility and precision strength of the polarized beams operation in colliders, which we call the spin transparency (ST) [13]. Symmetry 2021, 13, 398. https://doi.org/10.3390/sym13030398 https://www.mdpi.com/journal/symmetry