Special Issue: Advances in Spin Physics

1. Introduction

The notion of spin entered physics about one hundred years ago when Uhlenbeck and Goudsmit introduced the internal degree of freedom for the electron- spin as a real physical characteristics instead of the so called non-mechanical strength used at first by Pauli under formulation of his famous principle. The history of spin discovery in detail is described in reference [1].

In fact, the notion of spin appeared from an intersection of the classical and quantum physics. The classical rotation was an original interpretation, but, in essence, spin appeared as a quantum notion. The Pauli principle and the concept of spin served as a starting point for the appearance of such fundamental notions as symmetry of the wave functions and statistics. According to C.N. Yang, the spin of electrons is a fundamental manifestation of the space-time structure [2].

Most particles have a non-zero spin and it is clear from recent experimental data that not only are the static properties of particles spin-dependent, but their interaction dynamics is also stronly spin-dependent. Moreover, spin structure of particles is determined not only by the spin of valence quarks—the spins and orbital momentum of other constituents also contribute.

Spin studies are the mostly experimentally driven field of investigations. Many experiments have contributed to this field. The EMC experimental result on measuring the spin-dependent structure function $g_1(x)$ has led to appearance of array of theoretical papers and served as motivator for the further experimental measurements. There are a lot of theoretical interpretations of the small value of quark contribution to the spin balance of proton found by the EMC but the situation regarding spin structure of proton remains to be obscured at present and the so called “spin crisis” still awaiting its resolution.

The above interpretation are based on the modern theory of strong interactions Quantum Chromodynamics (QCD). The perturbative QCD meets serious difficulties when compared with the results of polarization experiments. The problem is in s-channel helicity conservation in QCD. The smallness of current quark masses result in the small corrections to this conservation law and small polarization at the quark level. At the hadron level, polarization is large. The most serious contradiction is the large polarization of $\mathsf{\Lambda }$ hyperons observed in the collisions of the unpolarized proton beams. Such bad situation has been improved partially by the semiclassical model construction. Evidently, non-perturbative effects in QCD, confinement and spontaneous breaking of chiral symmetry, should play a major role in explanation of spin effects.

Spin degrees of freedom are responsible for many various fundamental properties of matter and their neglect as an inessential complication is a prejudice reflecting merely absence of the possibilities for the experimental studies of spin effects. These studies require state of art of the experimental techniques.

2. Contributions

The Reference [3] reviews the role of spin in high energy hadron–hadron and lepton–hadron interactions. It concerns mainly the nonperturbative sector of QCD, the roles of pomeron, odderon, unitarity, analyticity for spin observables and dependence of differential cross-section on the Mandelstam variables s and t with emphasis on Regge trajectories. It discusses the spin structure of proton also and conclusion made that there was no spin crisis but there were problems in the interpretation of the experimental results. Explicit models and fits presented in the review.

Reference [4] also discusses soft diffraction phenomena in elastic $pp$ scattering. It discusses the Coulomb–Nucleon phase factor and dependencies of differential cross-section of elastic $pp$-scattering on t at small values of t and in the region of diffraction minimum. Description of analysing power $A_N$ is given and conclusion made that the experimental data analysis is in favor of the energy-independent part of the hadron spin-flip amplitude contribution.

Both above papers consider transverse spin structure of nucleon under use of models among other issues. This is a special subject of the Reference [5]. Extraction of the transverse-spin quark distributions from asymmetry data and symmetry arguments is the topic of this paper. The data are from the COMPASS measurements of charged pion leptoproduction on proton and deuteron targets. The transversity and the Sivers $u_v$ and $d_v$ distributions have been obtained in the analysis with the help of the simple symmetry relations without use of any models.

As it was mentioned, experimental studies of spin effects require sophisticated equipment. However, there is a spin effect with large values for spin observables which can be studied in the experiment with unpolarized colliding beams. It is polarization of $\mathsf{\Lambda }$ hyperon. Its value is about 30%, i.e., very large. No significant energy-dependence of this transverse polarization has been observed till CERN ISR energies. So, the already existing experimental environment at the CERN LHC can be used to perform measurements at the highest accelerator energies. Reference [6] discusses this possibility. It could help to resolve the notorious problem of the energy dependence of spin effects. The above paper allows one to get estimates on the size of the $\mathsf{\Lambda }$ hyperon polarization in the framework of the spin filtering mechanism.

The paper [7] reviews experimental techniques which are the most important subject for the experimental spin studies. The content of this paper is represented in the historical retrospective of developments in the area from the early 1960s till the recent years. This article is a review of the accelerator aspects of the polarized beam instrumentation: 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 and Figure-8 synchrotrons the discussion is focused on the newly discovered possibilities of further enhancing the flexibility and precision strength of the polarized beams operation in colliders. This paper enlighting up the heroic era of the accelerator problematics developments.

3. Conclusions

Experimental studies with unpolarized and polarized beams have remain an essential probes of particle and nuclear structures. The necessity of fundamental studies of the matter spin microstructure and dependence of dynamics of interaction 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. The particle spin orientation (longitudinal and transverse) is one of them. The search for new physics beyond the Standard model necessitates the high-precision experimentation with polarized beams. The study of the nucleon spin structure is one of the main goals of the Electron-Ion Collider EIC (BNL, Brookhaven, NY, USA) and the NICA collider (JINR, Dubna, Russia). 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. The details of spin degrees role, its studies and perspectivesstudies of these can be found in [3,4,5,6,7].