# Review of the journal Physics of Elementary Particles and Atomic Nuclei, # 47

Publications, 23 December 2016

The JINR review journal Physics of Elementary Particles and Atomic Nuclei, brief name Particles & Nuclei, published by leading physicists from Member States of JINR, as well as scientists from all over the world, review articles in this eminent journal examine elementary particle physics, problems of vacuum in quantum field theory, condensed matter problems, symmetries in physics, string theories and gravity, nuclear physics, automatic processing of experimental data, accelerators and related instrumentation, accelerator-based transmutation studies, ecological implications of present nuclear and conventional energy sources, energy amplifiers based on accelerators.

## # 47, Issue 5, 2016

*Bednyakov V.A.*

**Is It Possible to Discover a Dark Matter Particle with an Accelerator?**(eng, 4430 Кb)

The paper contains description of the main properties of the galactic dark matter (DM) particles, available approaches for detection of DM, main features of direct DM detection, ways to estimate prospects for the DM detection, the first collider search for a DM candidate within an Effective Field Theory (EFT), a complete review of ATLAS results of the DM candidate search with LHC Run~I, and a less complete review of “exotic” dark particle searches with other accelerators and not only.

From these considerations it follows that one is unable to prove, especially model-independently, a discovery of a DM particle with an accelerator or a collider. One can only obtain evidence of existence of a weakly interacting neutral particle, which could be or could not be the DM candidate.

The current LHC DM search program uses only the missing transverse energy signature. Non-observation of any excess above Standard Model expectations forces the LHC experiments to enter into the same fighting for the best exclusion curve, in which (almost) all direct and indirect DM search experiments permanently take place. But this fighting has very little (almost nothing) to do with a real possibility of discovering a DM particle. The true DM particles possess an exclusive galactic signature – annual modulation of a signal, which is accessible today only for direct DM detection experiments. There is no way for it with a collider or an accelerator.

Therefore, to prove the DM nature of a collider-discovered candidate, one must find the candidate in a direct DM experiment and demonstrate the galactic signature for the candidate. Furthermore, being observed, the DM particle must be implemented into a modern theoretical framework. The best candidate is the supersymmetry, which looks today inevitable for coherent interpretation of all available DM data.

*Morozov A.A.*

**Conformal Block Properties, AGT Hypothesis and Knot Polynomials**(rus, 950 Kb)

In this review we describe different properties of conformal blocks of the 2D conformal field theory. In particular, the connection between conformal blocks and partition function of 4D supersymmetric theory is discussed. Besides the interest of such a connection by itself it also provides practical simplifications of calculations in both theories. For the same purpose the representation of correlators in conformal theory as a matrix model varieties can be used. Integral form of such correlators allows one to generalize the results evaluated for Virasoro algebra to more complicated cases of $W$-algebras and quantum Virasoro algebras. This leads to the possible studies of more complicated structures in conformal field theory. The second part of the review is dedicated to the Chern-Simons theory. The interest which it arouses at the moment is due to its connection with the mathematical knot theory. This theory is quite an old subject that appeared in the 17th century. Its goal is to construct an algorithm which allows one to distinguish between different knots – contours in 3D space. The main approach to this problem, which is decribed in this review, is to construct the so-called knot invariants.

*Syska J.*

**Weak Bound State with the Nonzero Charge Density as the LHC 126.5 GeV State**(eng, 440 Кb)

The self-consistent model of classical field interactions formulated as the counterpart of the quantum electroweak model leads to homogeneous boson ground state solutions in presence of nonzero extended fermionic charge density fluctuations. Two different types of electroweak configurations of fields are analyzed. The first one has nonzero electric and weak charge fluctuations. The second one is electrically uncharged but weakly charged. Both types of configurations have two physically interesting solutions which possess masses equal to 126.67 GeV at the value of the scalar fluctuation potential parameter λ equal to ~ 0.0652. The spin zero electrically uncharged droplet, formed as a result of the decay of the charged one, is interpreted as the ~ 126.5 GeV state found in the Large Hadron Collider (LHC) experiment. The other two configurations correspond to solutions with masses equal to 123.7~GeV and λ equal to ~ 0.0498, and thus the algebraic mean of the masses of two central solutions, i.e., 126.67 and 123.7 GeV, is equal to 125.185 GeV. The problem of a mass of this kind of droplets will be considered on the basis of the phenomenon of the screening of the fluctuation of charges. Their masses are found in the thin wall approximation.

*Smirnov V.L., Vorozhtsov S.B.*

**Modern Compact Accelerators of Cyclotron Type for Medical Applications**(eng, 1975 Кb)

Ion beam therapy and hadron therapy are types of external beam radiotherapy. Recently, the vast majority of patients have been treated with protons and carbon ions. Typically, the types of accelerators used for therapy were cyclotrons and synchrocyclotrons. It is intuitively clear that a compact facility fits best to a hospital environment intended for particle therapy and medical diagnostics. Another criterion for selection of accelerators to be mentioned in this article is application of superconducting technology to the magnetic system design of the facility. Compact isochronous cyclotrons, which accelerate protons in the energy range of 9-30 MeV, have been widely used for production of radionuclides. Energy of 230 MeV has become canonical for all proton therapy accelerators. Similar application of a carbon beam requires ion energy of 430 MeV/u. Due to application of superconducting coils the magnetic field in these machines can reach 4-5 and even 9 T in some cases. Medical cyclotrons with an ironless or nearly ironless magnetic system that have a number of advantages over the classical accelerators are at the development stage. In this work, an attempt is made to describe some conceptual and technical features of modern accelerators under consideration. The emphasis is placed on the magnetic and acceleration systems along with the beam extraction unit, which are very important from the point of view of the facility compactness and compliance with the strict medical requirements.

*Drivotin O.I., Ovsyannikov D.A.*

**Stationary Self-Consistent Distributions for Charged Particle Beam in Magnetic Field**(eng, 450 kb)

A review of analytical solutions of the Vlasov equation for a charged particle beam is given. These results are analyzed on the base of a common approach developed by the authors of the article. According to this method, the space of integrals of motion is introduced, integrals of motion being regarded as coordinates in it. At that, specifying of a self-consistent distribution is reduced to specifying of a density in this space. Such an approach allows one to simplify construction and analysis of various self-consistent distributions. Particularly, in some cases it is possible to obtain new solutions considering linear combinations of known solutions. This approach also gives a possibility to provide pictorial geometric representation of self-consistent distributions in the space of motion integrals.