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The possibility of using spin connection components as basic quantization variables of a conformal version of General Relativity is studied. The considered model contains gravitational degrees of freedom and a scalar dilaton field. The standard tetrad formalism is applied. Properties of spin connections in this model are analyzed. Secondary quantization of the chosen variables is performed. The gravitational part of the model action turns out to be quadratic with respect to the spin connections. So at the quantum level the model looks trivial, i.e., without quantum self-interactions. Meanwhile the correspondence to General Relativity is preserved at the classical level., Comment: 14 pages

Radiative corrections due to initial state radiation in electron-positron annihilation are calculated within the QED structure function approach. Results are shown in the next-to-leading logarithmic approximation up to $O(\alpha^4 L^3)$ order, where $L=\ln(s/m_e^2)$ is the large logarithm. Several mistakes in previous calculations are corrected. The results are relevant for future high-precision experiments at $e^+e^-$ colliders., Comment: 9 pages, 2 figures

Luminosity monitoring at $e^+e^-$ colliders is investigated using SANC Monte Carlo event generator ReneSANCe and integrator MCSANC for simulation of Bhabha scattering at low angles. Results are presented for center-of-mass energies of the Z boson resonance and 240 GeV for the conditions of typical luminosity detectors. It is shown that taking into account bremsstrahlung events with extremely low electron scattering angles is relevant to match the precision tags of the future electron-positron colliders., Comment: Submitted to Chinese Physics C

Higher-order QED radiative corrections to muon decay spectrum are evaluated within the QED structure function approach in the next-to-leading order logarithmic approximation. New analytical results are given in the $\mathcal{O}\left(\alpha^3 \ln^2(m_\mu^2/m_e^2)\right)$ order. Earlier results in $\mathcal{O}\left(\alpha^2 \ln^1(m_\mu^2/m_e^2)\right)$ and $\mathcal{O}\left(\alpha^3 \ln^3(m_\mu^2/m_e^2)\right)$ orders are partially corrected. Numerical estimates of different contributions are presented.

Calculation of higher-order radiative corrections to unpolarized muon decay spectrum is discussed. Results for the orders $\mathcal{O}(\alpha^2 L)$, $\mathcal{O}(\alpha^3 L^3)$ and $\mathcal{O}(\alpha^3 L^2)$ are presented.

The 3-3-1 model with neutral leptons contains four CP-even Higgs bosons when some constraints are imposed on the Higgs potential. Two Higgs bosons of this type are identified with the corresponding ones in the Two-Higgs-Doublet model (2HDM), an other being more massive does not couple with similar particles contained in the Standard Model (SM). The remaining particle is assumed to have no lepton-flavor-violating couplings. The contributions at one-loop order to $\mathrm{\Gamma}(\mathrm{H}\rightarrow l_il_j)$$(H \equiv h^0_1,h^0_2,h^0_3)$ come mainly from neutral leptons leading them to depend very strongly on mass of charged Higgs boson, masses and the mixing matrix ($V^L_{ab}$) of the neutral leptons. The numerical investigated results of $\mathrm{\Gamma}(\mathrm{H}\rightarrow l_il_j)$ in the spatial regions satisfying the experimental limit of lepton-flavor-violating decays of charged leptons (cLFV) indicate that the signal of SM-like Higgs boson ($\mathrm{\Gamma}(h^0_1\rightarrow l_il_j)$) approaches the upper bound of the experimental limit and $\mathrm{\Gamma}(\mathrm{H}\rightarrow l_il_j)$ can take large values in the case of $V^L_{ab} = U^L_{ab}(\pi/4,\pi/4,-\pi/4)$ and smaller in the case of $V^L_{ab} = U^L_{ab}(\pi/4,0,0)$. Further, some distinct properties of $\mathrm{\Gamma}(h^0_2\rightarrow l_il_j)$ and $\mathrm{\Gamma}(h^0_3\rightarrow l_il_j)$ are also discussed., Comment: 37 pages, 21 figures

Perturbative solutions for unpolarized QED parton distribution and fragmentation functions are presented explicitly in the next-to-leading logarithmic approximation. The scheme of iterative solution of QED evolution equations is described in detail. Terms up to $\mathcal{O}(\alpha^3L^2)$ are calculated analytically, where $L=\ln(\mu_F^2/m_e^2)$ is the large logarithm which depends on the factorization energy scale $\mu_F\gg m_e$. The results are process independent and relevant for future high-precision experiments., Comment: Presentation is improved, misprints are corrected

A theoretical description of elastic polarized muon-electron scattering is presented. Complete one-loop electroweak radiative corrections are calculated with taking into account the exact dependence on the muon mass. The effects due to some higher order corrections and the electroweak scheme dependence are analyzed. The case of longitudinally polarized fermions in the initial state is investigated. Analytical results are derived with the help of the SANC system. Numerical results are presented for unpolarized and polarized cross sections. Calculations are realized in the Monte Carlo integrator MCSANCee and generator ReneSANCe which allow the implementation of any experimental cut used in the analysis of elastic $\mu - e$ scattering data., Comment: 28 pages, 8 tables, 8 figures

The Spin Physics Detector, a universal facility for studying the nucleon spin structure and other spin-related phenomena with polarized proton and deuteron beams, is proposed to be placed in one of the two interaction points of the NICA collider that is under construction at the Joint Institute for Nuclear Research (Dubna, Russia). At the heart of the project there is huge experience with polarized beams at JINR. The main objective of the proposed experiment is the comprehensive study of the unpolarized and polarized gluon content of the nucleon. Spin measurements at the Spin Physics Detector at the NICA collider have bright perspectives to make a unique contribution and challenge our understanding of the spin structure of the nucleon. In this document the Conceptual Design of the Spin Physics Detector is presented.

The possibility to use the width of the decay $\rho \to e^{+}e^{-}$ to fix the input parameter $g_\rho=5.0$ of the $SU(2) \times SU(2)$ chiral-symmetric Nambu--Jona-Lasinio model is discussed. It is shown that for a consistent simultaneous description of the processes $\rho \to e^{+}e^{-}$, $\rho \to \pi^{+}\pi^{-}$, $\tau^{-} \to \pi^{-}\pi^{0} \nu_{\tau}$, and $e^{+}e^{-} \to \pi^{+}\pi^{-}$ can be constructed. Taking into account the interaction of pions in the final state appears to be important. The obtained theoretical results for the considered processes are in a satisfactory agreement with experimental data., Comment: 4 pages, 6 figures, misprints are corrected

The processes $\tau^- \to \pi^- \pi^0 \nu_{\tau}$ and $e^{+}e^{-} \to \pi^{+} \pi^{-}$ are considered within the chiral Nambu--Jona-Lasinio model with taking into account the pion final state interactions beyond the leading $1/N_c$ approximation. The contribution of the loop correction caused by a $\rho$ meson exchange between the pions, which gives the main contribution in the P-wave channel, is caclulated. The results for both processes are in a satisfactory agreement with experimental data., Comment: 8 pages, 8 figures, formula (10) is corrected, numerical results are slightly changed

The emergence of a scale hierarchy in the case of spontaneous radiative breaking of conformal symmetry is discussed using the example of a simple quantum field theory model. The Coleman-Weinberg mechanism is implemented in the one-loop approximation of the effective potential of a scalar field interacting with a fermion field. The emergence of a hierarchy between the renormalization scale and the magnitude of the scalar field vacuum expectation value is shown. An effective model in the vicinity of the effective potential minimum is constructed, and absence of a direct renormalization group transition to the original theory is established. It is shown that effective model parameters measurement in the infrared region allows us to determine the scale that limits the applicability region of the model., Comment: 7 pages

Forward-backward (charge) asymmetry in the processes of $e^+e^-$ annihilation into a pair of charged pseudoscalar mesons is recalculated in the one-loop approximation. The exact dependence on the meson masses is taken into account. Results known in the literature are partially corrected. The bulk of the charge asymmetry appears due to double-photon exchange in $s$ channel. Experimental studies of the asymmetry can be used to verify the point-like approximation used in calculation of radiative corrections due to emission of photons by pions or kaons., Comment: 8 pages, 2 figures

The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates with a 100 TeV proton-proton collider. It offers a vast new domain of exploration in particle physics, with orders of magnitude advances in terms of Precision, Sensitivity and Energy. The implementation plan foresees, as a first step, an Electroweak Factory electron-positron collider. This high luminosity facility, operating between 90 and 365 GeV centre-of-mass energy, will study the heavy particles of the Standard Model, Z, W, Higgs, and top with unprecedented accuracy. The Electroweak Factory $e^+e^-$ collider constitutes a real challenge to the theory and to precision calculations, triggering the need for the development of new mathematical methods and software tools. A first workshop in 2018 had focused on the first FCC-ee stage, the Tera-Z, and confronted the theoretical status of precision Standard Model calculations on the Z-boson resonance to the experimental demands. The second workshop in January 2019, which is reported here, extended the scope to the next stages, with the production of W-bosons (FCC-ee-W), the Higgs boson (FCC-ee-H) and top quarks (FCC-ee-tt). In particular, the theoretical precision in the determination of the crucial input parameters, alpha_QED, alpha_QCD, M_W, m_t at the level of FCC-ee requirements is thoroughly discussed. The requirements on Standard Model theory calculations were spelled out, so as to meet the demanding accuracy of the FCC-ee experimental potential. The discussion of innovative methods and tools for multi-loop calculations was deepened. Furthermore, phenomenological analyses beyond the Standard Model were discussed, in particular the effective theory approaches. The reports of 2018 and 2019 serve as white papers of the workshop results and subsequent developments., Comment: Published version

The global time in Geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of the square root of the ratio of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The explored Hamiltonian system appeared to be non-conservative. The Hamiltonian equations of motion of gravitational field in the global time are written. Relations between different time intervals (coordinate, intrinsic, proper) are obtained., Comment: 11 pages; format is changed; arXiv admin note: substantial text overlap with arXiv:1710.01528

Application of nonlinear symmetry realisation technique to gravity is studied. We identify the simplest extensions of the Poincare group suitable for nonlinear realisation. Among them only one model is suitable for description of massless spin-2 states. This model, unlike general relativity, describes states with well-defined mass that lack a linear interaction with the matter states. We argue that this phenomenon points on a necessity to draw a distinction between gravitational states with well defined masses and states that participate in interaction with matter., Comment: Minor corrections

Group theoretical realizations containing the electroweak sector of the Standard Model are discussed from the supersymmetry point of view. Dynamical breaking of the symmetry is performed and the corresponding quadratic (super Yang-Mills) Lagrangian is obtained. Supercoherent states of the Klauder-Perelomov type are defined to enlarge the symmetry taking into account the geometry of the coset based in the simplest supergroup SU (2 | 1) as the structural basis of the electroweak sector of the SM. The extended model is superintegrable and the superconnection in the odd part takes a dynamical character. The physical and geometrical implications of the additional degrees of freedom interpreted as a hidden sector of the representation are briefly discussed., Comment: 24 pages 7 figures. arXiv admin note: text overlap with arXiv:hep-th/9708052 by other authors

The angular asymmetry in decays of polarized muons and tau leptons is discussed. Both the standard $V-A$ Fermi model and the general parameterization via Michel parameters are considered. Numerical importance of contributions suppressed by charged lepton mass ratio is underlined. Contribution of the second order QED correction is estimated in the leading logarithm approximation., Comment: 8 pages, version to appear in IJMPA

The quantum Casimir condensate of a conformal massive scalar field in a compact Friedmann universe is considered in the static approximation. The Abel-Plana formula is used for renormalization of divergent series in the condensate calculation. A differential relation between the static Casimir energy density and static Casimir condensate is derived., Comment: 7 pages, 1 figure, misprints corrected

Lecture notes with a brief introduction to Quantum field theory and the Standard Model are presented. The lectures were given at the 2017 European School of High-Energy Physics. The main features, the present status, and problems of the Standard Model are discussed., Comment: 35 pages

Radiative corrections to the $h\rightarrow Z\gamma$ are evaluated in the one-loop approximation. The unitary gauge gauge is used. The analytic result is expressed in terms of the Passarino-Veltman functions. The calculations are applicable for the Standard Model as well for a wide class of its gauge extensions. In particular, the decay width of a charged Higgs boson $H^\pm \rightarrow W^\pm\gamma$ can be derived. The consistence of our formulas and several specific earlier results is shown., Comment: 33 pages, 3 figures, a new section (V) and references were improved in the published version

The global time is defined in covariant form under the condition of a constant mean curvature slicing of spacetime. The background static metric is taken in the tangent space. The global intrinsic time is identified with the logarithmic function of the mean value of the ratio of the square root of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The Hamiltonian system appears to be non-conservative. The Hamiltonian equations of motion of gravitational field in the global time are written., Comment: 5 pages

Nonlinear realizations of the SO(4,2) group are discussed from the point of view of symmetries. Dynamical symmetry breaking is introduced. One linear and one quadratic model in curvature are constructed. Coherent states of the Klauder-Perelomov type are defined for both cases taking into account the coset geometry. A new spontaneous compactification mechanism is defined in the subspace invariant under the stability subgroup. The physical implications of the symmetry rupture in the context of non-linear realizations and direct gauging are analyzed and briefly discussed., Comment: 25 pages, no figures.arXiv admin note: text overlap with arXiv:1602.06776 by other authors

Quantum behavior of the John Lagrangian from the Fab Four class of Covariant Galileons is stud- ied. We consider one-loop corrections to the John interaction due to cubic scalar field interactions. Counter Terms are calculated, one of them belongs to the Fab Four class, the other one to Covariant Galileons. The role of quantum corrections in context of cosmological applications is discussed., Comment: 7 pages, 5 figures; minor corrections added

Radiaitve mechanism of conformal symmetry breaking in a comformal-invariant version of the Standard Model is considered. The Coleman-Weinberg mechanism of dimensional transmutation in this system gives rise to finite vacuum expectation values and, consequently, masses of scalar and spinor fields. A natural bootstrap between the energy scales of the top quark and Higgs boson is suggested., Comment: 8 pages

The neutrino and Higgs sectors in the $\mbox{SU(2)}_1 \times \mbox{SU(2)}_2 \times \mbox{U(1)}_Y $ model with lepton-flavor non-universality are discussed. We show that active neutrinos can get Majorana masses from radiative corrections, after adding only new singly charged Higgs bosons. The mechanism for generation of neutrino masses is the same as in the Zee models. This also gives a hint to solving the dark matter problem based on similar ways discussed recently in many radiative neutrino mass models with dark matter. Except the active neutrinos, the appearance of singly charged Higgs bosons and dark matter does not affect significantly the physical spectrum of all particles in the original model. We indicate this point by investigating the Higgs sector in both cases before and after singly charged scalars are added into it. Many interesting properties of physical Higgs bosons, which were not shown previously, are explored. In particular, the mass matrices of charged and CP-odd Higgs fields are proportional to the coefficient of triple Higgs coupling $\mu$. The mass eigenstates and eigenvalues in the CP-even Higgs sector are also presented. All couplings of the SM-like Higgs boson to normal fermions and gauge bosons are different from the SM predictions by a factor $c_h$, which must satisfy the recent global fit of experimental data, namely $0.995<|c_h|<1$. We have analyzed a more general diagonalization of gauge boson mass matrices, then we show that the ratio of the tangents of the $W-W'$ and $Z-Z'$ mixing angles is exactly the cosine of the Weinberg angle, implying that number of parameters is reduced by 1. Signals of new physics from decays of new heavy fermions and Higgs bosons at LHC and constraints of their masses are also discussed., Comment: 40 pages, 1 figure; Journal vesion

This report was prepared in the context of the LPCC "Electroweak Precision Measurements at the LHC WG" and summarizes the activity of a subgroup dedicated to the systematic comparison of public Monte Carlo codes, which describe the Drell-Yan processes at hadron colliders, in particular at the CERN Large Hadron Collider (LHC). This work represents an important step towards the definition of an accurate simulation framework necessary for very high-precision measurements of electroweak (EW) observables such as the $W$ boson mass and the weak mixing angle. All the codes considered in this report share at least next-to-leading-order (NLO) accuracy in the prediction of the total cross sections in an expansion either in the strong or in the EW coupling constant. The NLO fixed-order predictions have been scrutinized at the technical level, using exactly the same inputs, setup and perturbative accuracy, in order to quantify the level of agreement of different implementations of the same calculation. A dedicated comparison, again at the technical level, of three codes that reach next-to-next-to-leading-order (NNLO) accuracy in quantum chromodynamics (QCD) for the total cross section has also been performed. These fixed-order results are a well-defined reference that allows a classification of the impact of higher-order sets of radiative corrections. Several examples of higher-order effects due to the strong or the EW interaction are discussed in this common framework. Also the combination of QCD and EW corrections is discussed, together with the ambiguities that affect the final result, due to the choice of a specific combination recipe., Comment: 92 pages, report of the working group on precision calculations for Drell-Yan processes

Radiative muon and tau lepton decays are described within the model-independent approach with the help of generalized Michel parameters. The exact dependence on charged lepton masses is taken into account. The results are relevant for modern and future experiments on muon and tau lepton decays., Comment: 10 pages, typos are corrected, references are updated

Von Neumann's procedure is applied for quantization of General Relativity. We quantize the initial data of dynamical variables at the Planck epoch, where the Hubble parameter coincides with the Planck mass. These initial data are defined via the Fock simplex in the tangent Minkowskian space-time and the Dirac conformal interval. The Einstein cosmological principle is applied for the average of the spatial metric determinant logarithm over the spatial volume of the visible Universe. We derive the splitting of the general coordinate transformations into the diffeomorphisms (as the object of the second N\"other theorem) and the initial data transformations (as objects of the first N\"other theorem). Following von Neumann, we suppose that the vacuum state is a quantum ensemble. The vacuum state is degenerated with respect to quantum numbers of non-vacuum states with the distribution function that yields the Casimir effect in gravidynamics in analogy to the one in electrodynamics. The generation functional of the perturbation theory in gravidynamics is given as a solution of the quantum energy constraint. We discuss the region of applicability of gravidynamics and its possible predictions for explanation of the modern observational and experimental data., Comment: 14 pages, updated version with extended discussion