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In this work, we investigate a new class of transverse momentum dependent functions (TMDs) as known as align-spin (AS) functions, employing the framework of twisted quark states. We reveal that these twisted (vortex) quark states serve as effective tools for the study of TMDs, thereby facilitating a comprehensive analysis of AS-functions. The proposed method is quite general and can be used for the standard TMDs. In contrast to the previous studies, the presented approach focuses on the leading order of interactions, providing a simplified and robust alternative to the methods based on the traditional $\mathbb{S}$-matrix expansion. We highlight that the critical dependence of transverse momentum arises not only from interactions but also from significant contributions linked to orbital angular momentum (OAM), influenced by the transverse momentum characteristics of correlators. Using a cylindrical formulation for twisted states, we can combine the properties of plane-wave particles with a description stemmed from spherical harmonics, resulting in well-defined propagation directions accompanied by essential OAM projections. In particular, this innovative framework opens a new window for the direct investigations of AS-functions, generating the unique angular $\phi$-dependence of differential cross sections. It also points towards promising applications in experimental particle physics., Comment: 12 pages in JHEP style

In this review, we outline the main features of the non-local gauge, named the contour gauge. The contour gauge belongs to the axial type of gauges and extends the local gauge used in the most of approaches. The geometry of gluon fields and the path-dependent formalism are the essential tools for the description of non-local gauges. The principle feature of the contour gauge is that there are no the residual gauges which are left in the finite domain of space. In the review, we present the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. The Hamiltonian formalism is turned out to be a very convenient framework for the understanding of contour gauges. The comprehensive comparison analysis of the local and non-local gauges advocates the advantage of the contour gauge use. We show that the appropriate use the contour gauge leads to the existence of extra diagram contributions. These additional contributions, first, restore the gauge invariance of the hadron tensor and, second, give the important terms for the observable quantities. We also demonstrate the significant role of the additional diagrams to form the relevant contour in the Wilson path-ordered exponential. Ultimately, it leads to the spurious singularity fixing. Moreover, in the present review, we discuss in detail the problem of spin and orbital angular momentum separation. We show that in $SU(3)$ gauge theories the gluon decomposition on the physical and pure gauge components has a strong mathematical evidence provided the contour gauge conception has been used. In addition, we prove that the contour gauge possesses the special kind of residual gauge that manifests at the boundary of space. Besides, the boundary field configurations can be associated with the pure gauge fields., Comment: 54 pages in JHEP style and 6 figures. arXiv admin note: substantial text overlap with arXiv:1612.03010, arXiv:2105.02719

We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new analytical term to the Tikhonov regularization of Moore-Penrose's inversion procedure, we derive new optimization conditions that extend the Tikhonov regularization framework and influence the fitting parameter. This enhancement yields a more robust and accurate reconstruction of physical quantities, demonstrating its potential impact on various studies. We illustrate the significance of new term through schematic examples of physical applications, highlighting its relevance to diverse fields. Our findings provide a valuable tool for improving inversion methods and their applications in physics and beyond., Comment: 13 pages in JHEP style; the improved version, it matches the journal variant

We consider the model of a single-mode quantum nonlinear oscillator with the fourth (Kerr) and sixth (over-Kerr) orders of nonlinearity in the presence of fluctuations of the driving field. We demonstrate that the presence of the amplitude noise does not significantly affect the multi-photon Rabi transitions for the Kerr oscillator, and, in contrast, suppresses these oscillations for the over- Kerr oscillator. We explain the suppression of multi-photon transitions in the over-Kerr oscillator by quasienergy fluctuations caused by noise in field amplitude. In contrast, for the Kerr oscillator, these fluctuations cancel each other for two resonant levels due to the symmetry in the oscillator quasienergy spectrum.

We present the further development of the vacuum massless integrations. In particular, in the Gorishny-Isaev formula, it has been shown that the delta function representing UV-regime should be treated within the sequential approach. It allows us to resolve the problem of vacuum integrations related to the analytical continuation of diagram indices., Comment: 6 pages; Based on the materials presented as a talk at The XXVth International Baldin-Burov Seminar on High Energy Physics Problems, September, 21st 2023, Dubna

In this note we present the important details regarding the massless vacuum integrations which are not outlined in the literature. In particular, it has been shown how the delta-function represents either UV-regime or IR-regime. In the case of vacuum integration, we advocate the use of sequential approach to the singular generated functions (distributions). The sequential approach is extremely useful for many practical applications, in particular, in the effective potential method., Comment: 8 pages

We present the second part of a paper series devoted to the study of the multi-loop effective potential evolution in $\varphi^4$-theory using the conformal symmetry. In this paper, we demonstrate that the conformal symmetry can still be useful for the effective potential approach even at the presence of the mass parameter. To this goal, it is necessary to introduce the special treatment of the mass terms as sorts of interaction in an asymptotical expansion of the generating functional. The introduced vacuum $V_{z,x}$-operation is the main tool to the algebraic scheme of anomalous dimension calculations. It is shown that the vacuum $V_{z,x}$-operation transforms the given Green functions to the corresponding vacuum integrations which generate the effective potential., Comment: 17 pages, 6 figures; the version matches the journal variant

We begin a series of two papers that is devoted to the study of the multi-loop effective potential evolution in $\varphi^4$-theory using the conformal symmetry. In the first part, we introduce and describe in detail the vacuum $V_{z,x}$-operation ($"V"$ stems from "vacuum", $\{z,x\}$ imply the corresponding coordinates) that transforms the given Green functions to the corresponding vacuum integrations which generate the effective potential. Our operation can be considered as an inverse procedure compared to the Gorishni-Isaev method. To the final goal, it is necessary to introduce also the special treatment of the mass terms as sorts of "interaction" in an asymptotical expansion of the generating functional., Comment: 14 pages, 3 figures; the version matches the journal variant

We advocate the existence of a new type of $k_\perp$-dependent functions. In contrast to the well-known Boer-Mulders function, the presented new functions can be associated with the collective alignment of quark spin vectors. Moreover, the new functions are sensitive to the transverse motion of partons inside hadrons, which are linked to the spin alignment of partons, and they are initiated by the interactions encoded in the corresponding correlators., Comment: 11 pages, 1 figure; Based on the materials presented at the ICQFTHEPC-22, Dubna, July 18th - 21st, 2022

We consider the model of two coupled oscillators with Kerr nonlinearities in the rotating-wave approximation. We demonstrate that for a certain set of parameters of the model, the multi-photon transitions occur between many pairs of the oscillator states simultaneously. Also, the position of the multi-photon resonances does not depend on the coupling strength between two oscillators. We prove rigorously that this is a consequence of a certain symmetry of the perturbation theory series for the model. In addition, we analyse the model in the quasi-classical limit by considering the dynamics of the pseudo-angular momentum. We identify the multi-photon transitions with the tunnelling transitions between the degenerate classical trajectories on the Bloch sphere.

In the paper we focus on the study of the functional complexity of the Lorentz parametrizing functions in connection with the time-reversal transformations. We argue that the interactions encoded in the corresponding correlators of non-local quark(-gluon) operators generate additional sources of functional complexity for the parametrizing functions which are not discussed in the literature. We also revisit the Lorentz parametrization of different correlators given by the hadron matrix elements of the non-local operators. The evidences for the new parametrizing function existence have been presented., Comment: 17 pages, 4 figures

Within the archetypal factorization procedure, we study the gluon pole contributions manifesting in the nucleon-lepton hard processes of hadron production. We prove the dominant role of gluon pole contributions in the processes of such kind. We analyse the different sources of complexity associated with the gluon pole functions. As a practical application, we derive a new single spin asymmetry related directly to the gluon poles which can be studied experimentally., Comment: 34 pages, 4 figures; the improved version matches the journal variant

We argue the existence of new $k_\perp$-dependent functions which can be manifested in the Drell-Yan (SIDIS)-like processes. The presented new functions resemble the well-known Boer-Mulders function associated with the quark spin asymmetry, but in contrast they are sensitive to the transverse motion of partons inside the hadron due to the collective alignment of quark spin vectors., Comment: 13 pages, 1 Figure; altered version: explanations and clarifications added

In Quantum Field Theory, we discuss the main features of the (non-local) contour gauge which extends the local axial-type gauge used in most approaches. Based on the gluon geometry, we demonstrate that the contour gauge does not suffer from the residual gauge. We discuss the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. Having compared the local and non-local gauges, we again advocate the advantage of the contour gauge use., Comment: 9 pages, 2 figures; typos fixed and explanations added

Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about the possibility to separate the spin AM from the orbital AM in the gauge invariant manner are based on the ansatz that the gluon field can be presented in form of the decomposition where the physical gluon components are additive to the pure gauge gluon components, i.e. $A_\mu = A_\mu^{\text{phys}}+A_\mu^{\text{pure}}$. In the present paper, we show that in the non-Abelian gauge theory this gluon decomposition has a strong mathematical evidence in the frame of the contour gauge conception. In other words, we reformulate the gluon decomposition ansatz as a theorem on decomposition and, then, we use the contour gauge to prove this theorem. In the first time, we also demonstrate that the contour gauge possesses the special kind of residual gauge related to the boundary field configurations and expressed in terms of the pure gauge fields. As a result, the trivial boundary conditions lead to the inference that the decomposition includes the physical gluon configurations only provided the contour gauge condition., Comment: 6 pages, 2 figures; a few typos have been fixed; the version includes the extended References

We considered the multiphoton resonance in the periodically driven quantum oscillator with Kerr nonlinearity in the presence of weak high-order nonlinearities. Multiphoton resonance leads to the emergence of peaks and dips in the dependence of the stationary occupations of the stable states on detuning. We demonstrated that due to high-order nonlinearities, these peaks and dips acquire additional fine structure and split into several closely spaced ones. Quasiclassically, multiphoton resonance is treated as tunneling between the regions of the oscillator phase portrait, and the fine structure of the multiphoton resonance is a consequence of a special quasienergy dependence of the tunneling rate between different regions of the classical phase portrait. For different values of damping and high-order nonlinearity coefficients, we identified the domain of quasienergies where tunneling strongly influences the system kinetics. The corresponding tunneling term in the Fokker-Planck equation in quasienergy space was derived directly from the quantum master equation.

We report the prediction of a new type of Dyakonov surface waves that propagate along the flat strip of the interface between two dielectrics with negative anisotropy. It is shown that the surface waves condition is satisfied for negatively anisotropic dielectrics due to specific boundaries of the strip waveguide confined between two metallic plates. Such modes are studied by the perturbation theory in the approximation of weak anisotropy. The existence of Dyakonov surface waves in negative uniaxial crystals motivates us to reconsider the list of materials suitable for their practical implementation. We believe that this work opens a new unexplored research area in the field of surface waves., Comment: 5 pages, 4 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.

In this note, we demonstrate in detail the $\xi$-process implementation applied to the deeply virtual Compton scattering amplitude to ensure both the QCD and QED gauge invariance. The presented details are also important for understanding of the contour gauge used in different processes., Comment: 7 pages, 3 figures; a few typos are fixed

The effective potential is known to be given by the vacuum diagrams. In this paper we show that the massive loop integrations corresponding to the vacuum diagrams can be expressed through the massless loop integrations with the corresponding massive prefactor provided the special treatment of $\delta(0)$-singularity. In its turn, the massless loop integrations provide the useful instrument for the conformal symmetry application., Comment: 4 pages, 3 figures

We theoretically study Dyakonov surface waveguide modes that propagate along the planar strip interfacial waveguide between two uniaxial dielectrics. We demonstrate that due to the one-dimensional electromagnetic confinement, Dyakonov surface waveguide modes can propagate in the directions that are forbidden for the classical Dyakonov surface waves at the infinite interface. We show that this situation is similar to a waveguide effect and formulate the resonance conditions at which Dyakonov surface waveguide modes exist. We demonstrate that the propagation of such modes without losses is possible. We also consider a case of two-dimensional confinement, where the interface between two anisotropic dielectrics is bounded in both orthogonal directions. We show that such a structure supports Dyakonov surface cavity modes. Analytical results are confirmed by comparing with full-wave solutions of Maxwell's equations. We believe that our work paves the way towards new insights in the field of surface waves in anisotropic media., Comment: 15 pages, 6 figures

We study Dyakonov surface waveguide modes in a waveguide represented by an interface of two anisotropic media confined between two air half-spaces. We analyze such modes in terms of perturbation theory in the approximation of weak anisotropy. We show that in contrast to conventional Dyakonov surface waves that decay monotonically with distance from the interface, Dyakonov waveguide modes can have local maxima of the field intensity away from the interface. We confirm our analytical results by comparing them with full-wave electromagnetic simulations. We believe that this work can bring new ideas in the research of Dyakonov surface waves., Comment: 5 pages, 3 figures

We present an analytical and numerical study of the fluorescence spectra of a bistable driven system by means of Keldysh diagram technique in pseudo--particle representation. The spectra exhibit smooth transition between ultra-quantum and the quasiclassical limits and indicate the threshold value of the external field when changing of the most probable stable state occurs. The analysis of the fluorescence spectra also allows to determine the most probable stable state of the system. It was also shown that at integer and half-integer detuning-nonlinearity ratio multiphoton resonance leads to abrupt changes in fluorescence spectra. It was also revealed that the fluorescence spectra are symmetric in the limit of zero environment temperature. The predicted features of the spectra could be observed in experiments with ultra-high quality resonators in either microwave or optical domain.

We outline the developed approach within the light-cone sum rules at the leading order for calculation of the gravitational form factors related to the nucleon valence quark combinations. The predictions for the gravitational form factor $D(t)$ ($D$-term contributions) have been presented., Comment: 5 pages, 1 figure, the References added; to appear in the proceedings of DSPIN-19

We revisit the standard representation of the (inverse) Radon transform which is well-known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional contribution which is essentially related to the generalized transverse-momentum dependent parton distribution and double-distribution functions. We discuss the possible relationship of this term with the Sivers function., Comment: 11 pages, 2 figures, the present version matches the Journal variant

The non-equilibrium statistics and kinetics of a simple bistable system (resonantly driven nonlinear oscillator coupled to reservoir) have been investigated by means of master equation for the density matrix and quasiclassical Fokker-Planck equation in quasienergy space. We found out that the system's statistical and kinetic properties drastically change when the quasienergy states become nearly degenerate and the occupation of the most excited state is strongly enhanced. It has been revealed that in nearly degenerate case a new critical quasienergy parameter emerges. Below the critical quasienergy value the eigenstates are superpositions of the quasiclassical states from different phase space regions, while above this value the eigenstates correspond to only one particular region of the phase space. We have also generalized Keldysh theory for ionization of atoms in the electromagnetic field for bistable systems. It has been demonstrated that Keldysh parameter in bistability region is large when pumping intensity is smaller than the critical value. It has been shown by direct calculations that multi-photon transition amplitude coincides with the tunneling amplitude. So, multi-photon transitions and tunneling between the regions of the phase space are just the same effects. We also demonstrated that for bistable systems the Keldysh parameter logarithmically depends on the external field amplitude., Comment: 11 pages, 6 figures

Using the light-cone sum rules at leading order, we present an approach to perform the preliminary upper estimation for the nucleon gravitational form factor $D(t)$ ($D$-term contribution). Comparison with the experimental data and with the results of different models is discussed., Comment: 6 pages, 2 figures; The Special Issue "QCD and Hadron Structure" devoted to the memory of Prof. G.V. Efimov. arXiv admin note: substantial text overlap with arXiv:1902.00094

We develop an approach based on the light-cone sum rules at the leading order of $\alpha_S$ to calculate the gravitational form factors $A(t)$ and $B(t)$ for the valence quark combinations in nucleon. Within the proposed model, the predictions for the gravitational form factor $D(t)$ ($D$-term contributions) have been presented. Comparison with the experimental data and with the results of different models is discussed., Comment: 10 pages, 8 figures; Typos fixed; the version matches the journal variant

Bistability of nonlinear resonantly driven oscillator in the presence of external noise is analyzed by means of classical Fokker-Planck equation in quasienergy space with account for tunneling effects and by quantum master equation in quasienergy states representation. Two time scales responsible for different stages of bistable system relaxation have been obtained. We found out that the slow relaxation rate caused by fluctuation--induced transitions between different stable states can be enhanced by several orders due to tunneling effects. It was also revealed that tunneling between nearly degenerate quasienergy states and resonant multiphoton transitions between the genuine eigenstates of the nonlinear oscillator are just the similar effects. It was demonstrated that the quasienergy states in the bistability region corresponding to higher amplitude are squeezed. The degree of squeezing is determined by the ratio between nonlinearity and detuning, so the uncertainty of one quadrature can be considerably smaller than the quantum limit. It was found out that tunneling effects can enhance the generation of output oscillator squeezed states. It is shown that 1D Fokker--Planck equation is a quasiclassical limit of a quantum master equation.

We calculate the hadron tensor related to the photon-induced Drell-Yan process, with incoming nucleon being transversally polarised. We predict the new single spin asymmetry which probes gluon poles and which is expressed in terms of photon (both chiral-odd and chiral-even) distribution amplitudes and chiral-odd nucleon function stemming from the nucleon transverse polarization., Comment: 6 pages, 3 figures; Appendix has been added

Transverse momentum distributions and generalized parton distributions provide a comprehensive framework for the three-dimensional imaging of the nucleon and the nucleus experimentally using deeply virtual semi-exclusive and exclusive processes. The advent of combined high luminosity facilities and large acceptance detector capabilities enables experimental investigation of the partonic structure of hadrons with time-like virtual probes, in complement to the rich on-going space-like virtual probe program. The merits and benefits of the dilepton production channel for nuclear structure studies are discussed within the context of the International Workshop on Nucleon and Nuclear Structure through Dilepton Production taking place at the European Center for Theoretical Studies in Nuclear Physics and Related Areas (ECT$^{\star}$) of Trento. Particularly, the double deeply virtual Compton scattering, the time-like Compton scattering, the deeply virtual meson production, and the Drell-Yan processes are reviewed and a strategy for high impact experimental measurements is proposed., Comment: 21 pages, 23 figures, Conference proceedings

Based on the use of contour gauge and collinear factorization, we propose a new set of single spin asymmetry which can be measured in polarized Drell-Yan process by SPD@NICA. We stress that the discussed single transverse spin asymmetries exist owing to the gluon poles manifesting in the twist-3 or twist-2$\otimes$twist-3 parton distributions related to the transverse-polarized Drell-Yan process., Comment: 5 pages, 1 figure, Contribution to the proceedings of XVII Workshop on High Energy Spin Physics DSPIN-17, September 11-15, Dubna

We study the Drell-Yan process in the polarized pion-nucleon scattering. We calculate the $U(1)_\text{em}$ gauge invariant hadron tensors. To this end, we have to take into account two diagrams---the standard diagram and an additional one---both diagrams are required to get the gauge invariant hadron tensor. We obtain a new single transverse spin asymmetry that probes gluon poles and chiral-odd distribution functions. The process of pion-nucleon scattering in the limit of large Feynman $x$ is described by a convolution of two non-collinear exclusive-channel distribution amplitudes, which demonstrates the duality between different factorization regimes., Comment: 6 pages, 3 figures. Contribution to the proceedings of XVII Workshop on High Energy Spin Physics (DSPIN-17), September 11-15, Dubna, Russia