arXiv subjects

Andrey Tarasov

Publications and source records attributed to Andrey Tarasov.

At least 19 recordsLinked to original sources

arXiv2026

Orbital angular momentum at small $x$ in the large $N_c\&N_f$ limit

We extend the small-$x$ analysis of the quark and gluon orbital angular momentum (OAM) distributions in the proton from the large-$N_c$ limit considered in our earlier works to the large-$N_c\&N_f$ limit, in which the numbers of quark colors $N_c$ and flavors $N_f$ are large with their ratio held fixed. Working in the double-logarithmic approximation (DLA), summing powers of $α_s \ln^2(1/x)$ with $α_s$ the strong coupling and $x$ the proton's momentum fraction carried by a parton, we correct the small-$x$ operator expression for the quark OAM distribution suggested earlier in \cite{Kovchegov:2024wjs} and relate both the quark and gluon OAM distributions to the impact-parameter moments of the polarized dipole amplitudes. We derive the large-$N_c\&N_f$ evolution equations for these moment amplitudes in the DLA; these include a new equation for the moment amplitude governing the quark OAM. We then solve these evolution equations numerically together with the helicity evolution for $N_f = 2,3,4,5,6$ and $N_c =3$. We find that, similar to the large-$N_c$ case, the OAM distributions share a common small-$x$ intercept with the helicity distributions, $L_{q+\bar{q}}(x,Q^2) \sim L_G(x,Q^2) \sim ΔΣ(x,Q^2) \sim ΔG(x,Q^2) \sim \left(\frac{1}{x} \right)^{α_h}$ with the intercept $α_h \approx {3.48 \sqrt{α_s N_c/2π}}$ for $N_f = N_c = 3$ (cf.~\cite{Borden:2025ehe}): this result, along with $α_h$ for other values of $N_f \neq 0$ that we studied, is smaller than the intercept of $3.66\sqrt{α_s N_c/2π}$ found in the large-$N_c$ limit. We also compute the ratios of the OAM distributions to the helicity parton distribution functions as $x\to 0$, obtaining $L_{q+\bar{q}}(x,Q^2)/ΔΣ(x,Q^2) \approx -1.01$ and $L_G(x,Q^2)/ΔG(x,Q^2) \approx -1.94$ at $Q^2=10\, \mathrm{GeV}^2$, with both ratios being nearly independent of $N_f$.

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arXiv2026

Back-to-back dijet production in DIS at arbitrary Bjorken-x: TMD gluon distributions to twist-3 accuracy

We derive the gluon transverse-momentum-dependent (TMD) operator structure of back-to-back quark-antiquark dijet production in deep inelastic scattering at arbitrary Bjorken-x to twist-3 accuracy. Working at leading order in the strong coupling and in the kinematic regime where the transverse momentum imbalance of the jets is much smaller than their individual transverse momenta, we perform a systematic gradient expansion of the quark propagator in a background gluon field. This expansion organizes multiple interactions with the target in terms of longitudinal Wilson lines and gauge-invariant field-strength insertions, yielding a TMD description valid beyond the strict high-energy eikonal (x -> 0) approximation. We obtain explicit cross sections for longitudinally and transversely polarized virtual photons, identifying all contributing gluon TMD operators up to twist-3, including structures involving F_+-, F_ij, and three-gluon correlators. The full longitudinal phase associated with Bjorken-x is retained throughout. In the small-x limit, our results reproduce the known sub-eikonal expressions obtained in the Color Glass Condensate framework, establishing a direct connection between the general-x TMD expansion and high-energy factorization. We further reduce the operator basis using equations of motion, minimizing the number of independent nonperturbative matrix elements entering the cross section. This work provides a systematic foundation for extending TMD analyses of dijet production beyond leading twist, establishing a unified operator framework valid at arbitrary Bjorken x that smoothly interpolates between moderate- and small-x descriptions of gluon TMDs.

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arXiv2026

Back-to-back dijet production in DIS at arbitrary Bjorken-x: TMD quark distributions to twist-3 accuracy

We study the contributions of target quark background to quark-gluon and quark-antiquark dijet productions cross sections in deep inelastic scattering (DIS) at arbitrary Bjorken-$x$. Using the background-field method, we organize the leading-order dijet production cross section in terms of bilocal quark and trilocal quark--gluon--quark correlators. The former provides the contributions of the leading-twist as well as the kinematical and dynamical twist-three quark transverse-momentum-dependent (TMD) distributions, while the latter encode contributions of the dynamical twist-three TMD distributions. {Together with the gluon distributions derived in Ref.~\cite{Mukherjee:2026cte}}, these results provide the complete leading-order cross section for back-to-back dijet production in DIS at arbitrary Bjorken-$x$ to twist-three accuracy. This theoretical framework extends the TMD description of the process beyond the small-$x$ eikonal regime and provides the necessary tools for analyzing data from the future Electron--Ion Collider.

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arXiv2026

Efficient computation of the N-th rank QED polarization tensor: Universal worldline structure of form factors

We derived in arXiv:2206.04188 arXiv:2211.15712 a compact expression for the $N$-th rank QED polarization tensor $Π_{μ_1\cdots μ_N}(k_1,\cdots,k_N)$ in a $(0+1)$-dimensional worldline framework. This fully off-shell object, a function of $N$ external photon four-momenta, is a key ingredient in high-order computations of cusp anomalous dimensions and lepton anomalous magnetic moments. We demonstrate here that $Π_{μ_1\cdots μ_N}$ can further be expressed simply in terms of a small number of independent ``head" form factors (each representing $(N-1)!/2$ Feynman diagrams) which have a universal structure in terms of sums over fermion Green functions and (propertime derivative of) their boson worldline superpartners. This worldline representation bypasses explicit Wick contractions and avoids tensor reductions to scalar loop integrals à la Passarino and Veltman, order by order in perturbation theory. We give explicit expressions for the $4$-th and $6$-th rank head form factors and provide a computer script generalizing these results to arbitrary $N$ external photons. The multiplicity of heads, and their growth with $N$, can be understood in terms of orbits of the permutation group. We employ the Burnside-Cauchy-Frobenius lemma to show that it scales as $e^{N-1}/\sqrt{N}$ terms as opposed to the $e^{N-1} N!/\sqrt{N}$ terms in conventional perturbation theory. We reexpress worldline parameter integrals that define the $4$-th rank heads as Feynman parameter integrals to reproduce the seminal results by Karplus and Neuman for the on-shell light-by-light amplitude and extend these to the fully off-shell case in massless QED employing a tailored integration-by-parts procedure. In a follow-up paper, we will discuss the direct computation of worldline integrals, potentially providing a further $N!$ advantage relative to Feynman diagram computations at high orders in perturbation theory.

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arXiv2026

DIS dijet production in Background Field Approach: General formalism and methods

We develop a general formalism for computing physical observables within the background field approach, based on representing propagators of the Feynman diagrams in the background fields as path-ordered exponents. This representation allows systematic expansion of the background fields onto arbitrary linear piecewise contours in coordinate space, yielding gauge-covariant QCD operators to any required order of the expansion. We apply this formalism to DIS dijet production and derive a general form of the cross section in terms of (anti)quark propagators in the background fields, valid in arbitrary kinematics. To demonstrate the versatility of our approach, we consider two kinematic limits. In the back-to-back limit, the expansion contour reduces to that of TMD operators. In this limit we recover the known leading-power results. In the small-$x$ regime, defined by the high-energy power counting for boosted background fields, the expansion contour assumes a staple-like shape. We find that, at the leading eikonal order, the transverse component of the background field $B_i$, though parametrically suppressed relative to the light-cone component, contributes non-trivially through the field-strength tensor $F_{-i}$ and the transverse gauge links. Setting $B_i = 0$ recovers the standard CGC result. We also demonstrate matching between the eikonal and back-to-back expansions, providing a quantitative dictionary between these two distinct kinematic regimes.

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arXiv2026

JIMWLK on a quantum computer

We propose a method for solving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution equation on quantum computers. Our approach exploits the reformulation of the JIMWLK equation as a Lindblad master equation governing the rapidity evolution of the hadronic density matrix, as established in prior work. To render the problem tractable for quantum simulation, we introduce several approximations: the two-dimensional transverse plane is reduced to a one-dimensional radial lattice by assuming azimuthal symmetry of the jump operators; the gauge group is restricted to $\mathrm{SU}(2)$; and the infinite Wilson lines of the JIMWLK equation are replaced by finite Wilson links along the light-cone direction. The resulting bosonic Hilbert space is truncated using the electric field basis familiar from Hamiltonian lattice gauge theory, with states restricted to angular momenta $j\leq j_{\mathrm{max}}$. We derive the matrix elements of the JIMWLK Lindblad jump operators in this basis. As a benchmark, we demonstrate rapid convergence of the fundamental dipole expectation value with $j_{\mathrm{max}}$ for both pure and mixed Gaussian initial density matrices. For the simplest truncation, $j_{\mathrm{max}} = 1/2$, we implement the Lindblad evolution using a quantum simulation algorithm verified with the Qiskit statevector simulator by decomposing the non-unitary evolution operator into a linear combination of unitaries. This work establishes a concrete pathway toward quantum simulation of high-energy QCD evolution equations, with direct relevance to the physics program of the Electron-Ion Collider.

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arXiv2025

Perturbative Corrections to Quark TMDPDFs in the Background-Field Method: Gauge Invariance, Equations of Motion, and Multiple Interactions

We calculate the perturbative corrections in the strong coupling to the unpolarized quark transverse-momentum dependent parton distribution function (TMDPDF) operator within a background-field framework, extending the approach of Ref. [1]. We focus on ensuring gauge invariance, identifying two key components needed: a gauge-invariant TMDPDF operator with a transverse gauge link at spatial infinity, and accounting of the equations of motion (EoM) of the background fields. We go beyond next-to-leading order in strong coupling expansion, considering multiple interactions with the background field at all orders of strong coupling. By examining the interplay between quark and gluon contributions, we show that spurious singularities, proportional to EoM, can be misinterpreted as genuine divergences in QCD factorization unless properly identified and removed.

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arXiv2025

First study of polarized proton-proton scattering with small-$x$ helicity evolution

We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-$x$ helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton ($pp$) scattering at parton momentum fractions $x < 0.1$. We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing $x < 0.1$. Employing the polarized small-$x$ pure-glue calculation of $pp\to gX$ for the jet production cross section, we modify the large-$N_c\&N_f$ KPS-CTT evolution equations by setting $N_f = 0$ to replicate the large-$N_c$ (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the $pp$ data have a considerable impact on the helicity PDFs at small $x$, reducing their uncertainties and leading to a total quark and gluon helicity in the proton for $x < 0.1$ of $-0.04 \pm 0.23$. Combining our analysis with the a recent JAM helicity PDF analysis of the world polarized data, which includes $x > 0.1$, we find a total quark and gluon helicity contribution for $x > 10^{-7}$ of between 0.02 and 0.51.

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arXiv2025

The role of the chiral anomaly in polarized deeply inelastic scattering III: Wess-Zumino-Witten contributions and chiral Ward identities for finite quark mass

We extend our prior results on the worldline computation of the axial vector-vector-vector (AVV) triangle anomaly in polarized deeply inelastic scattering (DIS) to the finite mass case by computing in addition the pseudoscalar-vector-vector (PVV) triangle graph. For the well-studied QED case, we show explicitly how the off-forward AVV pole exactly cancels an identical PVV pole. We then demonstrate the dramatic difference in QCD due to the chiral condensate, which qualitatively modifies anomalous Ward identities. As in the massless case, the anomaly pole in QCD is canceled by the dynamics of a primordial isosinglet pseudoscalar $\bar η$-meson, whose Wess-Zumino-Witten coupling to the topological charge density shifts the pole to the physical $η^\prime$ mass, with the finite quark mass contribution differing by $O(10\%)$ from the Witten-Veneziano formula. We obtain a compact analytic expression for the finite mass corrections to Shore and Veneziano's result that the proton's net quark helicity $ΔΣ\propto \sqrt{χ_{\rm QCD}' |_{m=0}(0)}$, the forward slope of the topological susceptibility in the chiral limit, and show they are of the order of a few percent. Our prior prediction that the polarized DIS structure function $g_1$ is quenched by sphaleron-like topological transitions at small $x$ is unaffected by quark mass effects. Our results illustrate how worldline computations of anomalous processes, in synergy with lattice computations and nonet chiral perturbation theory, can uncover novel nonperturbative features of QCD at the Electron-Ion collider.

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arXiv2024

Quark and Gluon Helicity Evolution at Small $x$: Revised and Updated

We revisit the problem of small Bjorken-$x$ evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave ($s$-channel) formalism. Earlier works on the subject in the same framework resulted in an evolution equation for the gluon field-strength $F^{12}$ and quark "axial current" ${\barψ}γ^+γ^5ψ$ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (DLA: summing powers of $α_s\,\ln^2(1/x)$ with $α_s$ the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, $\overleftarrow{D}^i\,{D}^i$, also sandwiched between the light-cone Wilson lines (with the repeated index $i=1,2$ summed over), was missing in the previous works. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, $D^i-\overleftarrow{D}^i$, which is related to the Jaffe-Manohar polarized gluon distribution. In this work we include this operator into small-$x$ helicity evolution, and construct a novel evolution mixing all three operators ($D^i-\overleftarrow{D}^i$, $F^{12}$, and ${\barψ}γ^+γ^5ψ$), generalizing the previous results. We also construct closed DLA evolution equations in the large-$N_c$ and large-$N_c\& N_f$ limits, with $N_c$ and $N_f$ the numbers of quark colors and flavors, respectively. Solving the large-$N_c$ equations numerically we obtain the following small-$x$ asymptotics of the quark and gluon helicity distributions $ΔΣ$ and $ΔG$, along with the $g_1$ structure function, \[ΔΣ(x,Q^2)\simΔG(x,Q^2)\sim g_1(x,Q^2)\sim\left(\frac{1}{x}\right)^{3.66\,\sqrt{\frac{α_s\,N_c}{2π}}},\] in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin.

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arXiv2024

TMD factorization bridging large and small x

QCD factorization takes different forms in the large-x and small-x regimes. At large-x, collinear factorization leads to the DGLAP evolution equation, while at small-x, rapidity factorization results in the BFKL equation. To unify these different regimes, a new TMD factorization based on the background field method is proposed. This factorization not only reduces to CSS and DGLAP in the large-x limit and BFKL in the small-x limit, but also defines a general evolution away from these regimes.

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arXiv2024

A unified description of DGLAP, CSS, and BFKL: TMD factorization bridging large and small x

This paper introduces a transverse-momentum dependent (TMD) factorization scheme designed to unify both large and small Bjorken-x regimes. We compute the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to the gluon TMD operator for an unpolarized hadron within this proposed scheme. This leads to the emergence of a new TMD evolution, incorporating those in transverse momentum, rapidity, and Bjorken-x. When matched to the collinear factorization scheme, our factorization scheme faithfully reproduces the well-established Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Collins-Soper-Sterman (CSS) evolutions. Conversely, matching with high-energy factorization not only yields the Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution but also reveals distinctive signatures of CSS logarithms. The development of this novel TMD factorization scheme, capable of seamlessly reconciling disparate Bjorken-x regimes and faithfully reproducing established QCD evolution equations, has the potential to significantly advance our comprehension of high-energy processes and three-dimensional parton structures of hadrons.

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arXiv2023

Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution

We analyze the world polarized deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data at low values of $x < 0.1$, using small-$x$ evolution equations for the flavor singlet and nonsinglet helicity parton distribution functions (hPDFs). The hPDFs for quarks, antiquarks, and gluons are extracted and evolved to lower values of $x$ to make predictions for the future Electron-Ion Collider (EIC). We improve on our earlier work by employing the more realistic large-$N_c\, \& N_f$ limit of the revised small-$x$ helicity evolution, and incorporating running coupling corrections along with SIDIS data into the fit. We find an anti-correlation between the signs of the gluon and $C$-even quark hPDFs as well as the $g_1$ structure function. While the existing low-$x$ polarized DIS and SIDIS data are insufficient to constrain the initial conditions for the polarized dipole amplitudes in the helicity evolution equations, future EIC data will allow more precise predictions for hPDFs and the $g_1$ structure function for $x$ values beyond those probed at the EIC. Using the obtained hPDFs, we discuss the contributions to the proton spin from quark and gluon spins at small $x$.

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arXiv2023

QED as a many-body theory of worldlines: II. All-order S-matrix formalism

In arXiv:2206.04188, we developed a first-quantized worldline formalism for all-order computations of amplitudes in QED. In particular, we demonstrated in this framework an all-order proof of the infrared safety of the Faddeev-Kulish (FK) S-matrix for virtual exchanges in the scattering of charged fermions. In this work, we extend the worldline formalism for both the Dyson and FK S-matrix to consider further the emission and absorption of arbitrary numbers of photons. We show how Low's theorem follows in this framework and derive Weinberg's theorem for the exponentiation of IR divergences. In particular, we extend our all-order proof of the IR safety of the FK S-matrix to both virtual exchanges and real photon emissions. We argue that the worldline approach leads to a modern Wilsonian interpretation of the IR safety of the FK S-matrix and provides a novel template for the treatment of IR divergences in real-time problems. Using Grassmannian integration methods, we derive a simple and powerful result for N-th rank vacuum polarization tensors. Applications of these methods will be discussed in follow-up work.

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arXiv2023

TMD Handbook

This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.

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arXiv2022

QED as a many-body theory of worldlines: I. General formalism and infrared structure

We discuss a reformulation of QED in which matter and gauge fields are integrated out explicitly, resulting in a many-body Lorentz covariant theory of 0+1 dimensional worldlines describing super-pairs of spinning charges interacting through Lorentz forces. This provides a powerful, string inspired definition of amplitudes to all loop orders. In particular, one obtains a more general formulation of Wilson loops and lines, with exponentiated dynamical fields and spin precession contributions, and worldline contour averages exactly defined through first quantized path integrals. We discuss in detail the attractive features of this formalism for high order perturbative computations. We show that worldline S-matrix elements, to all loop orders in perturbation theory, can be constructed to be manifestly free of soft singularities, with infrared (IR) divergences captured and removed by endpoint photon exchanges at infinity that are equivalent to the soft coherent dressings of the Dyson S-matrix proposed by Faddeev and Kulish. We discuss these IR structures and make connections with soft theorems, the Abelian exponentiation of IR divergences and cusp anomalous dimensions. Follow-up papers will discuss the efficient computation of cusp anomalous dimensions and universal features of soft theorems.

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arXiv2022

The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

In [1], we demonstrated that the structure function $g_1(x_B,Q^2)$ measured in polarized deeply inelastic scattering (DIS) is dominated by the triangle anomaly in both the Bjorken limit of large $Q^2$ and the Regge limit of small $x_B$. In the worldline formulation of quantum field theory, the triangle anomaly arises from the imaginary part of the worldline effective action. We show explicitly how a Wess-Zumino-Witten term coupling the topological charge density to a primordial isosinglet ${\bar η}$ arises in this framework. We demonstrate the fundamental role played by this contribution both in topological mass generation of the $η^\prime$ and in the cancellation of the off-forward pole arising from the triangle anomaly in the proton's helicity $Σ(Q^2)$. We recover the striking result by Shore and Veneziano that $Σ\propto \sqrt{χ'(0)}$, where $χ'$ is the slope of the QCD topological susceptibility in the forward limit. We construct an axion-like effective action for $g_1$ at small $x_B$ that describes the interplay between gluon saturation and the topology of the QCD vacuum. In particular, we outline the role of "over-the-barrier" sphaleron-like transitions in spin diffusion at small $x_B$. Such topological transitions can be measured in polarized DIS at a future Electron-Ion Collider.

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arXiv2022

Helicity Evolution at Small $x$: the Single-Logarithmic Contribution

We calculate single-logarithmic corrections to the small-$x$ flavor-singlet helicity evolution equations derived recently in the double-logarithmic approximation. The new single-logarithmic part of the evolution kernel sums up powers of $α_s \ln(1/x)$, which are an important correction to the dominant powers of $α_s \ln^2(1/x)$ summed up by the double-logarithmic kernel at small values of Bjorken $x$ and with $α_s$ the strong coupling constant. The single-logarithmic terms arise separately from either the longitudinal or transverse momentum integrals. Consequently, the evolution equations we derive employing the light-cone perturbation theory simultaneously include the small-$x$ evolution kernel and the leading-order polarized DGLAP splitting functions. We further enhance the equations by calculating the running coupling corrections to the kernel.

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