arXiv subjects

Tolga Altinoluk

Publications and source records attributed to Tolga Altinoluk.

At least 19 recordsLinked to original sources

arXiv2026

One-loop renormalization of the quark TMD in projectile light-cone gauge

We use the background field formalism to calculate next-to-leading-order corrections to a quark transverse momentum dependent parton distribution function (TMD) in the projectile light-cone gauge, i.e. $A^{+}=0$ for a left-moving target. We calculate the full result using the Mandelstam-Leibbrandt prescription for handling the light-cone singularity. From the one-loop renormalization of the quark TMD, we obtain the Collins-Soper-Sterman (CSS) evolution equations. The projectile light-cone gauge is widely used in calculations within the gluon saturation regime. Our work therefore opens a way to understanding the connections between the TMD and Colour Glass Condensate (CGC) approaches within the same framework.

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arXiv2026

Next-to-leading power gluon TMDs from back-to-back DIS dijets at next-to-eikonal accuracy at low x

We calculate next-to-leading power contributions to the gluon TMDs in DIS dijet production in the back-to-back limit at low x within the Color Glass Condensate (CGC) effective field theory at next-to-eikonal accuracy. We put a special emphasis on three-point correlation functions from CGC calculations, including their correspondence to an appropriately chosen definition of three- point TMDs within the aforementioned kinematical conditions. We also discuss importance of time ordering as well as momentum fraction space formulation of the correlators. Finally, we calculate the dijet cross section corresponding to the three-point CGC correlator as a combination of TMD functions.

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arXiv2026

NLO corrections to the NEik DIS structure functions

We summarize the next-to-leading order (NLO) corrections to next-to-eikonal (NEik) quark background contributions to DIS structure functions. At NEik accuracy, in addition to corrections arising from the gluon background field of the target, DIS structure functions receive contributions from the $t$-channel quark exchanges, represented by insertions of the quark background field of the target. The latter provide the lowest order contributions in $α_s$ at NEik accuracy. We show that the NLO corrections to the longitudinal NEik structure functions are finite, whereas those to the transverse NEik structure functions exhibit rapidity and ultraviolet (UV) divergences. We analyze these divergences and extract the finite contributions.

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arXiv2026

Quark Reggeization in QCD from the Wilson line formalism

We establish a Wilson-line formulation of quark Reggeization in QCD. An interpolating operator for the Reggeized quark is identified in terms of semi-infinite Wilson lines, and its nonlinear rapidity evolution is derived. We provide strong evidence that this operator remains an eigenstate of the rapidity evolution up to next-to-leading logarithmic accuracy. Within the leading logarithmic accuracy, we explicitly recover the one-loop quark Regge trajectory. Our results provide a first-principles operator framework for quark Reggeization and pave the way for a systematic all-order description of high-energy QCD amplitudes with $t$-channel quark exchange in terms of Wilson lines.

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arXiv2026

Reggeization of quarks from next-to-eikonal high-energy QCD

We develop a comprehensive Wilson-line formulation of quark Reggeization in QCD. Starting from a next-to-eikonal operator built from a semi-infinite Wilson line and a background-quark insertion, we identify an interpolating operator for the Reggeized quark and derive its nonlinear rapidity evolution using the background-field method. In the dilute regime, its positive-signature component exhibits Regge-pole evolution governed by the quark Regge trajectory, whereas the negative-signature sector displays mixing between quark and gluon degrees of freedom, in accordance with its known Regge-cut structure. In the planar limit, this mixing is suppressed, and Reggeization emerges without an explicit signature projection, recovering signature degeneracy. We illustrate the universality of the construction by extracting the same Reggeized-quark operator from a more general Wilson-line operator describing a gluon-to-quark transition. Furthermore, we extend the formalism to massive quarks, deriving a coordinate-space evolution kernel whose Fourier transform reproduces the massive-quark Regge trajectory. Finally, from the leading operator-mixing structure of the evolution equation and signature arguments, we show that the Reggeized-quark interpolating operator is expected to remain an eigenstate of the rapidity evolution up to next-to-leading logarithmic accuracy.

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arXiv2026

From target to projectile: CSS evolution of quark TMD in different light-cone gauges

We calculate the one-loop corrections to the quark TMD in the projectile light-cone gauge using the background field formalism, with the Mandelstam-Leibbrandt (ML) prescription for the extra singularity present in the light-cone gauge propagator. We use the pure rapidity regulator for rapidity divergences. The Collins-Soper-Sterman (CSS) evolution equations are obtained after one-loop renormalization of the quark TMD in this gauge. We discuss how the structure of the rapidity divergences and the double-logarithmic contributions to the CSS resummation compares with the analogous calculation performed in the target light-cone gauge, and discuss the implications for the connection between the TMD factorization and Color Glass Condensate frameworks.

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arXiv2026

Back-to-back dijet production in DIS with finite-energy corrections and twist-3 gluon TMDs

This work presents the summary of calculation of the cross section of the dijet production in deep inelastic scattering at small x at next-to-eikonal accuracy. The cross section is calculated in the back-to-back limit of the produced jets using results obtained in our previous works. The cross section is expressed via the transverse-momentum-dependent (TMD) parton distributions. Specifically, we show how the next-to-eikonal corrections are related to the $x$ dependent phase of twist-2 gluon TMD and to twist-3 unpolarized gluon TMDs.

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arXiv2026

Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$

We compute the next-to-eikonal (NEik) power corrections to inclusive deep inelastic scattering (DIS) and semi-inclusive deep inelastic scattering (SIDIS) at low $x$ beyond dipole factorization, which represent the eikonal result. The analysis is restricted to contributions arising from t-channel quark exchanges, thereby probing the quark background field of the target. For a transversely polarized virtual photon, the NEik corrections to inclusive DIS are expressed in terms of quark and antiquark collinear parton distribution functions (PDFs), while the corresponding corrections to SIDIS are formulated in terms of the unpolarized quark transverse-momentum-dependent distribution (TMD). In contrast, for a longitudinally polarized photon, the NEik corrections to both inclusive DIS and SIDIS vanish at lowest order in $α_{s}$.

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arXiv2025

Dijet production in DIS off a large nucleus at next-to-eikonal accuracy in a Gaussian model within the CGC framework

We develop a Gaussian model to evaluate the decorated dipole and quadrupole operators that arise beyond the eikonal approximation in the Color Glass Condensate framework. While the method is general and applicable to arbitrary beyond-eikonal Wilson line structures, we employ it for dijet production in deep inelastic scattering at next-to-eikonal accuracy. After validating the model at the eikonal level, we compute all next-to-eikonal operator structures entering the dijet cross section. We show that some of them do not contribute to this observable, while others vanish identically. Therefore, in the Gaussian model next-to-eikonal corrections to dijet production in deep inelastic scattering originate solely from a given type of operators and from next-to-eikonal three-point correlators. The resulting expressions are provided in a form suitable for numerical implementation.

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arXiv2025

Next-to-Leading Order corrections to the Next-to-Eikonal DIS structure functions

We compute next-to-leading order (NLO) corrections to next-to-eikonal (NEik) quark background contributions to DIS structure functions. Among NEik corrections, $t$-channel quark exchanges provide the lowest order contributions in $α_s$, and can be represented as insertions of the quark background field of the target. At NLO, we compute NEik corrections induced by both quark and gluon background fields, and suppressed by an explicit factor of $α_s$. We show that the NLO corrections to the NEik longitudinal structure function are finite, while those to the NEik transverse structure function exhibit rapidity and UV divergences. These divergences are analyzed, and the finite contributions are extracted.

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arXiv2025

Exploring rapidity regularization schemes at low $x$ with the DIS longitudinal structure function

We propose three possible rapidity regulators for higher-order calculations in low $x$ QCD with gluon saturation, as alternatives to the usual lower cut-off for the integrals over the light-cone momentum $k^+$. These rapidity regulators are closely related to the $η$ regulator and to the pure rapidity regulator, which have been used primarily in studies of transverse-momentum-dependent (TMD) factorization within the soft-collinear effective theory (SCET). By choosing one of the three rapidity regulators that we propose, formulated in terms of $k^+$, $k^-$ or rapidity respectively, one can set from the start of the calculation in which of these three variables one wishes to formulate the low $x$ evolution equations, which is one of the main advantages of our approach. As a test of the viability of these rapidity regulators and of their practical implementation in higher order calculations with gluon saturation effects, we use them to revisit the calculation of the NLO corrections to the dipole factorization of the $F_L$ structure function in inclusive DIS at low $x$.

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arXiv2025

Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC

We study dijet production in pA collisions at forward rapidities at next-to-eikonal accuracy. We restrict ourselves to the next-to-eikonal corrections that are induced by the quark background field of the target. We consider all possible channels, compute scattering amplitudes both in general kinematics and in the back-to-back limit. By using these results, we compute the back-to-back production cross section and obtain a factorized expression with a quark TMD times associated hard factor for each channel.

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arXiv2025

Renormalization of the gluon distribution function in the background field formalism

We derive the Leading Order DGLAP evolution of gluon distribution function in the target light cone gauge starting from its standard operator definition. The derivation is performed using the background field formalism also employed in the Color Glass Condensate effective theory of small $x$ QCD. We adopt Mandelstam-Leibbrandt prescription to regulate in an unambiguous way the spurious singularity appearing in the light-cone gauge Feynman propagator. UV divergences are regulated via dimensional regularization. The methods introduced in this paper represent the first steps in the construction of a unified framework for QCD evolution, which could address collinear physics as well as small $x$ physics and gluon saturation.

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arXiv2025

One-loop renormalization of quark TMD in the light-cone gauge: CSS evolution

We calculate the one-loop corrections to the quark TMD in the light-cone gauge using the background field formalism, with the Mandelstam-Leibbrandt (ML) prescription for the extra singularity present in the light-cone gauge propagator. We use the pure rapidity regulator for rapidity divergences. The Collins-Soper-Sterman (CSS) evolution equations are indeed obtained from the one loop renormalization of the quark TMD. In this setup, the double log contribution to the CSS resummation is found to come from the ghost-like zero-mode from the ML prescription, in the diagrams with a gluon propagator ending on the transverse part of the gauge link at infinity.

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arXiv2025

SIDIS at small $x$ at next-to-leading order: transverse photon

We calculate the next-to-leading order corrections to single inclusive hadron production in deep inelastic scattering at small $x$ using the color glass condensate formalism, for the case when the exchanged photon is transversely polarized. We show all UV and soft divergences cancel while collinear and rapidity divergences result in scale evolution of quark-hadron fragmentation function and small-x evolution of dipole amplitudes, respectively.

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arXiv2025

Sudakov double logs in single-inclusive hadron production in DIS at small $x$ from the Color Glass Condensate formalism

We investigate the high $Q^2$ (photon virtuality) limit of single-inclusive hadron production in DIS (SIDIS) at small $x$, using the color glass condensate formalism at next-to-leading order. We focus on the $Λ_{QCD}^2 \ll \mathbf{p}_h^2 \ll Q^2$ kinematic regime where $\mathbf{p}_h$ is the produced hadron transverse momentum, and extract the Sudakov double logarithms. We further argue that compatibility between the CGC calculation and TMD factorization at one-loop order can only be achieved if the small-x evolution is kinematically constrained.

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arXiv2024

Forward parton-nucleus scattering at next-to-eikonal accuracy in the CGC

We derive the full next-to-eikonal (NEik) corrections to the gluon propagator from before to after traversing a highly boosted gluon background field, including corrections both beyond the shockwave limit and beyond the static limit in particular. After summarizing the results of the full NEik corrections to the before-to-after quark propagator computed in our earlier works, we also derive the before-to-inside, inside-to-inside and inside-to-after quark and gluon propagators, which are building blocks to calculate high-energy scattering processes at NEik order. Using these results and also including the NEik corrections that stem from interactions with the target via t-channel quark exchanges, we compute inclusive cross sections for quark and gluon production at forward rapidities in quark-nucleus and gluon-nucleus scatterings at NEik accuracy.

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arXiv2024

Back-to-back dijet production in DIS at next-to-eikonal accuracy and twist-3 gluon TMDs

We consider dijet production in deep inelastic scattering at small $x$, on a purely gluonic unpolarized target. Starting from earlier results obtained at next-to-eikonal accuracy in the high-energy limit, we perform the expansion in the back-to-back dijet limit, at next-to-leading power accuracy. We rewrite our results in the language of transverse-momentum-dependent (TMD) factorization, in terms of twist-2 and twist-3 TMD gluon distributions (gluon TMDs). Among the next-to-eikonal corrections, we find in particular twist-2 contributions corresponding to the $x$ dependent phase of the twist-2 gluon TMDs. We also find two types of twist-3 unpolarized gluon TMDs, as well as correlators of three gluon field strength tensors.

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