arXiv subjects

Yu Jiao Zhu

Publications and source records attributed to Yu Jiao Zhu.

At least 19 recordsLinked to original sources

arXiv2026

NNLO QCD corrections to hadron production in DIS at finite transverse momentum

We present the first calculation of hadron production in deep-inelastic scattering (DIS) at finite transverse momentum to next-to-next-to-leading order (NNLO) in perturbative QCD. To overcome the long-standing challenge of infrared divergences in semi-inclusive processes with identified final state hadrons at finite transverse momentum, we implement the recently developed qT-subtraction framework based on the recoil-free jet definition. By utilizing the winner-take-all recombination scheme, we achieve a consistent factorization for hadron-jet associated production, enabling the inclusion of $O(α_s^3)$ corrections. Our NNLO results generally demonstrate an improved convergence of the perturbative expansion and a reduction in scale uncertainties compared to previous next-to-leading order ones, especially for comparisons to multiplicity data from the ZEUS Collaboration. This work provides a high-precision theoretical foundation for the upcoming electron-ion collider era and establishes a new benchmark for the exploration of the nucleon's three-dimensional structure.

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arXiv2026

Polarized Semi-Inclusive Deep-Inelastic Scattering at $\mathcal O(α_s^3)$ in QCD

Unraveling the partonic origin of the proton spin requires precise determinations of polarized parton distribution functions (PDFs), which depend on comparably precise theoretical predictions for polarized scattering, particularly in view of the high-precision measurements anticipated at the future Electron-Ion Collider. We present the first next-to-next-to-next-to-leading order (N$^3$LO) QCD predictions for longitudinally polarized semi-inclusive deep-inelastic scattering (SIDIS) in a fully differential form, together with next-to-next-to-leading order predictions for the hadron transverse-momentum spectrum. These results are obtained by extending the two-dimensional transverse-momentum subtraction framework to the spin-dependent cross section. Together with the corresponding unpolarized calculation, these results enable consistent N$^3$LO predictions for longitudinal double-spin asymmetries and provide a precision baseline for future analyses of helicity PDFs and transverse-momentum-dependent helicity distributions.

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arXiv2026

Transverse-Momentum Subtraction for Semi-Inclusive Deep-Inelastic Scattering

Semi-Inclusive Deep-Inelastic Scattering provides unique access to the three-dimensional momentum and spin structure of the proton, enabling precise studies of parton dynamics and hadronization in QCD. We present a transverse-momentum subtraction approach applied to the detected hadron that enables efficient and precise calculation of higher-order QCD corrections to identified hadron production in Semi-Inclusive Deep-Inelastic Scattering. We demonstrate the success of the method through a next-to-next-to-leading order QCD calculation and provide fully differential phenomenological applications, which provide important ingredients for global analyses of fragmentation functions. Our method is applicable to next-to-next-to-next-to-leading order QCD corrections for both unpolarized and polarized semi-inclusive deep-inelastic scattering.

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arXiv2026

The N$^3$LO Twist-2 Matching of Helicity TMDs and SIDIS $q_\ast$ Spectrum

We compute the twist-2 matching of transverse momentum dependent (TMD) helicity parton distribution and fragmentation functions at next-to-next-to-next-to-leading order (N$^3$LO) in QCD. This calculation entails the complete set of next-to-next-to-leading order (NNLO) Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) splitting functions govering the evolution of helicity-dependent parton distribution functions (PDFs) and fragmentation functions (FFs). Within TMD factorization framework, we quantify the impact of radiative corrections by completing the next-to-next-to-next-to-leading logarithmic (N$^3$LL) prediction for lepton-hadron transverse momentum imbalance in semi-inclusive deep inelastic scattering (SIDIS). Our results provide the most precise theoretical input for probing the helicity structure and confined motion of quarks and gluons at future electron-ion collider (EIC).

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arXiv2026

Energy Correlators Resolving Proton Spin

We investigate the partonic origin of the proton longitudinal spin using spin-dependent energy correlators measured in lepton-hadron collisions with longitudinally polarized proton beams. These observables encode angular correlations in energy flow and are sensitive to the spin-momentum structure of confined partons. Using soft-collinear effective theory, we analyze the correlation patterns in both nearly back-to-back and forward limits, which establishes a direct correspondence with longitudinally polarized transverse momentum-dependent distributions (TMDs) and nucleon energy correlators (NECs). The TMDs and NECs allow consistent matching onto hard radiation regions and provide a comprehensive description of the transition from perturbative parton branching to nonperturbative confinement. Using renormalization group evolution, we obtain joint next-to-next-to-next-to-leading and next-to-next-to-leading logarithmic quantitative predictions for spin-dependent energy correlation patterns in the current and target fragmentation regions. The framework provides new theoretical insight into how the internal motion and spin of partons contribute to the formation of the proton longitudinal spin and offers an experimental paradigm for probing the interplay between color confinement and spin dynamics at the forthcoming Electron-Ion Collider.

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arXiv2026

The N$^3$LO Twist-2 Matching of Linearly Polarized Gluon TMDs

We compute the twist-2 matching of the transverse-momentum-dependent (TMD) linearly polarized gluon parton distribution and fragmentation functions at next-to-next-to-next-to-leading order (N$^3$LO) in QCD, supplemented by next-to-next-to-leading logarithmic (NNLL) small-$x$ resummation for the gluon TMD fragmentation functions. These results provide high-precision fixed-order and resummed inputs to TMD phenomenology, and constitute essential theoretical ingredients for future studies of the spin structure and three-dimensional tomography of hadrons at the Electron-Ion Collider (EIC).

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arXiv2026

Two-Dimensional Transverse-Momentum Subtraction and Semi-Inclusive Deep-Inelastic Scattering at N$^3$LO in QCD

Identified hadron production is essential for the study of nucleon structure and QCD hadronization at high energies. We present the first calculation of unpolarized semi-inclusive deep-inelastic scattering (SIDIS) at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. Our calculation is based on a novel method of two-dimensional transverse-momentum subtraction motivated by QCD factorization of soft and collinear singularities. The N$^3$LO corrections are moderate in general but can be significant in threshold regions, and exhibit excellent perturbative convergence and reduced scale variations. The fully differential framework allows for arbitrary selection cuts and directly enables precision nucleon tomography at the upcoming Electron-Ion Collider, establishing the theory foundation needed to match the anticipated experimental accuracy. Generalization of the method to calculations of polarized SIDIS is also feasible.

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arXiv2026

NNLO DGLAP splitting functions from collinear matching of TMDs

We report a complete computation of next-to-next-to-leading order (NNLO) helicity and transversity Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) splitting functions, in both space-like and time-like kinematics. These results are obtained from the next-to-next-to-next-to-leading order (N$^3$LO) twist-2 matching of polarized transverse-momentum-dependent (TMD) parton distribution and fragmentation functions, including helicity, quark transversity, and linearly polarized gluons. We compare our results with existing calculations in the literature and discuss both agreements and discrepancies. Our results provide all perturbative ingredients required for the computation of N$^3$LO differential cross sections below the resolution scale $q_{T\mathrm{cut}}$ in transverse-momentum subtraction and enable next-to-next-to-next-to-next-to-leading logarithmic (N$^4$LL) resummation of $q_T$ observables in the Sudakov region. We further determine the small-$x$ structure of the polarized matching coefficients through N$^3$LO. These fixed-order results furnish the data for future small-$x$ resummation in polarized TMD factorization, where high-energy logarithms and Sudakov logarithms become simultaneously relevant. Establishing a consistent joint treatment of polarized small-$x$ evolution and transverse-momentum resummation remains an important open direction toward uniform precision in spin-dependent phenomenology. Our results provide essential theoretical input for precision spin physics at the forthcoming Electron-Ion Collider.

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arXiv2026

The N$^3$LO Twist-2 Matching of TMD Quark Transversity

We present the first next-to-next-to-next-to-leading order (N$^3$LO) calculation of the twist-2 matching coefficients for transverse momentum dependent (TMD) quark transversity parton distribution and fragmentation functions in QCD. This matching relates the TMD quark transversity functions to their collinear counterparts in the large-transverse-momentum regime, and provides essential ingredients for precision TMD phenomenology involving transversely polarized beams. As part of our analysis, we derive the next-to-next-to-leading order (NNLO) DGLAP splitting functions for collinear transversity, confirming agreement with known space-like results for parton distribution functions and providing the new time-like splitting functions relevant for fragmentation functions. These results extend the perturbative toolkit for spin-dependent observables and establish the transversity sector on the same theoretical footing as unpolarized and helicity distributions. Our findings enable high-precision extractions of transversity PDFs and facilitate improved theoretical predictions for azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), especially in light of forthcoming data from the Electron-Ion Collider (EIC).

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arXiv2026

Energy Correlators in Semi-Inclusive Electron-Positron Annihilation

We investigate energy correlators in semi-inclusive electron-positron annihilation as precision probes of parton hadronization dynamics. Using soft-collinear effective theory, we analyze the correlation patterns between the examined hadron and the rest of QCD radiations in both large-angle and small-angle limits, which establishes a direct correspondence with transverse-momentum-dependent fragmentation functions and fragmentation energy correlators. The two complementary regimes encode the transition from perturbative parton branching to nonperturbative confinement, enabling a unified description of hadron formation across all kinematic regimes. Using renormalization group evolution, we obtain joint N${}^{3}$LL/NNLL quantitative predictions for energy correlations both in the sudakov and jet fragmentation region. Our results demonstrate that semi-inclusive energy correlators provide direct, theoretically controlled access to QCD dynamics underlying hadronization, opening new avenues for precision studies at future lepton colliders as well as through reanalyses of archival LEP data.

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arXiv2025

Double soft current at one-loop in QCD

We investigate the soft behavior of QCD amplitudes involving multiple Wilson lines and derive compact analytic expressions for double soft gluon and double soft quark emissions at one loop. The color correlations of the soft current exhibit a predominantly dipole structure, coupling to two hard legs at a time, apart from an abelian contribution that factorizes into products of one-loop and tree-level single soft currents, which may involve up to three hard legs. The kinematic dependence of the one-loop soft currents is expressed in terms of polylogarithmic functions, with explicit results presented for time-like kinematics. We further discuss the analytic continuation to other kinematic configurations and identify non-trivial crossing effects when continuing into incoming states. The squared amplitude is found to be invariant under crossing, which implies that the fully differential soft function and in particular the TMD soft function, remains universal up to three loops.

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arXiv2023

Two-loop QED corrections to the scattering of four massive leptons

We study two-loop corrections to the scattering amplitude of four massive leptons in quantum electrodynamics. These amplitudes involve previously unknown elliptic Feynman integrals, which we compute analytically using the differential equation method. In doing so, we uncover the details of the elliptic geometry underlying this scattering amplitude and show how to exploit its properties to obtain compact, easy-to-evaluate series expansions that describe the scattering of four massive leptons in QED in the kinematical regions relevant for Bhabha and Møller scattering processes.

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arXiv2023

Topology and geometry of elliptic Feynman amplitudes

We report on the analytic computation of the 2-loop amplitude for Bhabha scattering in QED. We study the analytic structure of the amplitude, and reveal its underlying connections to hyperbolic Coxeter groups and arithmetic geometries of elliptic curves.

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arXiv2022

The Four Loop QCD Rapidity Anomalous Dimension

The rapidity anomalous dimension controls the scaling of transverse momentum dependent observables in the Sudakov region. In a conformal theory it is equivalent to the soft anomalous dimension, but in QCD this relation is broken by anomalous terms proportional to the $β$-function. In this paper we first give a simple proof of this relation using two different representations of the energy-energy correlator observable. We then calculate the anomalous terms to three loops by computing the three-loop fully differential soft function to $\mathcal{O}(ε)$. Combined with recent perturbative data from the study of on-shell form factors and splitting functions, this allows us to derive the four loop rapidity anomalous dimension in QCD.

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arXiv2020

Unpolarized Quark and Gluon TMD PDFs and FFs at N$^3$LO

In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N$^3$LO) in QCD. The N$^3$LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient functions for TMD FFs exhibit double logarithmic enhancement at small momentum fraction $z$. We resum such logarithmic terms to the third order in the expansion of $α_s$. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.

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arXiv2020

Transverse-Energy-Energy Correlations in Deep Inelastic Scattering

Event shape observables have been widely used for precision QCD studies at various lepton and hadron colliders. We present the most accurate calculation of the transverse-energy-energy correlation event shape variable in deep-inelastic scattering. In the framework of soft-collinear effective theory the cross section is factorized as the convolution of the hard function, beam function, jet function and soft function in the back-to-back limit. A close connection to TMD factorization is established, as the beam function when combined with part of the soft function is identical to the conventional TMD parton distribution function, and the jet function is the second moment of the TMD fragmentation function matching coefficient. We validate our framework by comparing the obtained LO and NLO leading singular distributions to the full QCD calculations in the back-to-back limit. We report the resummed transverse-energy-energy correlation distributions up to N$^3$LL accuracy matched with the NLO cross section for the production of a lepton and two jets. Our work provides a new way to precisely study TMD physics at the future Electron-Ion Collider.

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arXiv2020

Analytic Continuation and Reciprocity Relation for Collinear Splitting in QCD

It is well-known that direct analytic continuation of DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as splitting functions are not analytic function of external momenta. However, splitting functions can be constructed from square of (generalized) splitting amplitudes. We establish the rule of analytic continuation for splitting amplitudes, and use them to determine the analytic continuation of certain holomorphic and anti-holomorphic part of splitting functions and transverse-momentum dependent distributions. In this way we derive the time-like splitting functions at three loops without ambiguity. We also propose a reciprocity relation for singlet splitting functions, and provide non-trivial evidence that it holds in QCD at least through three loops.

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arXiv2020

Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order

We report a calculation of the perturbative matching coefficients for the transverse-momentum-dependent parton distribution functions for quark at the next-to-next-to-next-to-leading order in QCD, which involves calculation of non-standard Feynman integrals with rapidity divergence. We introduce a set of generalized Integration-By-Parts equations, which allows an algorithmic evaluation of such integrals using the machinery of modern Feynman integral calculation.

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