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This work presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions (TMDs) at different rapidity scales, using lattice Quantum Chromodynamics (QCD). This is the first…

High Energy Physics - Lattice · Physics 2024-01-15 Artur Avkhadiev , Phiala Shanahan , Michael Wagman , Yong Zhao

This work presents a lattice quantum chromodynamics (QCD) calculation of the nonperturbative Collins-Soper kernel, which describes the rapidity evolution of quark transverse-momentum-dependent parton distribution functions. The kernel is…

High Energy Physics - Lattice · Physics 2021-12-22 Phiala Shanahan , Michael Wagman , Yong Zhao

The Collins-Soper kernel relates transverse momentum-dependent parton distribution functions (TMDPDFs) at different energy scales. For small parton transverse momentum $q_T\sim \Lambda_\text{QCD}$, this kernel is non-perturbative and can…

High Energy Physics - Lattice · Physics 2020-08-07 Phiala Shanahan , Michael Wagman , Yong Zhao

In the framework of large-momentum effective theory at one-loop matching accuracy, we perform a lattice calculation of the Collins-Soper kernel which governs the rapidity evolution of transverse-momentum-dependent (TMD) distributions. We…

We calculate the soft function using lattice QCD in the framework of large momentum effective theory incorporating the one-loop perturbative contributions. The soft function is a crucial ingredient in the lattice determination of light cone…

We present a lattice QCD calculation of the rapidity anomalous dimension of quark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS) kernel, up to transverse separations of about 1 fm. This unitary lattice calculation…

High Energy Physics - Lattice · Physics 2024-04-16 Dennis Bollweg , Xiang Gao , Swagato Mukherjee , Yong Zhao

We outline a general framework for evaluating the non-perturbative soft functions in the QCD instanton vacuum. In particular, from the soft function we derive the Collins-Soper (CS) kernel, which drives the rapidity evolution of the…

High Energy Physics - Phenomenology · Physics 2025-10-31 Wei-Yang Liu , Ismail Zahed , Yong Zhao

We present the first lattice quantum chromodynamics (QCD) calculation of the pion valence-quark transverse-momentum-dependent parton distribution function (TMDPDF) within the framework of large-momentum effective theory (LaMET). Using…

High Energy Physics - Lattice · Physics 2025-10-09 Dennis Bollweg , Xiang Gao , Jinchen He , Swagato Mukherjee , Yong Zhao

We present lattice results for the non-perturbative Collins-Soper (CS) kernel, which describes the energy-dependence of transverse momentum-dependent parton distributions (TMDs). The CS kernel is extracted from the ratios of first Mellin…

High Energy Physics - Lattice · Physics 2021-08-18 Maximilian Schlemmer , Alexey Vladimirov , Christian Zimmermann , Michael Engelhardt , Andreas Schäfer

This work presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions (TMDs) at different rapidity scales, using lattice quantum chromodynamics (QCD). This is the first such…

High Energy Physics - Lattice · Physics 2024-02-13 Artur Avkhadiev , Phiala E. Shanahan , Michael L. Wagman , Yong Zhao

The Collins-Soper kernel, which governs the energy evolution of transverse-momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key…

High Energy Physics - Phenomenology · Physics 2020-03-23 Markus A. Ebert , Iain W. Stewart , Yong Zhao

We present the first lattice QCD calculation of the rapidity anomalous dimension of transverse-momentum-dependent distributions (TMDs), i.e. the Collins-Soper (CS) kernel, employing the recently proposed Coulomb-gauge-fixed quasi-TMD…

High Energy Physics - Lattice · Physics 2024-07-16 Swagato Mukherjee , Dennis Bollweg , Xiang Gao , Yong Zhao

The Collins-Soper (CS) kernel governs the rapidity evolution of transverse-momentum-dependent (TMD) parton distributions, a cornerstone for QCD factorization and linking nucleon structure data across scales. Its nonperturbative behavior at…

In this work, we perform a lattice QCD study of the intrinsic, rapidity-independent soft function within the framework of large momentum effective theory. The computation is carried out using a gauge ensemble of $N_f=2+1+1$ clover-improved…

The Collins-Soper (CS) kernel is a nonperturbative function that characterizes the rapidity evolution of transverse-momentum-dependent parton distribution functions (TMDPDFs) and wave functions. In this Letter, we calculate the CS kernel…

The transverse momentum dependent (TMD) soft function and Collins-Soper (CS) kernel may be obtained by formulating the Wilson line in terms of auxiliary one-dimensional fermion fields on the lattice. Our computation takes place in the…

High Energy Physics - Lattice · Physics 2024-12-18 Anthony Francis , Issaku Kanamori , C. -J. David Lin , Wayne Morris , Yong Zhao

At small transverse momentum $q_T$, transverse-momentum dependent parton distribution functions (TMDPDFs) arise as genuinely nonperturbative objects that describe Drell-Yan like processes in hadron collisions as well as semi-inclusive…

High Energy Physics - Phenomenology · Physics 2019-02-21 Markus A. Ebert , Iain W. Stewart , Yong Zhao

We revisit the factorization of inclusive deep inelastic scattering near the kinematic threshold to explicitly track off-lightcone effects. Particle production develops around two opposite near-lightcone directions like in…

High Energy Physics - Phenomenology · Physics 2025-02-24 Andrea Simonelli , Alberto Accardi , Matteo Cerutti , Caroline S. R. Costa , Andrea Signori

We present a first joint extraction of the Collins-Soper kernel (CSK) combining experimental and lattice QCD data in the context of an analysis of transverse-momentum-dependent distributions (TMDs). Based on a neural-network…

High Energy Physics - Phenomenology · Physics 2025-10-31 Artur Avkhadiev , Valerio Bertone , Chiara Bissolotti , Matteo Cerutti , Yang Fu , Simone Rodini , Phiala Shanahan , Michael Wagman , Yong Zhao

The Collins-Soper (CS) kernel may be obtained through the TMD soft function by formulating the Wilson line in terms of 1-dimensional auxiliary fermion fields on the lattice. Our computation takes place in the region of the lattice that…

High Energy Physics - Lattice · Physics 2026-03-05 Anthony Francis , C. -J. David Lin , Wayne Morris , Yong Zhao
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