Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel

Abstract

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 objects using transverse-momentum-dependent (TMD) factorization. It consists of a rapidity-independent part called intrinsic soft function and a rapidity-dependent part called Collins-Soper kernel. We have adopted appropriate normalization when constructing the pseudo-scalar meson form factor that is needed in the determination of the intrinsic part and applied Fierz rearrangement to suppress the higher-twist effects. In the calculation of CS kernel we consider a CLS ensemble other than the MILC ensemble used in a previous study. We have also compared the applicability of determining the CS kernel using quasi TMDWFs and quasi TMDPDFs. As an example, the determined soft function is used to obtain the physical TMD wave functions (WFs) of pion and unpolarized iso-vector TMD parton distribution functions (PDFs) of proton.

24 pages, 19 figures, published version

References in corpus (10)

• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• On the Renormalizability of Quasi Parton Distribution Functions
• Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
• Soft-/rapidity- anomalous dimensions correspondence
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• Soft Factor Subtraction and Transverse Momentum Dependent Parton Distributions on Lattice
• Non-perturbative QCD effects in $q_T$ spectra of Drell-Yan and $Z$-boson production
• Nucleon Transverse Momentum-dependent Parton Distributions in Lattice QCD: Renormalization Patterns and Discretization Effects
• Factorization connecting continuum and lattice TMDs
• Transverse-momentum-dependent wave functions and Soft functions at one-loop in Large Momentum Effective Theory

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• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Generalized parton distributions from the pseudo-distribution approach on the lattice
• Light Cone Distribution Amplitude for the $\Lambda$ Baryon from Lattice QCD
• Polarized fragmenting jet functions in Inclusive and Exclusive Jet Production
• Collins-Soper Kernel in the QCD Instanton Vacuum
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Collinear and TMD distributions with dynamical soft-gluon resolution scale
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness
• A Unified Neural-Network Framework for Nucleon Imaging from Numerical Simulations of QCD
• Revisiting the time-ordering issue of TMD soft factors: causality, coordinate space analyticity and new equalities
• Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses