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

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arxiv 2306.06488 v3 pith:2GDDFEUP submitted 2023-06-10 hep-lat hep-exhep-ph

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

Lattice Parton Collaboration , Min-Huan Chu , Jin-Chen He , Jun Hua , Jian Liang , Xiangdong Ji , Andreas Sch\"afer , Hai-Tao Shu
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Yushan Su Lisa Walter Wei Wang Ji-Hao Wang Yi-Bo Yang Jun Zeng Qi-An Zhang
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classification hep-lat hep-exhep-ph
keywords functionsoftkernelintrinsiclatticepartcalculationcalled
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 4 Pith papers

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  1. First constraints on the nonperturbative gluon Collins-Soper kernel

    hep-lat 2026-07 conditional novelty 7.0

    First lattice-QCD constraints on the nonperturbative gluon Collins-Soper kernel are obtained at near-physical pion mass with uNNLL LaMET matching on a single a=0.15 fm ensemble.

  2. The Collins-Soper kernel from a vacuum soft function

    hep-lat 2026-06 unverdicted novelty 7.0

    The Collins-Soper kernel is extracted from lattice computations of a vacuum soft function, showing rapidity dependence consistent with Collins-Soper evolution, comparable errors to hadronic methods, and saturation at ...

  3. Multivariable Painleve'-II equation: connection formulas for asymptotic solutions

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    Asymptotically exact WKB connection formulas for a multivariable Painlevé-II system are obtained via the Demkov–Osherov model and used to scale excitations in vacuum decay.

  4. Unpolarized gluon PDF of the nucleon from lattice QCD at physical point in the continuum limit

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    A lattice QCD extraction of the nucleon gluon PDF using three lattice spacings, hybrid renormalization and NLO matching, extrapolated to the continuum and infinite-momentum limits, agrees with global fits while remain...