{
  "id": "1910.08569",
  "version": "v1",
  "published": "2019-10-18T18:02:09.000Z",
  "updated": "2019-10-18T18:02:09.000Z",
  "title": "Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD",
  "authors": [
    "Markus A. Ebert",
    "Iain W. Stewart",
    "Yong Zhao"
  ],
  "comment": "27 pages + appendices, 5 figures",
  "categories": [
    "hep-ph",
    "hep-lat",
    "nucl-th"
  ],
  "abstract": "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 ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI$^\\prime$/MOM) scheme, as well as the conversion factor from the RI$^\\prime$/MOM-renormalized quasi-TMDPDF to the $\\overline{\\rm MS}$ scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-18T18:02:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "collins-soper kernel",
      "lattice qcd",
      "transverse-momentum dependent parton distribution functions",
      "renormalization",
      "staple-shaped euclidean wilson line operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}