Abstract
We give a short overview of the renormalization properties of rectangular Wilson loops, the Polyakov loop correlator and the cyclic Wilson loop. We then discuss how to renormalize loops with more than one intersection, using the simplest non-trivial case as an illustrative example. Our findings expand on previous treatments. The generalized exponentiation theorem is applied to the Polyakov loop correlator and used to renormalize linear divergences in the cyclic Wilson loop.
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References
L. Susskind, “Weak and electromagnetic interactions at high energies,” Proceedings. Les Houches 1976 (North Holland, Amsterdam, 1977) p. 207.
L. S. Brown and W. I. Weisberger, “Remarks on the static potential in quantum chromodynamics,” Phys. Rev. D 20, 3239 (1979).
N. Brambilla, et al., Heavy Quarkonium Physics: CERN-2005-005 (CERN, Geneva, 2005), arXiv:hepph/0412158.
N. Brambilla, A. Pineda, J. Soto, and A. Vairo, “Effective field theories for heavy quarkonium,” Rev. Mod. Phys. 77, 1423 (2005), arXiv:hep-ph/0410047.
N. Brambilla, S. Eidelman, B. K. Heltsley, R. Vogt, G. T. Bodwin, E. Eichten, A. D. Frawley, A. B. Meyer, et al., “Heavy quarkonium: progress, puzzles, and opportunities,” Eur. Phys. J. C 71, 1534 (2011), arXiv:1010.5827[hep-ph].
V. S. Dotsenko and S. N. Vergeles, “Renormalizability of phase factors in the nonabelian gauge theory,” Nucl. Phys. B 169, 527 (1980).
G. P. Korchemsky and A. V. Radyushkin, “Renormalization of the Wilson loops beyond the leading order,” Nucl. Phys. B 283, 342 (1987).
L. D. McLerran and B. Svetitsky, “Quark liberation at high temperature: A Monte Carlo study of SU(2) gauge theory,” Phys. Rev. D 24, 450 (1981).
N. Brambilla, J. Ghiglieri, P. Petreczky, and A. Vairo, “The Polyakov loop and correlator of Polyakov loops at next-to-next-to-leading order,” Phys. Rev. D 82, 074019 (2010), arXiv:1007.5172[hep-ph].
M. Berwein, N. Brambilla, J. Ghiglieri, and A. Vairo, “Renormalization of the cyclic Wilson loop,” JHEP 1303, 069 (2013), arXiv:1212.4413[hep-th].
Y. Burnier, M. Laine, and M. Vepsäläinen, “Dimensionally regularized Polyakov loop correlators in hot QCD,” JHEP 1001, 054 (2010); Erratum: JHEP 1301, 180 (2013), arXiv:0911.3480[hep-ph].
R. A. Brandt, F. Neri, and M. Sato, “Renormalization of loop functions for all loops,” Phys. Rev. D 24, 879 (1981).
A. M. Polyakov, “Gauge fields as rings of glue,” Nucl. Phys. B 164, 171 (1980).
J. G. M. Gatheral, “Exponentiation of eikonal crosssections in nonabelian gauge theories,” Phys. Lett. B 133, 90 (1983).
J. Frenkel and J. C. Taylor, “Nonabelian eikonal exponentiation,” Nucl. Phys. B 246, 231 (1984).
E. Gardi, E. Laenen, G. Stavenga, and C. D. White, “Webs in multiparton scattering using the replica trick,” JHEP 1011, 155 (2010), arXiv:1008.0098[hep-ph].
E. Gardi, J. M. Smillie, and C. D. White, “The nonabelian exponentiation theorem for multiple Wilson lines,” JHEP 1306, 088 (2013), arXiv:1304.7040[hep-ph].
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Berwein, M., Brambilla, N. & Vairo, A. Renormalization of loop functions in QCD. Phys. Part. Nuclei 45, 656–663 (2014). https://doi.org/10.1134/S1063779614040029
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DOI: https://doi.org/10.1134/S1063779614040029