Abstract
Perturbative series of some quantities in quantum field theories, such as the pole mass of a quark, suffer from a kind of divergence called renormalon divergence. In this paper, the leading renormalon in the pole mass is investigated, and a map is introduced to suppress this renormalon. The inverse of the map is then used to generate the leading renormalon and obtain an expression to calculate its overall normalization. Finally, the overall normalization of the leading renormalon of the pole mass is calculated for several values of quark flavors.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I.I.Y. Bigi, M.A. Shifman, N.G. Uraltsev and A.I. Vainshtein, The Pole mass of the heavy quark. Perturbation theory and beyond, Phys. Rev. D 50 (1994) 2234 [hep-ph/9402360] [INSPIRE].
M. Beneke and V.M. Braun, Heavy quark effective theory beyond perturbation theory: Renormalons, the pole mass and the residual mass term, Nucl. Phys. B 426 (1994) 301 [hep-ph/9402364] [INSPIRE].
A.S. Kronfeld, The Perturbative pole mass in QCD, Phys. Rev. D 58 (1998) 051501 [hep-ph/9805215] [INSPIRE].
C.M. Bender and T.T. Wu, Anharmonic oscillator, Phys. Rev. 184 (1969) 1231 [INSPIRE].
T. Kawai and Y. Takei, Algebraic analysis of singular perturbation theory, volume 227, Translations of Mathematical Monographs Iwanami Series in Modern Mathematics, American Mathematical Society, Providence RI U.S.A. (2005) [Bull. Lond. Math. Soc. 40 (2008) 723].
M. Beneke, Renormalons, Phys. Rept. 317 (1999) 1 [hep-ph/9807443] [INSPIRE].
M. Beneke, More on ambiguities in the pole mass, Phys. Lett. B 344 (1995) 341 [hep-ph/9408380] [INSPIRE].
C. Ayala, G. Cvetič and A. Pineda, The bottom quark mass from the ϒ(1S) system at NNNLO, JHEP 09 (2014) 045 [arXiv:1407.2128] [INSPIRE].
A.V. Oppenheim and R.W. Schafer, Discrete-time signal processing, Pearson Higher Education (2010).
L.S. Brown, L.G. Yaffe and C.-X. Zhai, Large-order perturbation theory for the electromagnetic current-current correlation function, Phys. Rev. D 46 (1992) 4712 [hep-ph/9205213] [INSPIRE].
T. Lee, Renormalons beyond one loop, Phys. Rev. D 56 (1997) 1091 [hep-th/9611010] [INSPIRE].
T. Lee, Normalization constants of large order behavior, Phys. Lett. B 462 (1999) 1 [hep-ph/9908225] [INSPIRE].
A. Pineda, Determination of the bottom quark mass from the ϒ(1S) system, JHEP 06 (2001) 022 [hep-ph/0105008] [INSPIRE].
A.H. Hoang, A. Jain, I. Scimemi and I.W. Stewart, Infrared Renormalization Group Flow for Heavy Quark Masses, Phys. Rev. Lett. 101 (2008) 151602 [arXiv:0803.4214] [INSPIRE].
P. Ball, M. Beneke and V.M. Braun, Resummation of (β 0 α s )n corrections in QCD: Techniques and applications to the τ hadronic width and the heavy quark pole mass, Nucl. Phys. B 452 (1995) 563 [hep-ph/9502300] [INSPIRE].
M. Beneke and V.M. Braun, Naive nonabelianization and resummation of fermion bubble chains, Phys. Lett. B 348 (1995) 513 [hep-ph/9411229] [INSPIRE].
P. Marquard, A.V. Smirnov, V.A. Smirnov, M. Steinhauser and D. Wellmann, \( \overline{\mathrm{MS}} \) -on-shell quark mass relation up to four loops in QCD and a general SU(N ) gauge group, Phys. Rev. D 94 (2016) 074025 [arXiv:1606.06754] [INSPIRE].
M. Beneke, P. Marquard, P. Nason and M. Steinhauser, On the ultimate uncertainty of the top quark pole mass, arXiv:1605.03609 [INSPIRE].
T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions, Nucl. Phys. B 196 (1982) 189 [INSPIRE].
R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey and D.E. Knuth, On the Lambert W function, Adv. Comput. Math. 5 (1996) 329 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1701.00347
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Komijani, J. A discussion on leading renormalon in the pole mass. J. High Energ. Phys. 2017, 62 (2017). https://doi.org/10.1007/JHEP08(2017)062
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2017)062