Abstract
Combining recent perturbative analyses on the static QCD potential and the quark pole mass, we find that, for the heavy quarkonium states \( c\overline{c} \), \( b\overline{b} \) and \( t\overline{t} \), (1) ultra-soft (US) corrections in the binding energies are small, and (2) there is a stronger cancellation of IR contributions than what has been predicted by renormalon dominance hypothesis. By contrast, for a hypothetical heavy quarkonium system with a small number of active quark flavors (n l ≈ 0), we observe evidence that renormalon dominance holds accurately and that non-negligible contributions from US corrections exist. In addition, we examine contributions of renormalons at u = −1. As an important consequence, we improve on a previous prediction for possible achievable accuracy of top quark \( \overline{\mathrm{MS}} \)-mass measurement at a future linear collider and estimate that in principle 20-30 MeV accuracy is reachable.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Quark Mass Relations to Four-Loop Order in Perturbative QCD, Phys. Rev. Lett. 114 (2015) 142002 [arXiv:1502.01030] [INSPIRE].
C. Anzai, Y. Kiyo and Y. Sumino, Static QCD potential at three-loop order, Phys. Rev. Lett. 104 (2010) 112003 [arXiv:0911.4335] [INSPIRE].
A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Three-loop static potential, Phys. Rev. Lett. 104 (2010) 112002 [arXiv:0911.4742] [INSPIRE].
Y. Sumino, Estimate of 4-loop Pole-M S Mass Relation from Static QCD Potential, Phys. Lett. B 728 (2014) 73 [arXiv:1309.5436] [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].
C. Bauer, G.S. Bali and A. Pineda, Compelling Evidence of Renormalons in QCD from High Order Perturbative Expansions, Phys. Rev. Lett. 108 (2012) 242002 [arXiv:1111.3946] [INSPIRE].
T. Appelquist, M. Dine and I.J. Muzinich, The Static Limit of Quantum Chromodynamics, Phys. Rev. D 17 (1978) 2074 [INSPIRE].
M.B. Voloshin, On Dynamics of Heavy Quarks in Nonperturbative QCD Vacuum, Nucl. Phys. B 154 (1979) 365 [INSPIRE].
H. Leutwyler, How to Use Heavy Quarks to Probe the QCD Vacuum, Phys. Lett. B 98 (1981) 447 [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, Potential NRQCD: An Effective theory for heavy quarkonium, Nucl. Phys. B 566 (2000) 275 [hep-ph/9907240] [INSPIRE].
B.A. Kniehl and A.A. Penin, Ultrasoft effects in heavy quarkonium physics, Nucl. Phys. B 563 (1999) 200 [hep-ph/9907489] [INSPIRE].
N. Brambilla, Y. Sumino and A. Vairo, Quarkonium spectroscopy and perturbative QCD: a new perspective, Phys. Lett. B 513 (2001) 381 [hep-ph/0101305] [INSPIRE].
N. Brambilla, Y. Sumino and A. Vairo, Quarkonium spectroscopy and perturbative QCD: massive quark loop effects, Phys. Rev. D 65 (2002) 034001 [hep-ph/0108084] [INSPIRE].
Y. Kiyo and Y. Sumino, Perturbative heavy quarkonium spectrum at next-to-next-to-next-to-leading order, Phys. Lett. B 730 (2014) 76 [arXiv:1309.6571] [INSPIRE].
Y. Sumino, A connection between the perturbative QCD potential and phenomenological potentials, Phys. Rev. D 65 (2002) 054003 [hep-ph/0104259] [INSPIRE].
S. Recksiegel and Y. Sumino, Perturbative QCD potential, renormalon cancellation and phenomenological potentials, Phys. Rev. D 65 (2002) 054018 [hep-ph/0109122] [INSPIRE].
S. Necco and R. Sommer, The N (f ) = 0 heavy quark potential from short to intermediate distances, Nucl. Phys. B 622 (2002) 328 [hep-lat/0108008] [INSPIRE].
A. Pineda, The Static potential: Lattice versus perturbation theory in a renormalon based approach, J. Phys. G 29 (2003) 371 [hep-ph/0208031] [INSPIRE].
S. Recksiegel and Y. Sumino, Comparing the QCD potential in perturbative QCD and lattice QCD at large distances, Eur. Phys. J. C 31 (2003) 187 [hep-ph/0212389] [INSPIRE].
A. Bazavov, N. Brambilla, X. Garcia i Tormo, P. Petreczky, J. Soto and A. Vairo, Determination of α s from the QCD static energy: An update, Phys. Rev. D 90 (2014) 074038 [arXiv:1407.8437] [INSPIRE].
A. Hoang, P. Ruiz-Femenia and M. Stahlhofen, Renormalization Group Improved Bottom Mass from Upsilon Sum Rules at NNLL Order, JHEP 10 (2012) 188 [arXiv:1209.0450] [INSPIRE].
C. Ayala and G. Cvetič, Calculation of binding energies and masses of quarkonia in analytic QCD models, Phys. Rev. D 87 (2013) 054008 [arXiv:1210.6117] [INSPIRE].
A.A. Penin and N. Zerf, Bottom Quark Mass from Υ Sum Rules to \( \mathcal{O}\left({\alpha}_s^3\right) \), JHEP 04 (2014) 120 [arXiv:1401.7035] [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].
M. Beneke, A. Maier, J. Piclum and T. Rauh, The bottom-quark mass from non-relativistic sum rules at NNNLO, Nucl. Phys. B 891 (2015) 42 [arXiv:1411.3132] [INSPIRE].
Quarkonium Working Group collaboration, N. Brambilla et al., Heavy quarkonium physics, hep-ph/0412158 [INSPIRE].
N. Brambilla et al., Heavy quarkonium: progress, puzzles and opportunities, Eur. Phys. J. C 71 (2011) 1534 [arXiv:1010.5827] [INSPIRE].
M. Baak et al., The Electroweak Fit of the Standard Model after the Discovery of a New Boson at the LHC, Eur. Phys. J. C 72 (2012) 2205 [arXiv:1209.2716] [INSPIRE].
M. Ciuchini, E. Franco, S. Mishima and L. Silvestrini, Electroweak Precision Observables, New Physics and the Nature of a 126 GeV Higgs Boson, JHEP 08 (2013) 106 [arXiv:1306.4644] [INSPIRE].
Gfitter Group collaboration, M. Baak et al., The global electroweak fit at NNLO and prospects for the LHC and ILC, Eur. Phys. J. C 74 (2014) 3046 [arXiv:1407.3792] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
M. Beneke and V.M. Braun, Naive non-Abelianization and resummation of fermion bubble chains, Phys. Lett. B 348 (1995) 513 [hep-ph/9411229] [INSPIRE].
R. Lee, P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment, JHEP 03 (2013) 162 [arXiv:1301.6481] [INSPIRE].
M. Beneke, More on ambiguities in the pole mass, Phys. Lett. B 344 (1995) 341 [hep-ph/9408380] [INSPIRE].
M. Neubert, Exploring the invisible renormalon: Renormalization of the heavy quark kinetic energy, Phys. Lett. B 393 (1997) 110 [hep-ph/9610471] [INSPIRE].
M. Beneke, Renormalons, Phys. Rept. 317 (1999) 1 [hep-ph/9807443] [INSPIRE].
A. Pineda, Heavy Quarkonium and Nonrelativistic Effective Field Theories, Ph.D. Thesis, Barcelona University, Barcelona Spain (1998).
A.H. Hoang, M.C. Smith, T. Stelzer and S. Willenbrock, Quarkonia and the pole mass, Phys. Rev. D 59 (1999) 114014 [hep-ph/9804227] [INSPIRE].
M. Beneke, A Quark mass definition adequate for threshold problems, Phys. Lett. B 434 (1998) 115 [hep-ph/9804241] [INSPIRE].
Y. Kiyo and Y. Sumino, Perturbative heavy quarkonium spectrum at next-to-next-to-next-to-leading order, Phys. Lett. B 730 (2014) 76 [arXiv:1309.6571] [INSPIRE].
Y. Sumino, Static QCD potential at r < Λ − 1 QCD : Perturbative expansion and operator-product expansion, Phys. Rev. D 76 (2007) 114009 [hep-ph/0505034] [INSPIRE].
Y. Sumino, Understanding Interquark Force and Quark Masses in Perturbative QCD, arXiv:1411.7853 [INSPIRE].
M. Beneke, Y. Kiyo and K. Schuller, Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin, Nucl. Phys. B 714 (2005) 67 [hep-ph/0501289] [INSPIRE].
A.A. Penin and M. Steinhauser, Heavy quarkonium spectrum at O(α 5 s m q ) and bottom/top quark mass determination, Phys. Lett. B 538 (2002) 335 [hep-ph/0204290] [INSPIRE].
Y. Kiyo and Y. Sumino, Full Formula for Heavy Quarkonium Energy Levels at Next-to-next-to-next-to-leading Order, Nucl. Phys. B 889 (2014) 156 [arXiv:1408.5590] [INSPIRE].
Y. Kiyo and Y. Sumino, Top mass determination and O(α 5 s m) correction to toponium 1S energy level, Phys. Rev. D 67 (2003) 071501 [hep-ph/0211299] [INSPIRE].
A.H. Hoang, Z. Ligeti and A.V. Manohar, B decay and the Upsilon mass, Phys. Rev. Lett. 82 (1999) 277 [hep-ph/9809423] [INSPIRE].
P.M. Stevenson, Optimized Perturbation Theory, Phys. Rev. D 23 (1981) 2916 [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
M. Beneke, A quark mass definition adequate for threshold problems, Phys. Lett. B 434 (1998) 115 [hep-ph/9804241] [INSPIRE].
M. Beneke and M. Steinhauser, Non-relativistic high-energy physics: top production and dark matter annihilation, Nucl. Part. Phys. Proc. 261-262 (2015) 378 [arXiv:1506.07962].
M. Beneke, Y. Kiyo, P. Marquard, A. Penin, J. Piclum and M. Steinhauser, Next-to-next-to-next-to-leading order QCD prediction for the top anti-top S-wave pair production cross section near threshold in e + e − annihilation, arXiv:1506.06864 [INSPIRE].
S. Recksiegel and Y. Sumino, Improved perturbative QCD prediction of the bottomonium spectrum, Phys. Rev. D 67 (2003) 014004 [hep-ph/0207005] [INSPIRE].
M. Martinez and R. Miquel, Multiparameter fits to the tt threshold observables at a future e + e − linear collider, Eur. Phys. J. C 27 (2003) 49 [hep-ph/0207315] [INSPIRE].
T. Horiguchi et al., Study of top quark pair production near threshold at the ILC, arXiv:1310.0563 [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: 1506.06542
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
Kiyo, Y., Mishima, G. & Sumino, Y. Strong IR cancellation in heavy quarkonium and precise top mass determination. J. High Energ. Phys. 2015, 84 (2015). https://doi.org/10.1007/JHEP11(2015)084
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)084