Abstract
We obtain an improved determination of the normalization constant of the first infrared renormalon of the pole mass (and the singlet static potential). For N f = 3 it reads N m = 0.563(26). Charm quark effects in the bottom quark mass determination are carefully investigated. Finally, we determine the bottom quark mass using the NNNLO perturbative expression for the \( \boldsymbol{\Upsilon} (1S) \) mass. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to pole mass renormalon. Our result for the \( \overline{\mathrm{MS}} \) mass reads \( {\overline{m}}_b\left({m}_b\right)=4201(43) \) MeV.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Fischler, Quark - anti-Quark Potential in QCD, Nucl. Phys. B 129 (1977) 157 [INSPIRE].
A. Billoire, How Heavy Must Be Quarks in Order to Build Coulombic \( q\overline{q} \) Bound States, Phys. Lett. B 92 (1980) 343 [INSPIRE].
Y. Schröder, The Static potential in QCD to two loops, Phys. Lett. B 447 (1999) 321 [hep-ph/9812205] [INSPIRE].
A. Pineda and F.J. Yndurain, Calculation of quarkonium spectrum and m b , m c to order α 4 S , Phys. Rev. D 58 (1998) 094022 [hep-ph/9711287] [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, The Heavy quarkonium spectrum at order mα 5 s ln α s , Phys. Lett. B 470 (1999) 215 [hep-ph/9910238] [INSPIRE].
B.A. Kniehl, A.A. Penin, V.A. Smirnov and M. Steinhauser, Potential NRQCD and heavy quarkonium spectrum at next-to-next-to-next-to-leading order, Nucl. Phys. B 635 (2002) 357 [hep-ph/0203166] [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].
A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Fermionic contributions to the three-loop static potential, Phys. Lett. B 668 (2008) 293 [arXiv:0809.1927] [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].
W.E. Caswell and G.P. Lepage, Effective Lagrangians for Bound State Problems in QED, QCD and Other Field Theories, Phys. Lett. B 167 (1986) 437 [INSPIRE].
G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125 [Erratum ibid. D 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
A. Pineda and J. Soto, Effective field theory for ultrasoft momenta in NRQCD and NRQED, Nucl. Phys. Proc. Suppl. 64 (1998) 428 [hep-ph/9707481] [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].
M. Beneke and A. Signer, The Bottom MS-bar quark mass from sum rules at next-to-next-to-leading order, Phys. Lett. B 471 (1999) 233 [hep-ph/9906475] [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].
A. Pineda, Determination of the bottom quark mass from the \( \boldsymbol{\Upsilon} (1S) \) system, JHEP 06 (2001) 022 [hep-ph/0105008] [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].
T. Lee, Heavy quark mass determination from the quarkonium ground state energy: A Pole mass approach, JHEP 10 (2003) 044 [hep-ph/0304185] [INSPIRE].
C. Contreras, G. Cvetič and P. Gaete, Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation, Phys. Rev. D 70 (2004) 034008 [hep-ph/0311202] [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. Pineda, Heavy quarkonium and nonrelativistic effective field theories, PhD. Thesis, [INSPIRE].
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].
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].
A.H. Hoang and T. Teubner, Top quark pair production close to threshold: Top mass, width and momentum distribution, Phys. Rev. D 60 (1999) 114027 [hep-ph/9904468] [INSPIRE].
Y. Kiyo and Y. Sumino, O(α 5 s m) quarkonium 1S spectrum in large-β 0 approximation and renormalon cancellation, Phys. Lett. B 496 (2000) 83 [hep-ph/0007251] [INSPIRE].
A.H. Hoang, Bottom quark mass from \( \boldsymbol{\Upsilon} \) mesons: Charm mass effects, hep-ph/0008102 [INSPIRE].
G.S. Bali, C. Bauer, A. Pineda and C. Torrero, Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory, Phys. Rev. D 87 (2013) 094517 [arXiv:1303.3279] [INSPIRE].
N. Brambilla, X. Garcia i Tormo, J. Soto and A. Vairo, Precision determination of r 0Λ − MS from the QCD static energy, Phys. Rev. Lett. 105 (2010) 212001 [Erratum ibid. 108 (2012) 269903] [arXiv:1006.2066] [INSPIRE].
R. Tarrach, The Pole Mass in Perturbative QCD, Nucl. Phys. B 183 (1981) 384 [INSPIRE].
N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Three Loop Relation of Quark (Modified) Ms and Pole Masses, Z. Phys. C 48 (1990) 673 [INSPIRE].
K.G. Chetyrkin and M. Steinhauser, Short distance mass of a heavy quark at order α 3 s , Phys. Rev. Lett. 83 (1999) 4001 [hep-ph/9907509] [INSPIRE].
K. Melnikov and T.v. Ritbergen, The Three loop relation between the MS-bar and the pole quark masses, Phys. Lett. B 482 (2000) 99 [hep-ph/9912391] [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].
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].
T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The Four loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [INSPIRE].
M. Czakon, The Four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [INSPIRE].
S. Bekavac, A. Grozin, D. Seidel and M. Steinhauser, Light quark mass effects in the on-shell renormalization constants, JHEP 10 (2007) 006 [arXiv:0708.1729] [INSPIRE].
A.H. Hoang and A.V. Manohar, Charm effects in the MS-bar bottom quark mass from \( \boldsymbol{\Upsilon} \) mesons, Phys. Lett. B 483 (2000) 94 [hep-ph/9911461] [INSPIRE].
M. Melles, The Static QCD potential in coordinate space with quark masses through two loops, Phys. Rev. D 62 (2000) 074019 [hep-ph/0001295] [INSPIRE].
P. Ball, M. Beneke and V.M. Braun, Resummation of (β 0 α s)n corrections in QCD: Techniques and applications to the tau hadronic width and the heavy quark pole mass, Nucl. Phys. B 452 (1995) 563 [hep-ph/9502300] [INSPIRE].
M. Peter, The Static quark - anti-quark potential in QCD to three loops, Phys. Rev. Lett. 78 (1997) 602 [hep-ph/9610209] [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, The Infrared behavior of the static potential in perturbative QCD, Phys. Rev. D 60 (1999) 091502 [hep-ph/9903355] [INSPIRE].
T. Appelquist, M. Dine and I.J. Muzinich, The Static Limit of Quantum Chromodynamics, Phys. Rev. D 17 (1978) 2074 [INSPIRE].
M. Beneke, More on ambiguities in the pole mass, Phys. Lett. B 344 (1995) 341 [hep-ph/9408380] [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].
M. Beneke, Renormalons, Phys. Rept. 317 (1999) 1 [hep-ph/9807443] [INSPIRE].
M. Neubert, Exploring the invisible renormalon: Renormalization of the heavy quark kinetic energy, Phys. Lett. B 393 (1997) 110 [hep-ph/9610471] [INSPIRE].
G. Cvetič, Infrared renormalons and analyticity structure in pQCD, Phys. Rev. D 67 (2003) 074022 [hep-ph/0211226] [INSPIRE].
J.R. Ellis, I. Jack, D.R.T. Jones, M. Karliner and M.A. Samuel, Asymptotic Pade approximant predictions: Up to five loops in QCD and SQCD, Phys. Rev. D 57 (1998) 2665 [hep-ph/9710302] [INSPIRE].
U. Aglietti and Z. Ligeti, Renormalons and confinement, Phys. Lett. B 364 (1995) 75 [hep-ph/9503209] [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, The Static potential: Lattice versus perturbation theory in a renormalon based approach, J. Phys. G 29 (2003) 371 [hep-ph/0208031] [INSPIRE].
G. Cvetič, Estimate of the three loop contribution to the QCD static potential from renormalon cancellation, J. Phys. G 30 (2004) 863 [hep-ph/0309262] [INSPIRE].
A.G. Grozin and M. Neubert, Higher order estimates of the chromomagnetic moment of a heavy quark, Nucl. Phys. B 508 (1997) 311 [hep-ph/9707318] [INSPIRE].
A. Pineda and J. Segovia, Improved determination of heavy quarkonium magnetic dipole transitions in potential nonrelativistic QCD, Phys. Rev. D 87 (2013) 074024 [arXiv:1302.3528] [INSPIRE].
G.S. Bali, C. Bauer and A. Pineda, The static quark self-energy at O(α 20 ) in perturbation theory, arXiv:1311.0114 [INSPIRE].
A.L. Kataev and V.T. Kim, Peculiar features of the relations between pole and running heavy quark masses and estimates of the O(α 4 s ) contributions, Phys. Part. Nucl. 41 (2010) 946 [arXiv:1001.4207] [INSPIRE].
Y. Sumino, Estimate of 4-loop \( Pole\hbox{-} \overline{MS} \) Mass Relation from Static QCD Potential, Phys. Lett. B 728 (2014) 73 [arXiv:1309.5436] [INSPIRE].
D. Eiras and J. Soto, Light fermion finite mass effects in non-relativistic bound states, Phys. Lett. B 491 (2000) 101 [hep-ph/0005066] [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
B.A. Kniehl and A.A. Penin, Ultrasoft effects in heavy quarkonium physics, Nucl. Phys. B 563 (1999) 200 [hep-ph/9907489] [INSPIRE].
A. Hoang, P. Ruiz-Femenia and M. Stahlhofen, Renormalization Group Improved Bottom Mass from \( \boldsymbol{\Upsilon} \) Sum Rules at NNLL Order, JHEP 10 (2012) 188 [arXiv:1209.0450] [INSPIRE].
A.A. Penin and N. Zerf, Bottom Quark Mass from \( \boldsymbol{\Upsilon} \) Sum Rules to \( \mathcal{O}\left({\alpha}_s^3\right) \), JHEP 04 (2014) 120 [arXiv:1401.7035] [INSPIRE].
A. Pineda and A. Signer, Renormalization group improved sum rule analysis for the bottom quark mass, Phys. Rev. D 73 (2006) 111501 [hep-ph/0601185] [INSPIRE].
F. Bernardoni, B. Blossier, J. Bulava, M. Della Morte, P. Fritzsch et al., The b-quark mass from non-perturbative N f = 2 Heavy Quark Effective Theory at O(1/m h ), Phys. Lett. B 730 (2014) 171 [arXiv:1311.5498] [INSPIRE].
J.H. Kühn, M. Steinhauser and C. Sturm, Heavy Quark Masses from Sum Rules in Four-Loop Approximation, Nucl. Phys. B 778 (2007) 192 [hep-ph/0702103] [INSPIRE].
S. Bodenstein, J. Bordes, C.A. Dominguez, J. Penarrocha and K. Schilcher, Bottom-quark mass from finite energy QCD sum rules, Phys. Rev. D 85 (2012) 034003 [arXiv:1111.5742] [INSPIRE].
HPQCD collaboration, A.J. Lee et al., Mass of the b quark from lattice NRQCD and lattice perturbation theory, Phys. Rev. D 87 (2013) 074018 [arXiv:1302.3739] [INSPIRE].
K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Strong coupling constant with flavor thresholds at four loops in the MS scheme, Phys. Rev. Lett. 79 (1997) 2184 [hep-ph/9706430] [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: 1407.2128
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
Ayala, C., Cvetič, G. & Pineda, A. The bottom quark mass from the \( \boldsymbol{\Upsilon} (1S) \) system at NNNLO. J. High Energ. Phys. 2014, 45 (2014). https://doi.org/10.1007/JHEP09(2014)045
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2014)045