Skip to main content
SpringerLink
Account
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

Precise determination of αs from relativistic quarkonium sum rules

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 16 March 2020
  • Volume 2020, article number 94, (2020)
  • Cite this article
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
Precise determination of αs from relativistic quarkonium sum rules
Download PDF
  • Diogo Boito1 &
  • Vicent Mateu  ORCID: orcid.org/0000-0003-0902-50122,3 

  • 327 Accesses

  • 10 Citations

  • 1 Altmetric

  • Explore all metrics

A preprint version of the article is available at arXiv.

Abstract

We determine the strong coupling αs(mZ ) from dimensionless ratios of roots of moments of the charm- and bottom-quark vector and charm pseudo-scalar correlators, dubbed \( {R}_q^{X,n}\equiv \left({M}_q^{X,n}\right)\frac{1}{n}/{\left({M}_q^{X,n+1}\right)}^{\frac{1}{n+1}}, \) with X = V, P , as well as from the 0-th moment of the charm pseudo-scalar correlator, \( {M}_c^{P,0}. \) In the quantities we use, the mass dependence is very weak, entering only logarithmically, starting at 𝒪\( \left({\alpha}_s^2\right). \) We carefully study all sources of uncertainties, paying special attention to truncation errors, and making sure that order-by-order convergence is maintained by our choice of renormalization scale variation. In the computation of the experimental uncertainty for the moment ratios, the correlations among individual moments are properly taken into account. Additionally, in the perturbative contributions to experimental vector-current moments, αs(mZ) is kept as a free parameter such that our extraction of the strong coupling is unbiased and based only on experimental data. The most precise extraction of αs from vector correlators comes from the ratio of the charm-quark moments \( {R}_c^{V,2} \) and reads αs(mZ) = 0.1168±0.0019, as we have recently discussed in a companion letter. From bottom moments, using the ratio \( {R}_c^{V,2} \), we find αs (mZ) = 0.1186±0.0048. Our results from the lattice pseudo-scalar charm correlator agree with the central values of previous determinations, but have larger uncertainties due to our more conservative study of the perturbative error. Averaging the results obtained from various lattice inputs for the n = 0 moment we find αs(mZ) = 0.1177±0.0020. Combining experimental and lattice information on charm correlators into a single fit we obtain αs(mZ) = 0.1170±0.0014, which is the main result of this article.

Article PDF

Download to read the full article text

Similar content being viewed by others

Charm quark mass with calibrated uncertainty

Article Open access 14 February 2017

Strong IR cancellation in heavy quarkonium and precise top mass determination

Article Open access 12 November 2015

Strong coupling constant from moments of quarkonium correlators revisited

Article Open access 24 January 2022
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. A. Pich, J. Rojo, R. Sommer and A. Vairo, Determining the strong coupling: status and challenges, PoS(Confinement2018)035 [arXiv:1811.11801] [INSPIRE].

  2. G.P. Salam, The strong coupling: a theoretical perspective, in From my vast repertoire. . . : guido Altarelli’s legacy, A. Levy et al. eds., World Scientific, Singapore (2019), arXiv:1712.05165 [INSPIRE].

  3. B. Dehnadi, A.H. Hoang, V. Mateu and S.M. Zebarjad, Charm mass determination from QCD charmonium sum rules at order \( {\alpha}_s^3, \) , JHEP 09 (2013) 103 [arXiv:1102.2264] [INSPIRE].

    Article  ADS  Google Scholar 

  4. G. Corcella and A.H. Hoang, Uncertainties in the MS-bar bottom quark mass from relativistic sum rules, Phys. Lett. B 554 (2003) 133 [hep-ph/0212297] [INSPIRE].

  5. B. Dehnadi, A.H. Hoang and V. Mateu, Bottom and charm mass determinations with a convergence test, JHEP 08 (2015) 155 [arXiv:1504.07638] [INSPIRE].

    Article  Google Scholar 

  6. M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, QCD and resonance physics. Theoretical foundations, Nucl. Phys. B 147 (1979) 385 [INSPIRE].

  7. M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, QCD and resonance physics: applications, Nucl. Phys. B 147 (1979) 448 [INSPIRE].

    Article  ADS  Google Scholar 

  8. HPQCD collaboration, High-precision charm-quark mass from current-current correlators in lattice and continuum QCD, Phys. Rev. D 78 (2008) 054513 [arXiv:0805.2999] [INSPIRE].

  9. C. McNeile et al., High-precision c and b masses and QCD coupling from current-current correlators in lattice and continuum QCD, Phys. Rev. D 82 (2010) 034512 [arXiv:1004.4285] [INSPIRE].

  10. Y. Maezawa and P. Petreczky, Quark masses and strong coupling constant in 2 + 1 flavor QCD, Phys. Rev. D 94 (2016) 034507 [arXiv:1606.08798] [INSPIRE].

  11. P. Petreczky and J.H. Weber, Strong coupling constant and heavy quark masses in (2 + 1)-flavor QCD, Phys. Rev. D 100 (2019) 034519 [arXiv:1901.06424] [INSPIRE].

  12. K. Nakayama, B. Fahy and S. Hashimoto, Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass, Phys. Rev. D 94 (2016) 054507 [arXiv:1606.01002] [INSPIRE].

  13. D. Boito and V. Mateu, Precise αs determination from charmonium sum rules, arXiv:1912.06237 [INSPIRE].

  14. A.O.G. Kallen and A. Sabry, Fourth order vacuum polarization, Kong. Dan. Vid. Sel. Mat. Fys. Med. 29N17 (1955) 1.

  15. K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, Heavy quark vacuum polarization to three loops, Phys. Lett. B 371 (1996) 93 [hep-ph/9511430] [INSPIRE].

  16. K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, Three loop polarization function and \( O\left({\alpha}_S^2\right) \) corrections to the production of heavy quarks, Nucl. Phys. B 482 (1996) 213 [hep-ph/9606230] [INSPIRE].

  17. R. Boughezal, M. Czakon and T. Schutzmeier, Four-loop tadpoles: applications in QCD, Nucl. Phys. Proc. Suppl. 160 (2006) 160 [hep-ph/0607141] [INSPIRE].

  18. M. Czakon and T. Schutzmeier, Double fermionic contributions to the heavy-quark vacuum polarization, JHEP 07 (2008) 001 [arXiv:0712.2762] [INSPIRE].

    ADS  Google Scholar 

  19. A. Maier, P. Maierhofer and P. Marquard, Higher moments of heavy quark correlators in the low energy limit at \( O\left({\alpha}_s^3\right), \)Nucl. Phys. B 797 (2008) 218 [arXiv:0711.2636] [INSPIRE].

    Google Scholar 

  20. A. Maier and P. Marquard, Validity of Padé approximations in vacuum polarization at three- and four-loop order, Phys. Rev. D 97 (2018) 056016 [arXiv:1710.03724] [INSPIRE].

  21. K.G. Chetyrkin, J.H. Kuhn and C. Sturm, Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD, Eur. Phys. J. C 48 (2006) 107 [hep-ph/0604234] [INSPIRE].

  22. R. Boughezal, M. Czakon and T. Schutzmeier, Charm and bottom quark masses from perturbative QCD, Phys. Rev. D 74 (2006) 074006 [hep-ph/0605023] [INSPIRE].

  23. C. Sturm, Moments of heavy quark current correlators at four-loop order in perturbative QCD, JHEP 09 (2008) 075 [arXiv:0805.3358] [INSPIRE].

    Article  ADS  Google Scholar 

  24. A. Maier, P. Maierhofer and P. Marqaurd, The second physical moment of the heavy quark vector correlator at \( O\left({\alpha}_s^3\right), \) Phys. Lett. B 669 (2008) 88 [arXiv:0806.3405] [INSPIRE].

    Article  ADS  Google Scholar 

  25. A. Maier, P. Maierhofer, P. Marquard and A.V. Smirnov, Low energy moments of heavy quark current correlators at four loops, Nucl. Phys. B 824 (2010) 1 [arXiv:0907.2117] [INSPIRE].

    Article  ADS  Google Scholar 

  26. A.H. Hoang, V. Mateu and S. Mohammad Zebarjad, Heavy quark vacuum polarization function at \( O\left({\alpha}_s^2\right) \) \( O\left({\alpha}_s^3\right), \)Nucl. Phys. B 813 (2009) 349 [arXiv:0807.4173] [INSPIRE].

    MATH  Google Scholar 

  27. Y. Kiyo, A. Maier, P. Maierhofer and P. Marquard, Reconstruction of heavy quark current correlators at \( O\left({\alpha}_s^3\right), \) Nucl. Phys. B 823 (2009) 269 [arXiv:0907.2120] [INSPIRE].

    MATH  Google Scholar 

  28. D. Greynat and S. Peris, Resummation of threshold, low- and high-energy expansions for heavy-quark correlators, Phys. Rev. D 82 (2010) 034030 [Erratum ibid. D 82 (2010) 119907] [arXiv:1006.0643] [INSPIRE].

  29. D. Greynat, P. Masjuan and S. Peris, Analytic reconstruction of heavy-quark two-point functions at \( O\left({\alpha}_s^3\right), \) Phys. Rev. D 85 (2012) 054008 [arXiv:1104.3425] [INSPIRE].

  30. S.A. Larin and J.A.M. Vermaseren, The three loop QCD β-function and anomalous dimensions, Phys. Lett. B 303 (1993) 334 [hep-ph/9302208] [INSPIRE].

  31. 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].

  32. J.A.M. Vermaseren, S.A. Larin and T. van Ritbergen, The four loop quark mass anomalous dimension and the invariant quark mass, Phys. Lett. B 405 (1997) 327 [hep-ph/9703284] [INSPIRE].

  33. K.G. Chetyrkin, Quark mass anomalous dimension to \( O\left({\alpha}_S^4\right), \) Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [INSPIRE].

  34. M. Czakon, The four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [INSPIRE].

  35. P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Quark mass and field anomalous dimensions to 𝒪\( \left({\alpha}_s^5\right), \) JHEP 10 (2014) 076 [arXiv:1402.6611] [INSPIRE].

  36. T. Luthe, A. Maier, P. Marquard and Y. Schröder, Five-loop quark mass and field anomalous dimensions for a general gauge group, JHEP 01 (2017) 081 [arXiv:1612.05512] [INSPIRE].

    Article  ADS  Google Scholar 

  37. T. Luthe, A. Maier, P. Marquard and Y. Schröder, The five-loop β-function for a general gauge group and anomalous dimensions beyond Feynman gauge, JHEP 10 (2017) 166 [arXiv:1709.07718] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  38. V. Mateu and P.G. Ortega, Bottom and charm mass determinations from global fits to \( Q\overline{Q} \) bound states at N3 LO, JHEP 01 (2018) 122 [arXiv:1711.05755] [INSPIRE].

    Article  ADS  Google Scholar 

  39. G. Rossum, Python reference manual, technical report, Amsterdam The Netherlands (1995).

  40. Wolfram Research Inc., Mathematica, Version 12.0, Champaign, U.S.A. (2019).

  41. V.A. Novikov et al., Charmonium and gluons: basic experimental facts and theoretical introduction, Phys. Rept. 41 (1978) 1 [INSPIRE].

    Article  ADS  Google Scholar 

  42. P.A. Baikov, V.A. Ilyin and V.A. Smirnov, Gluon condensate fit from the two loop correction to the coefficient function, Phys. Atom. Nucl. 56 (1993) 1527 [INSPIRE].

    ADS  Google Scholar 

  43. S. Narison and R. Tarrach, Higher dimensional renormalization group invariant vacuum condensates in quantum chromodynamics, Phys. Lett. 125B (1983) 217 [INSPIRE].

    Article  ADS  Google Scholar 

  44. B.L. Ioffe, QCD at low energies, Prog. Part. Nucl. Phys. 56 (2006) 232 [hep-ph/0502148] [INSPIRE].

  45. K. Chetyrkin et al., Precise charm- and bottom-quark masses: theoretical and experimental uncertainties, Theor. Math. Phys. 170 (2012) 217 [arXiv:1010.6157] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  46. D.J. Broadhurst et al., Two loop gluon condensate contributions to heavy quark current correlators: exact results and approximations, Phys. Lett. B 329 (1994) 103 [hep-ph/9403274] [INSPIRE].

  47. Particle Data Group collaboration, Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].

  48. J.H. Kuhn, 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].

  49. Particle Data Group collaboration, Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].

  50. K.G. Chetyrkin et al., Addendum to “Charm and bottom quark masses: an update”, Phys. Rev. D 96 (2017) 116007 [arXiv:1710.04249] [INSPIRE].

    ADS  Google Scholar 

  51. Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].

  52. BES collaboration, Measurement of the total cross-section for hadronic production by e+ e− annihilation at energies between 2.6 GeV–5 GeV, Phys. Rev. Lett. 84 (2000) 594 [hep-ex/9908046] [INSPIRE].

  53. BES collaboration, Measurements of the cross-section for e+ e− → hadrons at center-of-mass energies from 2 GeV to 5 GeV, Phys. Rev. Lett. 88 (2002) 101802 [hep-ex/0102003] [INSPIRE].

  54. BES collaboration, Measurement of cross sections for D0\( \overline{D} \)0 and D+ D− production in e+ e− annihilation at \( \sqrt{s} \) = 3.773 GeV, Phys. Lett. B 603 (2004) 130 [hep-ex/0411013] [INSPIRE].

  55. BES collaboration, Measurements of the cross-sections for e+ e− → hadrons at 3.650 GeV, 3.6648 GeV, 3.773 GeV and the branching fraction for ψ(3770) → non \( D\overline{D} \) , Phys. Lett. B 641 (2006) 145 [hep-ex/0605105] [INSPIRE].

  56. M. Ablikim et al., Measurements of the continuum Ruds and R values in e+ e− annihilation in the energy region between 3.650 and 3.872 GeV, Phys. Rev. Lett. 97 (2006) 262001 [hep-ex/0612054] [INSPIRE].

  57. BES collaboration, R value measurements for e+ e− annihilation at 2.60 GeV, 3.07 GeV and 3.65 GeV, Phys. Lett. B 677 (2009) 239 [arXiv:0903.0900] [INSPIRE].

  58. A. Osterheld et al., Measurements of total hadronic and inclusive D∗ cross-sections in e+ e− annihilations between 3.87 GeV and 4.5 GeV, SLAC-PUB-4160 (1986).

  59. C. Edwards et al., Hadron production in e+ e− annihilation from s1/2 = 5 GeV to 7.4 GeV, SLAC-PUB-5160 (1990).

  60. CLEO collaboration, A Measurement of the total cross-section for e+ e− → hadrons at \( \sqrt{s} \) = 10.52 GeV, Phys. Rev. D 57 (1998) 1350 [hep-ex/9707018] [INSPIRE].

  61. CLEO collaboration, Observation of new structure in the e+ e− annihilation cross-section above \( b\overline{b} \) threshold, Phys. Rev. Lett. 54 (1985) 381 [INSPIRE].

  62. CLEO collaboration, Measurement of the total hadronic cross section in e+ e− annihilations below 10.56 GeV, Phys. Rev. D 76 (2007) 072008 [arXiv:0706.2813] [INSPIRE].

  63. CLEO collaboration, Measurement of charm production cross sections in e+ e− annihilation at energies between 3.97 and 4.26 GeV, Phys. Rev. D 80 (2009) 072001 [arXiv:0801.3418] [INSPIRE].

  64. A.E. Blinov et al., The measurement of R in e+ e− annihilation at center-of-mass energies between 7.2 GeV and 10.34 GeV, Z. Phys. C 70 (1996) 31 [INSPIRE].

  65. L. Criegee and G. Knies, Review of e+ e− experiments with Pluto from 3 GeV to 31 GeV, Phys. Rept. 83 (1982) 151 [INSPIRE].

    Article  ADS  Google Scholar 

  66. G.S. Abrams et al., Measurement of the parameters of the ψ′′ (3770) resonance, Phys. Rev. D 21 (1980) 2716 [INSPIRE].

    ADS  Google Scholar 

  67. K. Hagiwara, A.D. Martin, D. Nomura and T. Teubner, Predictions for g − 2 of the muon and αQED \( \left({M}_Z^2\right), \) Phys. Rev. D 69 (2004) 093003 [hep-ph/0312250] [INSPIRE].

  68. J. Erler, P. Masjuan and H. Spiesberger, Charm quark mass with calibrated uncertainty, Eur. Phys. J. C 77 (2017) 99 [arXiv:1610.08531] [INSPIRE].

    Article  ADS  Google Scholar 

  69. V.V. Anashin et al., Measurement of Ruds and R between 3.12 and 3.72 GeV at the KEDR detector, Phys. Lett. B 753 (2016) 533 [arXiv:1510.02667] [INSPIRE].

  70. V.V. Anashin et al., Measurement of R between 1.84 and 3.05 GeV at the KEDR detector, Phys. Lett. B 770 (2017) 174 [arXiv:1610.02827] [INSPIRE].

  71. KEDR collaboration, Precise measurement of Ruds and R between 1.84 and 3.72 GeV at the KEDR detector, Phys. Lett. B 788 (2019) 42 [arXiv:1805.06235] [INSPIRE].

  72. iminuit team, iminuit – a python interface to minuit, https://github.com/scikit-hep/iminuit.

  73. F. James and M. Roos, Minuit — A system for function minimization and analysis of the parameter errors and correlations, Comput. Phys. Commun. 10 (1975) 343.

  74. S. Groote and A.A. Pivovarov, Low-energy gluon contributions to the vacuum polarization of heavy quarks, JETP Lett. 75 (2002) 221 [hep-ph/0103047] [INSPIRE].

  75. BaBar collaboration, Measurement of the e+ e− → \( b\overline{b} \) cross section between \( \sqrt{s} \) = 10.54 GeV and 11.20 GeV, Phys. Rev. Lett. 102 (2009) 012001 [arXiv:0809.4120] [INSPIRE].

  76. S. Zafeiropoulos et al., Strong running coupling from the gauge sector of domain wall lattice QCD with physical quark masses, Phys. Rev. Lett. 122 (2019) 162002 [arXiv:1902.08148] [INSPIRE].

    Article  ADS  Google Scholar 

  77. ETM collaboration, High statistics determination of the strong coupling constant in Taylor scheme and its OPE Wilson coefficient from lattice QCD with a dynamical charm, Phys. Rev. D 89 (2014) 014507 [arXiv:1310.3763] [INSPIRE].

  78. R. Abbate et al., Thrust at N3 LL with power corrections and a precision global fit for αs(mZ ), Phys. Rev. D 83 (2011) 074021 [arXiv:1006.3080] [INSPIRE].

  79. R. Abbate et al., Precision thrust cumulant moments at N 3 LL, Phys. Rev. D 86 (2012) 094002 [arXiv:1204.5746] [INSPIRE].

  80. A.H. Hoang, D.W. Kolodrubetz, V. Mateu and I.W. Stewart, Precise determination of αs from the C -parameter distribution, Phys. Rev. D 91 (2015) 094018 [arXiv:1501.04111] [INSPIRE].

  81. B. Chakraborty et al., High-precision quark masses and QCD coupling from nf = 4 lattice QCD, Phys. Rev. D 91 (2015) 054508 [arXiv:1408.4169] [INSPIRE].

  82. ALPHA collaboration, QCD coupling from a nonperturbative determination of the three-flavor Λ parameter, Phys. Rev. Lett. 119 (2017) 102001 [arXiv:1706.03821] [INSPIRE].

  83. TUMQCD collaboration, Determination of the QCD coupling from the static energy and the free energy, Phys. Rev. D 100 (2019) 114511 [arXiv:1907.11747] [INSPIRE].

  84. H. Flacher et al., Revisiting the global electroweak fit of the standard model and beyond with Gfitter, Eur. Phys. J. C 60 (2009) 543 [Erratum ibid. C 71 (2011) 1718] [arXiv:0811.0009] [INSPIRE].

  85. S. Alekhin, J. Blümlein, S. Moch and R. Placakyte, Parton distribution functions, αs and heavy-quark masses for LHC Run II, Phys. Rev. D 96 (2017) 014011 [arXiv:1701.05838] [INSPIRE].

  86. NNPDF collaboration, Precision determination of the strong coupling constant within a global PDF analysis, Eur. Phys. J. C 78 (2018) 408 [arXiv:1802.03398] [INSPIRE].

  87. L.A. Harland-Lang, A.D. Martin, P. Motylinski and R.S. Thorne, Uncertainties on αS in the MMHT2014 global PDF analysis and implications for SM predictions, Eur. Phys. J. C 75 (2015) 435 [arXiv:1506.05682] [INSPIRE].

  88. D. Boito et al., Strong coupling from the revised ALEPH data for hadronic τ decays, Phys. Rev. D 91 (2015) 034003 [arXiv:1410.3528] [INSPIRE].

  89. A. Pich and A. Rodríguez-Sánchez, Determination of the QCD coupling from ALEPH τ decay data, Phys. Rev. D 94 (2016) 034027 [arXiv:1605.06830] [INSPIRE].

  90. D. Boito et al., Strong coupling from e+ e− → hadrons below charm, Phys. Rev. D 98 (2018) 074030 [arXiv:1805.08176] [INSPIRE].

  91. A. Hoang, P. Ruiz-Femenia and M. Stahlhofen, Renormalization group improved bottom mass from ϒ sum rules at NNLL order, JHEP 10 (2012) 188 [arXiv:1209.0450] [INSPIRE].

  92. 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].

    Article  ADS  Google Scholar 

  93. V. Mateu, P.G. Ortega, D.R. Entem and F. Fernández, Calibrating the naïve Cornell model with NRQCD, Eur. Phys. J. C 79 (2019) 323 [arXiv:1811.01982] [INSPIRE].

    Article  ADS  Google Scholar 

  94. K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Decoupling relations to \( O\left({\alpha}_s^3\right) \) and their connection to low-energy theorems, Nucl. Phys. B 510 (1998) 61 [hep-ph/9708255] [INSPIRE].

  95. K.G. Chetyrkin, J.H. Kuhn and C. Sturm, QCD decoupling at four loops, Nucl. Phys. B 744 (2006) 121 [hep-ph/0512060] [INSPIRE].

  96. Y. Schröder and M. Steinhauser, Four-loop decoupling relations for the strong coupling, JHEP 01 (2006) 051 [hep-ph/0512058] [INSPIRE].

Download references

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

  1. Instituto de Física de São Carlos, Universidade de São Paulo, CP369, São Carlos, 13570-970, Brazil

    Diogo Boito

  2. Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca, E-37008, Salamanca, Spain

    Vicent Mateu

  3. Instituto de Física Teórica UAM-CSIC, E-28049, Madrid, Spain

    Vicent Mateu

Authors
  1. Diogo Boito
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vicent Mateu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vicent Mateu.

Additional information

ArXiv ePrint: 2001.11041

Rights and permissions

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Boito, D., Mateu, V. Precise determination of αs from relativistic quarkonium sum rules. J. High Energ. Phys. 2020, 94 (2020). https://doi.org/10.1007/JHEP03(2020)094

Download citation

  • Received: 04 February 2020

  • Accepted: 01 March 2020

  • Published: 16 March 2020

  • DOI: https://doi.org/10.1007/JHEP03(2020)094

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • QCD Phenomenology
  • NLO Computations
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Cancel contracts here

Not affiliated

Springer Nature

© 2024 Springer Nature