Abstract
In this paper, we give comprehensive analyses for event shape observables in electron-positron annihilation by using the Principle of Maximum Conformality (PMC) which is a rigorous scale-setting method to eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions. Conventionally the renormalization scale and theoretical uncertainties in event shape observables are often evaluated by setting the scale to the center-of-mass energy \( \sqrt{s} \). The event shape distributions using this conventional scale setting are plagued by the large renormalization scale uncertainty and underestimate the experimental data. Moreover, since the renormalization scale is simply fixed to the center-of-mass energy \( \sqrt{s} \), only one value of the coupling αs at the single scale \( \sqrt{s} \) can be extracted. In contrast, the PMC renormalization scales are determined by absorbing the nonconformal β contributions that govern the behavior of the running coupling via the Renormalization Group Equation (RGE). The resulting PMC scales change with event shape kinematics, reflecting the virtuality of the underlying quark and gluon subprocess. The PMC scales thus yield the correct physical behavior of the scale and the PMC predictions agree with precise event shape distributions measured at the LEP experiment. More importantly, we can precisely determine the running of the QCD coupling constant αs(Q2) over a wide range of Q2 in perturbative domain from event shape distributions measured at a single center-of-mass energy \( \sqrt{s} \).
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References
ALEPH collaboration, Studies of QCD at e+e− centre-of-mass energies between 91-GeV and 209-GeV, Eur. Phys. J. C 35 (2004) 457 [INSPIRE].
DELPHI collaboration, A study of the energy evolution of event shape distributions and their means with the DELPHI detector at LEP, Eur. Phys. J. C 29 (2003) 285 [hep-ex/0307048] [INSPIRE].
OPAL collaboration, Measurement of event shape distributions and moments in e+e− → hadrons at 91-GeV-209-GeV and a determination of αs, Eur. Phys. J. C 40 (2005) 287 [hep-ex/0503051] [INSPIRE].
L3 collaboration, Studies of hadronic event structure in e+e− annihilation from 30-GeV to 209-GeV with the L3 detector, Phys. Rept. 399 (2004) 71 [hep-ex/0406049] [INSPIRE].
SLD collaboration, Measurement of αs(\( {M}_Z^2 \)) from hadronic event observables at the Z0 resonance, Phys. Rev. D 51 (1995) 962 [hep-ex/9501003] [INSPIRE].
R.K. Ellis, D.A. Ross and A.E. Terrano, The Perturbative Calculation of Jet Structure in e+e− Annihilation, Nucl. Phys. B 178 (1981) 421 [INSPIRE].
Z. Kunszt, Comment on the \( \mathcal{O} \)(\( {\alpha}_S^2 \)) Corrections to Jet Production in e+e− Annihilation, Phys. Lett. B 99 (1981) 429 [INSPIRE].
J.A.M. Vermaseren, K.J.F. Gaemers and S.J. Oldham, Perturbative QCD Calculation of Jet Cross-Sections in e+e− Annihilation, Nucl. Phys. B 187 (1981) 301 [INSPIRE].
K. Fabricius, I. Schmitt, G. Kramer and G. Schierholz, Higher Order Perturbative QCD Calculation of Jet Cross-Sections in e+e− Annihilation, Z. Phys. C 11 (1981) 315 [INSPIRE].
W.T. Giele and E.W.N. Glover, Higher order corrections to jet cross-sections in e+e− annihilation, Phys. Rev. D 46 (1992) 1980 [INSPIRE].
S. Catani and M.H. Seymour, The dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order, Phys. Lett. B 378 (1996) 287 [hep-ph/9602277] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Second-order QCD corrections to the thrust distribution, Phys. Rev. Lett. 99 (2007) 132002 [arXiv:0707.1285] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, NNLO corrections to event shapes in e+e− annihilation, JHEP 12 (2007) 094 [arXiv:0711.4711] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, EERAD3: Event shapes and jet rates in electron-positron annihilation at order \( {\alpha}_s^3 \), Comput. Phys. Commun. 185 (2014) 3331 [arXiv:1402.4140] [INSPIRE].
S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett. 101 (2008) 162001 [arXiv:0807.3241] [INSPIRE].
S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP 06 (2009) 041 [arXiv:0904.1077] [INSPIRE].
V. Del Duca, C. Duhr, A. Kardos, G. Somogyi and Z. Trócsányi, Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy, Phys. Rev. Lett. 117 (2016) 152004 [arXiv:1603.08927] [INSPIRE].
V. Del Duca et al., Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions, Phys. Rev. D 94 (2016) 074019 [arXiv:1606.03453] [INSPIRE].
S. Catani, L. Trentadue, G. Turnock and B.R. Webber, Resummation of large logarithms in e+e− event shape distributions, Nucl. Phys. B 407 (1993) 3 [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Principles of general final-state resummation and automated implementation, JHEP 03 (2005) 073 [hep-ph/0407286] [INSPIRE].
A. Banfi, H. McAslan, P.F. Monni and G. Zanderighi, A general method for the resummation of event-shape distributions in e+e− annihilation, JHEP 05 (2015) 102 [arXiv:1412.2126] [INSPIRE].
Y.-T. Chien and M.D. Schwartz, Resummation of heavy jet mass and comparison to LEP data, JHEP 08 (2010) 058 [arXiv:1005.1644] [INSPIRE].
T. Becher and G. Bell, NNLL Resummation for Jet Broadening, JHEP 11 (2012) 126 [arXiv:1210.0580] [INSPIRE].
R. Abbate, M. Fickinger, A.H. Hoang, V. Mateu and I.W. Stewart, Thrust at N3LL with Power Corrections and a Precision Global Fit for αs (mZ), Phys. Rev. D 83 (2011) 074021 [arXiv:1006.3080] [INSPIRE].
A.H. Hoang, D.W. Kolodrubetz, V. Mateu and I.W. Stewart, C-parameter distribution at N3LL’ including power corrections, Phys. Rev. D 91 (2015) 094017 [arXiv:1411.6633] [INSPIRE].
J.-y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, The Rapidity Renormalization Group, Phys. Rev. Lett. 108 (2012) 151601 [arXiv:1104.0881] [INSPIRE].
J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory, JHEP 05 (2012) 084 [arXiv:1202.0814] [INSPIRE].
P.A. Zyla et al., Review of Particle Physics, PTEP 2020 (2020) 083C01.
S.J. Brodsky and X.-G. Wu, Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops, Phys. Rev. D 85 (2012) 034038 [Erratum ibid. 86 (2012) 079903] [arXiv:1111.6175] [INSPIRE].
S.J. Brodsky and X.-G. Wu, Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality, Phys. Rev. Lett. 109 (2012) 042002 [arXiv:1203.5312] [INSPIRE].
S.J. Brodsky and L. Di Giustino, Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality, Phys. Rev. D 86 (2012) 085026 [arXiv:1107.0338] [INSPIRE].
M. Mojaza, S.J. Brodsky and X.-G. Wu, Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in Perturbative QCD, Phys. Rev. Lett. 110 (2013) 192001 [arXiv:1212.0049] [INSPIRE].
S.J. Brodsky, M. Mojaza and X.-G. Wu, Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations, Phys. Rev. D 89 (2014) 014027 [arXiv:1304.4631] [INSPIRE].
S.-Q. Wang, S.J. Brodsky, X.-G. Wu and L. Di Giustino, Thrust Distribution in Electron-Positron Annihilation using the Principle of Maximum Conformality, Phys. Rev. D 99 (2019) 114020 [arXiv:1902.01984] [INSPIRE].
S.-Q. Wang, S.J. Brodsky, X.-G. Wu, J.-M. Shen and L. Di Giustino, Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation, Phys. Rev. D 100 (2019) 094010 [arXiv:1908.00060] [INSPIRE].
S.J. Brodsky, G.P. Lepage and P.B. Mackenzie, On the Elimination of Scale Ambiguities in Perturbative Quantum Chromodynamics, Phys. Rev. D 28 (1983) 228 [INSPIRE].
M. Gell-Mann and F.E. Low, Quantum electrodynamics at small distances, Phys. Rev. 95 (1954) 1300 [INSPIRE].
S.J. Brodsky and X.-G. Wu, Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale, Phys. Rev. D 86 (2012) 054018 [arXiv:1208.0700] [INSPIRE].
X.-G. Wu et al., Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting, Rept. Prog. Phys. 78 (2015) 126201 [arXiv:1405.3196] [INSPIRE].
X.G. Wu, J.M. Shen, B.L. Du, X.D. Huang, S.Q. Wang and S.J. Brodsky, The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality, Prog. Part. Nucl. Phys. 108 (2019) 103706 arXiv:1903.12177.
X.-C. Zheng, X.-G. Wu, S.-Q. Wang, J.-M. Shen and Q.-L. Zhang, Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy, JHEP 10 (2013) 117 [arXiv:1308.2381] [INSPIRE].
J.-M. Shen, X.-G. Wu, B.-L. Du and S.J. Brodsky, Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting, Phys. Rev. D 95 (2017) 094006 [arXiv:1701.08245] [INSPIRE].
B.R. Webber, Estimation of power corrections to hadronic event shapes, Phys. Lett. B 339 (1994) 148 [hep-ph/9408222] [INSPIRE].
M. Beneke and V.M. Braun, Power corrections and renormalons in Drell-Yan production, Nucl. Phys. B 454 (1995) 253 [hep-ph/9506452] [INSPIRE].
E. Gardi and J. Rathsman, Renormalon resummation and exponentiation of soft and collinear gluon radiation in the thrust distribution, Nucl. Phys. B 609 (2001) 123 [hep-ph/0103217] [INSPIRE].
A.H. Hoang and I.W. Stewart, Designing gapped soft functions for jet production, Phys. Lett. B 660 (2008) 483 [arXiv:0709.3519] [INSPIRE].
N.G. Gracia and V. Mateu, Toward massless and massive event shapes in the large-β0 limit, JHEP 07 (2021) 229 [arXiv:2104.13942] [INSPIRE].
K.G. Chetyrkin, J.H. Kühn and M. Steinhauser, RunDec: A Mathematica package for running and decoupling of the strong coupling and quark masses, Comput. Phys. Commun. 133 (2000) 43 [hep-ph/0004189] [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].
M. Beneke, Renormalons, Phys. Rept. 317 (1999) 1 [hep-ph/9807443] [INSPIRE].
X.-G. Wu, S.J. Brodsky and M. Mojaza, The Renormalization Scale-Setting Problem in QCD, Prog. Part. Nucl. Phys. 72 (2013) 44 [arXiv:1302.0599] [INSPIRE].
S.J. Brodsky, G.F. de Teramond, H.G. Dosch and J. Erlich, Light-Front Holographic QCD and Emerging Confinement, Phys. Rept. 584 (2015) 1 [arXiv:1407.8131] [INSPIRE].
G. Kramer and B. Lampe, Jet production rates at LEP and the scale of αs, Z. Phys. A 339 (1991) 189 [INSPIRE].
T. Gehrmann, N. Häfliger and P.F. Monni, BLM Scale Fixing in Event Shape Distributions, Eur. Phys. J. C 74 (2014) 2896 [arXiv:1401.6809] [INSPIRE].
P. Pietrulewicz, S. Gritschacher, A.H. Hoang, I. Jemos and V. Mateu, Variable Flavor Number Scheme for Final State Jets in Thrust, Phys. Rev. D 90 (2014) 114001 [arXiv:1405.4860] [INSPIRE].
JADE collaboration, A study of event shapes and determinations of αs using data of e+e− annihilations at \( \sqrt{s} \) = 22 GeV to 44-GeV, Eur. Phys. J. C 1 (1998) 461 [hep-ex/9708034] [INSPIRE].
JADE collaboration, C parameter and jet broadening at PETRA energies, Phys. Lett. B 459 (1999) 326 [hep-ex/9903009] [INSPIRE].
G. Dissertori et al., Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e− annihilations, JHEP 08 (2009) 036 [arXiv:0906.3436] [INSPIRE].
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].
T. Becher and M.D. Schwartz, A precise determination of αs from LEP thrust data using effective field theory, JHEP 07 (2008) 034 [arXiv:0803.0342] [INSPIRE].
OPAL collaboration, Measurement of the running of the QED coupling in small-angle Bhabha scattering at LEP, Eur. Phys. J. C 45 (2006) 1 [hep-ex/0505072] [INSPIRE].
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Wang, SQ., Luo, CQ., Wu, XG. et al. New analyses of event shape observables in electron-positron annihilation and the determination of αs running behavior in perturbative domain. J. High Energ. Phys. 2022, 137 (2022). https://doi.org/10.1007/JHEP09(2022)137
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DOI: https://doi.org/10.1007/JHEP09(2022)137