Journal of High Energy Physics

, 2018:200 | Cite as

On the cutoff dependence of the quark mass parameter in angular ordered parton showers

  • André H. Hoang
  • Simon Plätzer
  • Daniel SamitzEmail author
Open Access
Regular Article - Theoretical Physics


We show that the presence of an infrared cutoff Q0 in the parton shower (PS) evolution for massive quarks implies that the generator quark mass corresponds to a Q0-dependent short-distance mass scheme and is therefore not the pole mass. Our analysis considers an angular ordered parton shower based on the coherent branching formalism for quasi-collinear stable heavy quarks and splitting functions at next-to-leading logarithmic (NLL) order, and it is based on the analysis of the peak of hemisphere jet mass distributions. We show that NLL shower evolution is sufficient to describe the peak jet mass at full next-to-leading order (NLO). We determine the relation of this short-distance mass to the pole mass at NLO. We also show that the shower cut Q0 affects soft radiation in a universal way for massless and quasi-collinear massive quark production. The basis of our analysis is (i) an analytic solution of the PS evolution based on the coherent branching formalism, (ii) an implementation of the infrared cut Q0 of the angular ordered shower into factorized analytic calculations in the framework of Soft-Collinear-Effective-Theory (SCET) and (iii) the dependence of the peak of the jet mass distribution on the shower cut. Numerical comparisons to simulations with the Herwig 7 event generator confirm our findings. Our analysis provides an important step towards a full understanding concerning the interpretation of top quark mass measurements based on direct reconstruction.


Quark Masses and SM Parameters Renormalization Regularization and Renormalons Effective Field Theories Perturbative QCD 


Open Access

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  1. [1]
    CMS collaboration, Measurement of the top quark mass using proton-proton data at \( \sqrt{(s)}=7 \) and 8 TeV, Phys. Rev. D 93 (2016) 072004 [arXiv:1509.04044] [INSPIRE].
  2. [2]
    ATLAS collaboration, Measurement of the top quark mass in the \( t\overline{t} \)dilepton channel from \( \sqrt{s}=8 \) TeV ATLAS data, Phys. Lett. B 761 (2016) 350 [arXiv:1606.02179] [INSPIRE].
  3. [3]
    CDF and D0 collaborations, T.E.W. Group, Combination of CDF and D0 results on the mass of the top quark using up to 9.7 fb −1 at the Tevatron, arXiv:1407.2682 [INSPIRE].
  4. [4]
    J. Bellm, G. Nail, S. Plätzer, P. Schichtel and A. Siódmok, Parton Shower Uncertainties with Herwig 7: Benchmarks at Leading Order, Eur. Phys. J. C 76 (2016) 665 [arXiv:1605.01338] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    J.R. Andersen et al., Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report, in 10th Les Houches Workshop on Physics at TeV Colliders (PhysTeV 2017) Les Houches, France, June 5–23, 2017, arXiv:1803.07977 [INSPIRE].
  6. [6]
    M. Dasgupta, F.A. Dreyer, K. Hamilton, P.F. Monni and G.P. Salam, Logarithmic accuracy of parton showers: a fixed-order study, JHEP 09 (2018) 033 [arXiv:1805.09327] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    H. Baer et al., The International Linear Collider Technical Design ReportVolume 2: Physics, arXiv:1306.6352 [INSPIRE].
  8. [8]
    D. Asner, A. Hoang, Y. Kiyo, R. Pöschl, Y. Sumino and M. Vos, Top quark precision physics at the International Linear Collider, in Proceedings, 2013 Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi (CSS2013): Minneapolis, MN, U.S.A., July 29 – August 6, 2013, arXiv:1307.8265 [INSPIRE].
  9. [9]
    M. Vos et al., Top physics at high-energy lepton colliders, arXiv:1604.08122 [INSPIRE].
  10. [10]
    A. Jain, I. Scimemi and I.W. Stewart, Two-loop Jet-Function and Jet-Mass for Top Quarks, Phys. Rev. D 77 (2008) 094008 [arXiv:0801.0743] [INSPIRE].ADSGoogle Scholar
  11. [11]
    M. Butenschoen, B. Dehnadi, A.H. Hoang, V. Mateu, M. Preisser and I.W. Stewart, Top Quark Mass Calibration for Monte Carlo Event Generators, Phys. Rev. Lett. 117 (2016) 232001 [arXiv:1608.01318] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    A.H. Hoang et al., Top-antitop pair production close to threshold: Synopsis of recent NNLO results, Eur. Phys. J. direct 2 (2000) 3 [hep-ph/0001286] [INSPIRE].
  13. [13]
    A.H. Hoang and I.W. Stewart, Top Mass Measurements from Jets and the Tevatron Top-Quark Mass, Nucl. Phys. Proc. Suppl. 185 (2008) 220 [arXiv:0808.0222] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    S. Fleming, A.H. Hoang, S. Mantry and I.W. Stewart, Jets from massive unstable particles: Top-mass determination, Phys. Rev. D 77 (2008) 074010 [hep-ph/0703207] [INSPIRE].
  15. [15]
    S. Fleming, A.H. Hoang, S. Mantry and I.W. Stewart, Top Jets in the Peak Region: Factorization Analysis with NLL Resummation, Phys. Rev. D 77 (2008) 114003 [arXiv:0711.2079] [INSPIRE].ADSGoogle Scholar
  16. [16]
    A.H. Hoang, The Top Mass: Interpretation and Theoretical Uncertainties, in Proceedings, 7th International Workshop on Top Quark Physics (TOP2014): Cannes, France, September 28 – October 3, 2014, arXiv:1412.3649 [INSPIRE].
  17. [17]
    M. Neubert, Heavy quark symmetry, Phys. Rept. 245 (1994) 259 [hep-ph/9306320] [INSPIRE].
  18. [18]
    A.V. Manohar and M.B. Wise, Heavy quark physics, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 10 (2000) 1 [INSPIRE].Google Scholar
  19. [19]
    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].ADSCrossRefGoogle Scholar
  20. [20]
    A.H. Hoang et al., The MSR mass and the \( \mathcal{O} \)QCD) renormalon sum rule, JHEP 04 (2018) 003 [arXiv:1704.01580] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    1712.02796 P. Nason, The Top Mass in Hadronic Collisions, arXiv:1712.02796 [INSPIRE].
  22. [22]
    T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
  23. [23]
    P. Skands, S. Carrazza and J. Rojo, Tuning PYTHIA 8.1: the Monash 2013 Tune, Eur. Phys. J. C 74 (2014) 3024 [arXiv:1404.5630] [INSPIRE].
  24. [24]
    A.H. Hoang, S. Mantry, A. Pathak and I.W. Stewart, Extracting a Short Distance Top Mass with Light Grooming, arXiv:1708.02586 [INSPIRE].
  25. [25]
    M. Dasgupta, A. Fregoso, S. Marzani and G.P. Salam, Towards an understanding of jet substructure, JHEP 09 (2013) 029 [arXiv:1307.0007] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    A.J. Larkoski, S. Marzani, G. Soyez and J. Thaler, Soft Drop, JHEP 05 (2014) 146 [arXiv:1402.2657] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    J. Kieseler, K. Lipka and S.-O. Moch, Calibration of the Top-Quark Monte Carlo Mass, Phys. Rev. Lett. 116 (2016) 162001 [arXiv:1511.00841] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    CMS collaboration, J.H. Kim, Alternative methods for top quark mass measurements at the CMS, EPJ Web Conf. 141 (2017) 08006 [INSPIRE].
  29. [29]
    ATLAS and CMS collaborations, M. Vos, Top-quark mass measurements at the LHC: alternative methods, PoS(TOP2015)035 (2016) [arXiv:1602.00428] [INSPIRE].
  30. [30]
    S. Adomeit, Top-quark mass measurements: Alternative techniques (LHC + Tevatron), in Proceedings, 7th International Workshop on Top Quark Physics (TOP2014): Cannes, France, September 28 – October 3, 2014, arXiv:1411.7917 [INSPIRE].
  31. [31]
    G. Corcella, R. Franceschini and D. Kim, Fragmentation Uncertainties in Hadronic Observables for Top-quark Mass Measurements, Nucl. Phys. B 929 (2018) 485 [arXiv:1712.05801] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    K. Agashe, R. Franceschini, D. Kim and M. Schulze, Top quark mass determination from the energy peaks of b-jets and B-hadrons at NLO QCD, Eur. Phys. J. C 76 (2016) 636 [arXiv:1603.03445] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    S. Biswas, K. Melnikov and M. Schulze, Next-to-leading order QCD effects and the top quark mass measurements at the LHC, JHEP 08 (2010) 048 [arXiv:1006.0910] [INSPIRE].ADSzbMATHGoogle Scholar
  34. [34]
    C.G. Lester and D.J. Summers, Measuring masses of semiinvisibly decaying particles pair produced at hadron colliders, Phys. Lett. B 463 (1999) 99 [hep-ph/9906349] [INSPIRE].
  35. [35]
    K.T. Matchev and M. Park, A general method for determining the masses of semi-invisibly decaying particles at hadron colliders, Phys. Rev. Lett. 107 (2011) 061801 [arXiv:0910.1584] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    CMS collaboration, Mass determination in the \( t\overline{t} \) system with kinematic endpoints, CMS-PAS-TOP-11-027 [INSPIRE].
  37. [37]
    CMS collaboration, Measurement of the top quark mass in the dileptonic \( t\overline{t} \) decay channel using the mass observables M bℓ , M T2 and M bℓν in pp collisions at \( \sqrt{s}=8 \) TeV, Phys. Rev. D 96 (2017) 032002 [arXiv:1704.06142] [INSPIRE].
  38. [38]
    G. Heinrich et al., NLO and off-shell effects in top quark mass determinations, JHEP 07 (2018) 129 [arXiv:1709.08615] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].
  40. [40]
    S. Ferrario Ravasio, T. Ježo, P. Nason and C. Oleari, A theoretical study of top-mass measurements at the LHC using NLO+PS generators of increasing accuracy, Eur. Phys. J. C 78 (2018) 458 [arXiv:1801.03944] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with Parton Shower simulations: the POWHEG method, JHEP 11 (2007) 070 [arXiv:0709.2092] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  43. [43]
    S. Frixione, P. Nason and G. Ridolfi, A positive-weight next-to-leading-order Monte Carlo for heavy flavour hadroproduction, JHEP 09 (2007) 126 [arXiv:0707.3088] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    J.M. Campbell, R.K. Ellis, P. Nason and E. Re, Top-Pair Production and Decay at NLO Matched with Parton Showers, JHEP 04 (2015) 114 [arXiv:1412.1828] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    T. Ježo, J.M. Lindert, P. Nason, C. Oleari and S. Pozzorini, An NLO+PS generator for \( t\overline{t} \) and Wt production and decay including non-resonant and interference effects, Eur. Phys. J. C 76 (2016) 691 [arXiv:1607.04538] [INSPIRE].ADSGoogle Scholar
  46. [46]
    J. Bellm et al., Herwig 7.0/Herwig++ 3.0 release note, Eur. Phys. J. C 76 (2016) 196 [arXiv:1512.01178] [INSPIRE].
  47. [47]
    J. Bellm et al., Herwig 7.1 Release Note, arXiv:1705.06919 [INSPIRE].
  48. [48]
    S. Frixione and A. Mitov, Determination of the top quark mass from leptonic observables, JHEP 09 (2014) 012 [arXiv:1407.2763] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    Y.L. Dokshitzer, V.A. Khoze and S.I. Troian, Particle spectra in light and heavy quark jets, J. Phys. G 17 (1991) 1481 [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    Y.L. Dokshitzer, V.A. Khoze and S.I. Troian, On specific QCD properties of heavy quark fragmentation (dead cone), J. Phys. G 17 (1991) 1602 [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    F. Maltoni, M. Selvaggi and J. Thaler, Exposing the dead cone effect with jet substructure techniques, Phys. Rev. D 94 (2016) 054015 [arXiv:1606.03449] [INSPIRE].ADSGoogle Scholar
  52. [52]
    G. Marchesini and B.R. Webber, Simulation of QCD Jets Including Soft Gluon Interference, Nucl. Phys. B 238 (1984) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    G. Marchesini and B.R. Webber, Monte Carlo Simulation of General Hard Processes with Coherent QCD Radiation, Nucl. Phys. B 310 (1988) 461 [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    S. Catani, B.R. Webber and G. Marchesini, QCD coherent branching and semiinclusive processes at large x, Nucl. Phys. B 349 (1991) 635 [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    S. Gieseke, P. Stephens and B. Webber, New formalism for QCD parton showers, JHEP 12 (2003) 045 [hep-ph/0310083] [INSPIRE].
  56. [56]
    F. Krauss and G. Rodrigo, Resummed jet rates for e + e annihilation into massive quarks, Phys. Lett. B 576 (2003) 135 [hep-ph/0303038] [INSPIRE].
  57. [57]
    G. Rodrigo and F. Krauss, Resummed jet rates for heavy quark production in e + e annihilation, Eur. Phys. J. C 33 (2004) S457 [hep-ph/0309325] [INSPIRE].
  58. [58]
    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].ADSCrossRefGoogle Scholar
  59. [59]
    R. Abbate, M. Fickinger, A.H. Hoang, V. Mateu and I.W. Stewart, Thrust at N 3 LL with Power Corrections and a Precision Global Fit for α s(M Z), Phys. Rev. D 83 (2011) 074021 [arXiv:1006.3080] [INSPIRE].ADSGoogle Scholar
  60. [60]
    E. Farhi, A QCD Test for Jets, Phys. Rev. Lett. 39 (1977) 1587 [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, N-Jettiness: An Inclusive Event Shape to Veto Jets, Phys. Rev. Lett. 105 (2010) 092002 [arXiv:1004.2489] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    S. Catani and L. Trentadue, Resummation of the QCD Perturbative Series for Hard Processes, Nucl. Phys. B 327 (1989) 323 [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    G.P. Korchemsky and G.F. Sterman, Power corrections to event shapes and factorization, Nucl. Phys. B 555 (1999) 335 [hep-ph/9902341] [INSPIRE].
  64. [64]
    C.F. Berger, T. Kucs and G.F. Sterman, Event shape/energy flow correlations, Phys. Rev. D 68 (2003) 014012 [hep-ph/0303051] [INSPIRE].
  65. [65]
    R.A. Davison and B.R. Webber, Non-Perturbative Contribution to the Thrust Distribution in e + e Annihilation, Eur. Phys. J. C 59 (2009) 13 [arXiv:0809.3326] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    M.D. Schwartz, Resummation and NLO matching of event shapes with effective field theory, Phys. Rev. D 77 (2008) 014026 [arXiv:0709.2709] [INSPIRE].ADSGoogle Scholar
  67. [67]
    T. Becher and M.D. Schwartz, A precise determination of α s from LEP thrust data using effective field theory, JHEP 07 (2008) 034 [arXiv:0803.0342] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    L.G. Almeida, S.D. Ellis, C. Lee, G. Sterman, I. Sung and J.R. Walsh, Comparing and counting logs in direct and effective methods of QCD resummation, JHEP 04 (2014) 174 [arXiv:1401.4460] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    A.V. Manohar and I.W. Stewart, The Zero-Bin and Mode Factorization in Quantum Field Theory, Phys. Rev. D 76 (2007) 074002 [hep-ph/0605001] [INSPIRE].
  70. [70]
    A.H. Hoang and I.W. Stewart, Designing gapped soft functions for jet production, Phys. Lett. B 660 (2008) 483 [arXiv:0709.3519] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    M. Bahr et al., Herwig++ Physics and Manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
    J.C. Collins and D.E. Soper, The Two Particle Inclusive Cross-section in e + e Annihilation at PETRA, PEP and LEP Energies, Nucl. Phys. B 284 (1987) 253 [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    S. Platzer and S. Gieseke, Coherent Parton Showers with Local Recoils, JHEP 01 (2011) 024 [arXiv:0909.5593] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  74. [74]
    D. Reichelt, P. Richardson and A. Siodmok, Improving the Simulation of Quark and Gluon Jets with Herwig 7, Eur. Phys. J. C 77 (2017) 876 [arXiv:1708.01491] [INSPIRE].ADSCrossRefGoogle Scholar
  75. [75]
    B.R. Webber, A QCD Model for Jet Fragmentation Including Soft Gluon Interference, Nucl. Phys. B 238 (1984) 492 [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    H. Contopanagos, E. Laenen and G.F. Sterman, Sudakov factorization and resummation, Nucl. Phys. B 484 (1997) 303 [hep-ph/9604313] [INSPIRE].
  77. [77]
    M. Beneke, Large order perturbation theory for a physical quantity, Nucl. Phys. B 405 (1993) 424 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  78. [78]
    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].
  79. [79]
    M. Beneke, More on ambiguities in the pole mass, Phys. Lett. B 344 (1995) 341 [hep-ph/9408380] [INSPIRE].
  80. [80]
    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].
  81. [81]
    A.H. Hoang and S. Kluth, Hemisphere Soft Function at \( \mathcal{O}\left({\alpha}_s^2\right) \) for Dijet Production in e + e Annihilation, arXiv:0806.3852 [INSPIRE].
  82. [82]
    A.H. Hoang, C. Lepenik and M. Preisser, On the Light Massive Flavor Dependence of the Large Order Asymptotic Behavior and the Ambiguity of the Pole Mass, JHEP 09 (2017) 099 [arXiv:1706.08526] [INSPIRE].ADSCrossRefGoogle Scholar
  83. [83]
    K. Hamilton and P. Richardson, A simulation of QCD radiation in top quark decays, JHEP 02 (2007) 069 [hep-ph/0612236] [INSPIRE].
  84. [84]
    A. Buckley et al., Rivet user manual, Comput. Phys. Commun. 184 (2013) 2803 [arXiv:1003.0694] [INSPIRE].ADSCrossRefGoogle Scholar
  85. [85]
    M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  86. [86]
    S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].
  87. [87]
    S. Platzer and S. Gieseke, Dipole Showers and Automated NLO Matching in Herwig++, Eur. Phys. J. C 72 (2012) 2187 [arXiv:1109.6256] [INSPIRE].ADSCrossRefGoogle Scholar
  88. [88]
    S. Hoeche, F. Krauss, M. Schonherr and F. Siegert, A critical appraisal of NLO+PS matching methods, JHEP 09 (2012) 049 [arXiv:1111.1220] [INSPIRE].ADSCrossRefGoogle Scholar
  89. [89]
    P. Nason and B. Webber, Next-to-Leading-Order Event Generators, Ann. Rev. Nucl. Part. Sci. 62 (2012) 187 [arXiv:1202.1251] [INSPIRE].ADSCrossRefGoogle Scholar
  90. [90]
    S. Platzer and M. Sjodahl, Subleading N c improved Parton Showers, JHEP 07 (2012) 042 [arXiv:1201.0260] [INSPIRE].ADSCrossRefGoogle Scholar
  91. [91]
    J.C. Collins, Spin Correlations in Monte Carlo Event Generators, Nucl. Phys. B 304 (1988) 794 [INSPIRE].ADSCrossRefGoogle Scholar
  92. [92]
    I.G. Knowles, Angular Correlations in QCD, Nucl. Phys. B 304 (1988) 767 [INSPIRE].ADSCrossRefGoogle Scholar
  93. [93]
    P. Richardson, Spin correlations in Monte Carlo simulations, JHEP 11 (2001) 029 [hep-ph/0110108] [INSPIRE].
  94. [94]
    S. Hoche, F. Krauss, M. Schonherr and F. Siegert, NLO matrix elements and truncated showers, JHEP 08 (2011) 123 [arXiv:1009.1127] [INSPIRE].ADSCrossRefGoogle Scholar
  95. [95]
    M. Beneke, P. Marquard, P. Nason and M. Steinhauser, On the ultimate uncertainty of the top quark pole mass, Phys. Lett. B 775 (2017) 63 [arXiv:1605.03609] [INSPIRE].ADSCrossRefGoogle Scholar
  96. [96]
    CMS collaboration, Projected improvement of the accuracy of top-quark mass measurements at the upgraded LHC, CMS-PAS-FTR-13-017 [INSPIRE].
  97. [97]
    CMS collaboration, ECFA 2016: Prospects for selected standard model measurements with the CMS experiment at the High-Luminosity LHC, CMS-PAS-FTR-16-006 [INSPIRE].
  98. [98]
    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].
  99. [99]
    A.H. Hoang, Z. Ligeti and A.V. Manohar, B decays in the upsilon expansion, Phys. Rev. D 59 (1999) 074017 [hep-ph/9811239] [INSPIRE].
  100. [100]
    A.H. Hoang, 1S and \( \overline{\mathrm{MS}} \) bottom quark masses from Upsilon sum rules, Phys. Rev. D 61 (2000) 034005 [hep-ph/9905550] [INSPIRE].
  101. [101]
    M. Beneke, A quark mass definition adequate for threshold problems, Phys. Lett. B 434 (1998) 115 [hep-ph/9804241] [INSPIRE].
  102. [102]
    The Herwig Event Generator, (2018).

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • André H. Hoang
    • 1
    • 2
  • Simon Plätzer
    • 1
  • Daniel Samitz
    • 1
    Email author
  1. 1.University of Vienna, Faculty of PhysicsWienAustria
  2. 2.Erwin Schrödinger International Institute for Mathematical PhysicsUniversity of ViennaWienAustria

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