Heavy-flavor parton distributions without heavy-flavor matching prescriptions

  • Valerio Bertone
  • Alexandre Glazov
  • Alexander Mitov
  • Andrew S. Papanastasiou
  • Maria Ubiali
Open Access
Regular Article - Theoretical Physics
  • 13 Downloads

Abstract

We show that the well-known obstacle for working with the zero-mass variable flavor number scheme, namely, the omission of \( \mathcal{O}(1) \) mass power corrections close to the conventional heavy flavor matching point (HFMP) μ b = m, can be easily overcome. For this it is sufficient to take advantage of the freedom in choosing the position of the HFMP. We demonstrate that by choosing a sufficiently large HFMP, which could be as large as 10 times the mass of the heavy quark, one can achieve the following improvements: 1) above the HFMP the size of missing power corrections \( \mathcal{O}(m) \) is restricted by the value of μ b and, therefore, the error associated with their omission can be made negligible; 2) additional prescriptions for the definition of cross-sections are not required; 3) the resummation accuracy is maintained and 4) contrary to the common lore we find that the discontinuity of α s and pdfs across thresholds leads to improved continuity in predictions for observables. We have considered a large set of proton-proton and electron-proton collider processes, many through NNLO QCD, that demonstrate the broad applicability of our proposal.

Keywords

Deep Inelastic Scattering (Phenomenology) QCD Phenomenology 

Notes

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.

References

  1. [1]
    J.C. Collins, D.E. Soper and G.F. Sterman, Factorization of hard processes in QCD, Adv. Ser. Direct. High Energy Phys. 5 (1989) 1 [hep-ph/0409313] [INSPIRE].
  2. [2]
    J.C. Collins, D.E. Soper and G.F. Sterman, Heavy particle production in high-energy hadron collisions, Nucl. Phys. B 263 (1986) 37 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    J.C. Collins, Hard scattering factorization with heavy quarks: a general treatment, Phys. Rev. D 58 (1998) 094002 [hep-ph/9806259] [INSPIRE].
  4. [4]
    NNPDF collaboration, R.D. Ball et al., A determination of the charm content of the proton, Eur. Phys. J. C 76 (2016) 647 [arXiv:1605.06515] [INSPIRE].
  5. [5]
    R.D. Ball, M. Bonvini and L. Rottoli, Charm in deep-inelastic scattering, JHEP 11 (2015) 122 [arXiv:1510.02491] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    R.D. Ball et al., Intrinsic charm in a matched general-mass scheme, Phys. Lett. B 754 (2016) 49 [arXiv:1510.00009] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  7. [7]
    NNPDF collaboration, R.D. Ball et al., Parton distributions from high-precision collider data, Eur. Phys. J. C 77 (2017) 663 [arXiv:1706.00428] [INSPIRE].
  8. [8]
    T.-J. Hou et al., CT14 intrinsic charm parton distribution functions from CTEQ-TEA global analysis, JHEP 02 (2018) 059 [arXiv:1707.00657] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    K. Symanzik, Infrared singularities and small distance behavior analysis, Commun. Math. Phys. 34 (1973) 7 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev. D 11 (1975) 2856 [INSPIRE].ADSGoogle Scholar
  11. [11]
    J.C. Collins, F. Wilczek and A. Zee, Low-energy manifestations of heavy particles: application to the neutral current, Phys. Rev. D 18 (1978) 242 [INSPIRE].ADSGoogle Scholar
  12. [12]
    J.C. Collins and W.-K. Tung, Calculating heavy quark distributions, Nucl. Phys. B 278 (1986) 934 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    M. Buza, Y. Matiounine, J. Smith, R. Migneron and W.L. van Neerven, Heavy quark coefficient functions at asymptotic values Q 2m 2, Nucl. Phys. B 472 (1996) 611 [hep-ph/9601302] [INSPIRE].
  14. [14]
    M. Buza, Y. Matiounine, J. Smith and W.L. van Neerven, Charm electroproduction viewed in the variable flavor number scheme versus fixed order perturbation theory, Eur. Phys. J. C 1 (1998) 301 [hep-ph/9612398] [INSPIRE].
  15. [15]
    J. Ablinger, J. Blumlein, S. Klein, C. Schneider and F. Wissbrock, The O(α s3) massive operator matrix elements of O(n f) for the structure function F 2(x, Q 2) and transversity, Nucl. Phys. B 844 (2011) 26 [arXiv:1008.3347] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  16. [16]
    J. Blumlein, A. Hasselhuhn, S. Klein and C. Schneider, The O(α s3 n f T F2 C A,F) contributions to the gluonic massive operator matrix elements, Nucl. Phys. B 866 (2013) 196, arXiv:1205.4184] [INSPIRE].
  17. [17]
    J. Ablinger et al., The transition matrix element A gq(N) of the variable flavor number scheme at O(α s3), Nucl. Phys. B 882 (2014) 263 [arXiv:1402.0359] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    J. Ablinger et al., The O(α s3 T F2) contributions to the gluonic operator matrix element, Nucl. Phys. B 885 (2014) 280 [arXiv:1405.4259] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    A. Behring et al., The logarithmic contributions to the O(α s3) asymptotic massive Wilson coefficients and operator matrix elements in deeply inelastic scattering, Eur. Phys. J. C 74 (2014) 3033 [arXiv:1403.6356] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    Y. Schröder and M. Steinhauser, Four-loop decoupling relations for the strong coupling, JHEP 01 (2006) 051 [hep-ph/0512058] [INSPIRE].
  21. [21]
    K.G. Chetyrkin, J.H. Kuhn and C. Sturm, QCD decoupling at four loops, Nucl. Phys. B 744 (2006) 121 [hep-ph/0512060] [INSPIRE].
  22. [22]
    B.A. Kniehl, A.V. Kotikov, A.I. Onishchenko and O.L. Veretin, Strong-coupling constant with flavor thresholds at five loops in the anti-MS scheme, Phys. Rev. Lett. 97 (2006) 042001 [hep-ph/0607202] [INSPIRE].
  23. [23]
    M.A.G. Aivazis, J.C. Collins, F.I. Olness and W.-K. Tung, Leptoproduction of heavy quarks. 2. A unified QCD formulation of charged and neutral current processes from fixed target to collider energies, Phys. Rev. D 50 (1994) 3102 [hep-ph/9312319] [INSPIRE].
  24. [24]
    R.S. Thorne and R.G. Roberts, An ordered analysis of heavy flavor production in deep inelastic scattering, Phys. Rev. D 57 (1998) 6871 [hep-ph/9709442] [INSPIRE].
  25. [25]
    R.S. Thorne and R.G. Roberts, A practical procedure for evolving heavy flavor structure functions, Phys. Lett. B 421 (1998) 303 [hep-ph/9711223] [INSPIRE].
  26. [26]
    M. Krämer, F.I. Olness and D.E. Soper, Treatment of heavy quarks in deeply inelastic scattering, Phys. Rev. D 62 (2000) 096007 [hep-ph/0003035] [INSPIRE].
  27. [27]
    R.S. Thorne, A variable-flavor number scheme for NNLO, Phys. Rev. D 73 (2006) 054019 [hep-ph/0601245] [INSPIRE].
  28. [28]
    W.K. Tung et al., Heavy quark mass effects in deep inelastic scattering and global QCD analysis, JHEP 02 (2007) 053 [hep-ph/0611254] [INSPIRE].
  29. [29]
    P.M. Nadolsky and W.-K. Tung, Improved formulation of global QCD analysis with zero-mass matrix elements, Phys. Rev. D 79 (2009) 113014 [arXiv:0903.2667] [INSPIRE].ADSGoogle Scholar
  30. [30]
    S. Forte, E. Laenen, P. Nason and J. Rojo, Heavy quarks in deep-inelastic scattering, Nucl. Phys. B 834 (2010) 116 [arXiv:1001.2312] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  31. [31]
    M. Guzzi, P.M. Nadolsky, H.-L. Lai and C.P. Yuan, General-mass treatment for deep inelastic scattering at two-loop accuracy, Phys. Rev. D 86 (2012) 053005 [arXiv:1108.5112] [INSPIRE].ADSGoogle Scholar
  32. [32]
    T. Han, J. Sayre and S. Westhoff, Top-quark initiated processes at high-energy hadron colliders, JHEP 04 (2015) 145 [arXiv:1411.2588] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    M. Cacciari, M. Greco and P. Nason, The p T spectrum in heavy flavor hadroproduction, JHEP 05 (1998) 007 [hep-ph/9803400] [INSPIRE].
  34. [34]
    S. Forte, D. Napoletano and M. Ubiali, Higgs production in bottom-quark fusion in a matched scheme, Phys. Lett. B 751 (2015) 331 [arXiv:1508.01529] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    S. Forte, D. Napoletano and M. Ubiali, Higgs production in bottom-quark fusion: matching beyond leading order, Phys. Lett. B 763 (2016) 190 [arXiv:1607.00389] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    F.I. Olness and W.-K. Tung, When is a heavy quark not a parton? Charged Higgs production and heavy quark mass effects in the QCD based parton model, Nucl. Phys. B 308 (1988) 813 [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    F.I. Olness and S.T. Riemersma, Leptoproduction of heavy quarks in the fixed and variable flavor schemes, Phys. Rev. D 51 (1995) 4746 [hep-ph/9409208] [INSPIRE].
  38. [38]
    M. Bonvini, A.S. Papanastasiou and F.J. Tackmann, Resummation and matching of b-quark mass effects in \( b\overline{b}H \) production, JHEP 11 (2015) 196 [arXiv:1508.03288] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    M. Bonvini, A.S. Papanastasiou and F.J. Tackmann, Matched predictions for the \( b\overline{b}H \) cross section at the 13 TeV LHC, JHEP 10 (2016) 053 [arXiv:1605.01733] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    J. Blumlein and W.L. van Neerven, Heavy flavor contributions to the deep inelastic scattering sum rules, Phys. Lett. B 450 (1999) 417 [hep-ph/9811351] [INSPIRE].
  41. [41]
    A.L. Kataev, G. Parente and A.V. Sidorov, Improved fits to the xF3 CCFR data at the next-to-next-to-leading order and beyond, Phys. Part. Nucl. 34 (2003) 20 [Erratum ibid. 38 (2007) 827] [Fiz. Elem. Chast. Atom. Yadra 34 (2003) 43] [hep-ph/0106221] [INSPIRE].
  42. [42]
    F. Maltoni, T. McElmurry, R. Putman and S. Willenbrock, Choosing the factorization scale in perturbative QCD, hep-ph/0703156 [INSPIRE].
  43. [43]
    F. Maltoni, G. Ridolfi and M. Ubiali, b-initiated processes at the LHC: a reappraisal, JHEP 07 (2012) 022 [Erratum ibid. 04 (2013) 095] [arXiv:1203.6393] [INSPIRE].
  44. [44]
    C. Degrande, M. Ubiali, M. Wiesemann and M. Zaro, Heavy charged Higgs boson production at the LHC, JHEP 10 (2015) 145 [arXiv:1507.02549] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    M. Lim, F. Maltoni, G. Ridolfi and M. Ubiali, Anatomy of double heavy-quark initiated processes, JHEP 09 (2016) 132 [arXiv:1605.09411] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    J.M. Campbell, R.K. Ellis, F. Maltoni and S. Willenbrock, Associated production of a Z boson and a single heavy quark jet, Phys. Rev. D 69 (2004) 074021 [hep-ph/0312024] [INSPIRE].
  47. [47]
    M. Cacciari, P. Nason and C. Oleari, Crossing heavy-flavor thresholds in fragmentation functions, JHEP 10 (2005) 034 [hep-ph/0504192] [INSPIRE].
  48. [48]
    B. Mele and P. Nason, The Fragmentation function for heavy quarks in QCD, Nucl. Phys. B 361 (1991) 626 [Erratum ibid. B 921 (2017) 841] [INSPIRE].
  49. [49]
    K. Melnikov and A. Mitov, Perturbative heavy quark fragmentation function through O(α s2), Phys. Rev. D 70 (2004) 034027 [hep-ph/0404143] [INSPIRE].
  50. [50]
    A. Mitov, Perturbative heavy quark fragmentation function through O(α s2): gluon initiated contribution, Phys. Rev. D 71 (2005) 054021 [hep-ph/0410205] [INSPIRE].
  51. [51]
    The xFitter Developers Team collaboration, V. Bertone et al., Impact of the heavy quark matching scales in PDF fits, Eur. Phys. J. C 77 (2017) 837 [arXiv:1707.05343] [INSPIRE].
  52. [52]
    S. Kretzer and I. Schienbein, Heavy quark initiated contributions to deep inelastic structure functions, Phys. Rev. D 58 (1998) 094035 [hep-ph/9805233] [INSPIRE].
  53. [53]
    R. Doria, J. Frenkel and J.C. Taylor, Counter example to nonabelian Bloch-Nordsieck theorem, Nucl. Phys. B 168 (1980) 93 [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    C. Di’Lieto, S. Gendron, I.G. Halliday and C.T. Sachrajda, A counter example to the Bloch-Nordsieck theorem in nonabelian gauge theories, Nucl. Phys. B 183 (1981) 223 [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    S. Catani, M. Ciafaloni and G. Marchesini, Noncancelling infrared divergences in QCD coherent state, Nucl. Phys. B 264 (1986) 588 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  56. [56]
    J. Collins, Foundations of perturbative QCD, Cambridge University Press, Cambridge U.K. (2011).CrossRefGoogle Scholar
  57. [57]
    C. Alexandrou et al., A complete non-perturbative renormalization prescription for quasi-PDFs, Nucl. Phys. B 923 (2017) 394 [arXiv:1706.00265] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  58. [58]
    K. Orginos, A. Radyushkin, J. Karpie and S. Zafeiropoulos, Lattice QCD exploration of parton pseudo-distribution functions, Phys. Rev. D 96 (2017) 094503 [arXiv:1706.05373] [INSPIRE].ADSGoogle Scholar
  59. [59]
    E.R. Nocera, H.-W. Lin, F. Olness, K. Orginos and J. Rojo, The PDFLattice2017 workshop: a summary report, PoS(DIS2017)211 [arXiv:1709.01511] [INSPIRE].
  60. [60]
    J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    M. Brucherseifer, F. Caola and K. Melnikov, On the NNLO QCD corrections to single-top production at the LHC, Phys. Lett. B 736 (2014) 58 [arXiv:1404.7116] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    E.L. Berger, J. Gao, C.P. Yuan and H.X. Zhu, NNLO QCD corrections to t-channel single top-quark production and decay, Phys. Rev. D 94 (2016) 071501 [arXiv:1606.08463] [INSPIRE].ADSGoogle Scholar
  64. [64]
    F. Maltoni, T. McElmurry and S. Willenbrock, Inclusive production of a Higgs or Z boson in association with heavy quarks, Phys. Rev. D 72 (2005) 074024 [hep-ph/0505014] [INSPIRE].
  65. [65]
    ATLAS collaboration, Measurement of differential cross sections of isolated-photon plus heavy-flavour jet production in pp collisions at \( \sqrt{s}=8 \) TeV using the ATLAS detector, Phys. Lett. B 776 (2018) 295 [arXiv:1710.09560] [INSPIRE].
  66. [66]
    S. Forte, A. Isgrò and G. Vita, Do we need N 3 LO parton distributions?, Phys. Lett. B 731 (2014) 136 [arXiv:1312.6688] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    ATLAS collaboration, Measurements of top-quark pair to Z-boson cross-section ratios at \( \sqrt{s}=13 \) , 8, 7 TeV with the ATLAS detector, JHEP 02 (2017) 117 [arXiv:1612.03636] [INSPIRE].
  68. [68]
    S. Alekhin et al., HERAFitter, Eur. Phys. J. C 75 (2015) 304 [arXiv:1410.4412] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    V. Bertone, S. Carrazza and J. Rojo, APFEL: a PDF evolution library with QED corrections, Comput. Phys. Commun. 185 (2014) 1647 [arXiv:1310.1394] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  70. [70]
    M. Czakon, D. Heymes and A. Mitov, Dynamical scales for multi-TeV top-pair production at the LHC, JHEP 04 (2017) 071 [arXiv:1606.03350] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    M. Epele, C.A. Garcia Canal and R. Sassot, Role of heavy quarks in light hadron fragmentation, Phys. Rev. D 94 (2016) 034037 [arXiv:1604.08427] [INSPIRE].ADSGoogle Scholar
  72. [72]
    D.P. Anderle, F. Ringer and M. Stratmann, Fragmentation functions at next-to-next-to-leading order accuracy, Phys. Rev. D 92 (2015) 114017 [arXiv:1510.05845] [INSPIRE].ADSGoogle Scholar
  73. [73]
    NNPDF collaboration, V. Bertone et al., A determination of the fragmentation functions of pions, kaons and protons with faithful uncertainties, Eur. Phys. J. C 77 (2017) 516 [arXiv:1706.07049] [INSPIRE].
  74. [74]
    ZEUS, H1 collaboration, H. Abramowicz et al., Combination of measurements of inclusive deep inelastic e ± p scattering cross sections and QCD analysis of HERA data, Eur. Phys. J. C 75 (2015) 580 [arXiv:1506.06042] [INSPIRE].
  75. [75]
    ZEUS, H1 collaboration, H. Abramowicz et al., Combination and QCD Analysis of Charm Production Cross Section Measurements in Deep-Inelastic ep Scattering at HERA, Eur. Phys. J. C 73 (2013) 2311 [arXiv:1211.1182] [INSPIRE].
  76. [76]
    H1 collaboration, F.D. Aaron et al., Measurement of the charm and beauty structure functions using the H1 vertex detector at HERA, Eur. Phys. J. C 65 (2010) 89 [arXiv:0907.2643] [INSPIRE].
  77. [77]
    ZEUS collaboration, H. Abramowicz et al., Measurement of beauty and charm production in deep inelastic scattering at HERA and measurement of the beauty-quark mass, JHEP 09 (2014) 127 [arXiv:1405.6915] [INSPIRE].
  78. [78]
    C.W. Bauer, N. Ferland and B.R. Webber, Standard model parton distributions at very high energies, JHEP 08 (2017) 036 [arXiv:1703.08562] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Physics and AstronomyVU University AmsterdamHV AmsterdamThe Netherlands
  2. 2.Nikhef, Science Park 105XG AmsterdamThe Netherlands
  3. 3.DESY HamburgHamburgGermany
  4. 4.Cavendish LaboratoryUniversity of CambridgeCambridgeU.K.
  5. 5.DAMTPUniversity of CambridgeCambridgeU.K.

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