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Charm quark mass dependence in a global QCD analysis

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Abstract

We study the effect of the charm quark mass in the CTEQ global analysis of parton distribution functions (PDFs) of the proton. Constraints on the \(\overline{\mathrm{MS}}\) mass of the charm quark are examined at the next-to-next-to-leading order (NNLO) accuracy in the S-ACOT-χ heavy-quark factorization scheme. The value of the charm quark mass from the hadronic scattering data in the CT10 NNLO fit, including semi-inclusive charm production in DIS at HERA collider, is found to agree with the world average value. Various approaches for constraining m c in the global analysis and impact on LHC cross sections are reviewed.

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Notes

  1. The evolution of α s and PDFs is carried out using the HOPPET computer code [43], configured so that transitions from N f to N f+1 flavors occur at the \(\overline{\mathrm{MS}}\) masses.

  2. For example, m c (m c )=1.15 GeV translates into \(m_{c}^{\mathrm{pole}}=1.31, 1.54, 1.86~\mathrm{GeV}\) using one, two, three loops in the conversion formula with α s (M Z )=0.118.

  3. Starting from O(\(\alpha_{s}^{2}\)), contributions with up to four massive quarks in the final state can appear. In such terms, we still use \(\chi=x (1+4m_{c}^{2}/Q^{2} )\), given their smallness in the total result [29].

  4. A broadscale argument is also available that the probability distribution \(\mathcal{P}(m_{c})\propto \exp (-\chi^{2}(m_{c})/2 )\) on which the Δχ 2=1 criterion is based underestimates the confidence levels in PDF fits [83].

  5. Similar λ dependence is observed for the truncated conversion.

  6. The CT10 or MSTW-like tolerance criteria lead to about the same boundaries.

References

  1. W.-K. Tung, H.-L. Lai, A. Belyaev, J. Pumplin, D. Stump, C.-P. Yuan, J. High Energy Phys. 0702, 053 (2007). arXiv:hep-ph/0611254

    Article  ADS  Google Scholar 

  2. P.M. Nadolsky, H.-L. Lai, Q.-H. Cao, J. Huston, J. Pumplin, D. Stump, C.-P. Yuan, Phys. Rev. D 78, 013004 (2008). arXiv:0802.0007

    Article  ADS  Google Scholar 

  3. F. Aaron, et al. (H1 and ZEUS Collaboration), J. High Energy Phys. 1001, 109 (2010). arXiv:0911.0884

    Article  ADS  Google Scholar 

  4. H. Abramowicz et al. (H1 Collaboration ZEUS Collaboration), (2012). arXiv:1211.1182

  5. J. Sanchez Guillen, J. Miramontes, M. Miramontes, G. Parente, O. Sampayo, Nucl. Phys. B 353, 337 (1991)

    Article  ADS  Google Scholar 

  6. W. van Neerven, E. Zijlstra, Phys. Lett. B 272, 127 (1991)

    Article  ADS  Google Scholar 

  7. E. Zijlstra, W. van Neerven, Phys. Lett. B 273, 476 (1991)

    Article  ADS  Google Scholar 

  8. E. Laenen, S. Riemersma, J. Smith, W. van Neerven, Nucl. Phys. B 392, 162 (1993)

    Article  ADS  Google Scholar 

  9. S. Riemersma, J. Smith, W. van Neerven, Phys. Lett. B 347, 143 (1995). arXiv:hep-ph/9411431

    Article  ADS  Google Scholar 

  10. B. Harris, J. Smith, Nucl. Phys. B 452, 109 (1995). arXiv:hep-ph/9503484

    Article  ADS  Google Scholar 

  11. S. Moch, J. Vermaseren, A. Vogt, Phys. Lett. B 606, 123 (2005). arXiv:hep-ph/0411112

    Article  ADS  Google Scholar 

  12. J. Vermaseren, A. Vogt, S. Moch, Nucl. Phys. B 724, 3 (2005). arXiv:hep-ph/0504242

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. J. Blumlein, A. De Freitas, W. van Neerven, S. Klein, Nucl. Phys. B 755, 272 (2006). arXiv:hep-ph/0608024

    Article  ADS  Google Scholar 

  14. I. Bierenbaum, J. Blumlein, S. Klein, Nucl. Phys. B 820, 417 (2009). arXiv:0904.3563

    Article  ADS  MATH  Google Scholar 

  15. J. Ablinger, J. Blumlein, S. Klein, C. Schneider, F. Wissbrock, Nucl. Phys. B 844, 26 (2011). arXiv:1008.3347

    Article  ADS  MATH  Google Scholar 

  16. J. Blumlein, A. Hasselhuhn, S. Klein, C. Schneider, Nucl. Phys. B 866, 196 (2013). arXiv:1205.4184

    Article  ADS  Google Scholar 

  17. J. Ablinger, J. Blumlein, S. Klein, C. Schneider, F. Wissbrock, (2011). arXiv:1106.5937

  18. J. Ablinger, J. Blumlein, A. Hasselhuhn, S. Klein, C. Schneider et al., PoS RADCOR2011, 031 (2011). arXiv:1202.2700

  19. J. Ablinger, J. Blumlein, A. Hasselhuhn, S. Klein, C. Schneider et al., Nucl. Phys. B 864, 52 (2012). arXiv:1206.2252

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. J. Ablinger, J. Blumlein, A. De Freitas, A. Hasselhuhn, S. Klein et al., (2012). arXiv:1212.5950

  21. J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012)

    Article  ADS  Google Scholar 

  22. M. Aivazis, J.C. Collins, F.I. Olness, W.-K. Tung, Phys. Rev. D 50, 3102 (1994). arXiv:hep-ph/9312319

    Article  ADS  Google Scholar 

  23. M. Buza, Y. Matiounine, J. Smith, W. van Neerven, Eur. Phys. J. C 1, 301 (1998). arXiv:hep-ph/9612398

    ADS  Google Scholar 

  24. A. Chuvakin, J. Smith, W. van Neerven, Phys. Rev. D 61, 096004 (2000). arXiv:hep-ph/9910250

    Article  ADS  Google Scholar 

  25. R. Thorne, R. Roberts, Phys. Lett. B 421, 303 (1998). arXiv:hep-ph/9711223

    Article  ADS  Google Scholar 

  26. R. Thorne, R. Roberts, Phys. Rev. D 57, 6871 (1998). arXiv:hep-ph/9709442

    Article  ADS  Google Scholar 

  27. R. Thorne, Phys. Rev. D 73, 054019 (2006). arXiv:hep-ph/0601245

    Article  ADS  Google Scholar 

  28. S. Forte, E. Laenen, P. Nason, J. Rojo, Nucl. Phys. B 834, 116 (2010). arXiv:1001.2312

    Article  ADS  MATH  Google Scholar 

  29. M. Guzzi, P.M. Nadolsky, H.-L. Lai, C.-P. Yuan, Phys. Rev. D 86, 053005 (2012). arXiv:1108.5112

    Article  ADS  Google Scholar 

  30. M. Kramer, F.I. Olness, D.E. Soper, Phys. Rev. D 62, 096007 (2000). arXiv:hep-ph/0003035

    Article  ADS  Google Scholar 

  31. W.-K. Tung, S. Kretzer, C. Schmidt, J. Phys. G 28, 983 (2002). arXiv:hep-ph/0110247

    Article  ADS  Google Scholar 

  32. J. Gao, M. Guzzi, J. Huston, H.-L. Lai, Z. Li, P. Nadolsky, J. Pumplin, D. Stump, C.-P. Yuan, (2013). arXiv:1302.6246

  33. A. Martin, W. Stirling, R. Thorne, G. Watt, Eur. Phys. J. C 70, 51 (2010). arXiv:1007.2624

    Article  ADS  Google Scholar 

  34. S. Alekhin, J. Blumlein, K. Daum, K. Lipka, S. Moch, (2012). arXiv:1212.2355

  35. N. Gray, D.J. Broadhurst, W. Grafe, K. Schilcher, Z. Phys. C 48, 673 (1990)

    Article  ADS  Google Scholar 

  36. K. Chetyrkin, M. Steinhauser, Nucl. Phys. B 573, 617 (2000). arXiv:hep-ph/9911434

    Article  ADS  Google Scholar 

  37. K. Melnikov, T.v. Ritbergen, Phys. Lett. B 482, 99 (2000). arXiv:hep-ph/9912391

    Article  ADS  Google Scholar 

  38. P. Marquard, L. Mihaila, J. Piclum, M. Steinhauser, Nucl. Phys. B 773, 1 (2007). arXiv:hep-ph/0702185

    Article  ADS  MATH  Google Scholar 

  39. I.I. Bigi, M.A. Shifman, N. Uraltsev, A. Vainshtein, Phys. Rev. D 50, 2234 (1994). arXiv:hep-ph/9402360

    Article  ADS  Google Scholar 

  40. M. Beneke, V.M. Braun, Nucl. Phys. B 426, 301 (1994). arXiv:hep-ph/9402364

    Article  ADS  Google Scholar 

  41. M. Beneke, Phys. Rep. 317, 1 (1999). arXiv:hep-ph/9807443

    Article  ADS  Google Scholar 

  42. P.M. Nadolsky, W.-K. Tung, Phys. Rev. D 79, 113014 (2009). arXiv:0903.2667

    Article  ADS  Google Scholar 

  43. G.P. Salam, J. Rojo, Comput. Phys. Commun. 180, 120 (2009). arXiv:0804.3755

    Article  ADS  Google Scholar 

  44. K. Chetyrkin, J.H. Kuhn, M. Steinhauser, Comput. Phys. Commun. 133, 43 (2000). arXiv:hep-ph/0004189

    Article  ADS  MATH  Google Scholar 

  45. S. Alekhin, S. Moch, Phys. Lett. B 699, 345 (2011). arXiv:1011.5790

    Article  ADS  Google Scholar 

  46. J.C. Collins, Phys. Rev. D 58, 094002 (1998). arXiv:hep-ph/9806259

    Article  ADS  Google Scholar 

  47. A. Benvenuti et al. (BCDMS Collaboration), Phys. Lett. B 223, 485 (1989)

    Article  ADS  Google Scholar 

  48. A. Benvenuti et al. (BCDMS Collaboration), Phys. Lett. B 237, 592 (1990)

    Article  ADS  Google Scholar 

  49. M. Arneodo et al. (New Muon Collaboration), Nucl. Phys. B 483, 3 (1997). arXiv:hep-ph/9610231

    Article  ADS  Google Scholar 

  50. J. Berge, H. Burkhardt, F. Dydak, R. Hagelberg, M. Krasny et al., Z. Phys. C 49, 187 (1991)

    Article  Google Scholar 

  51. U.-K. Yang et al. (CCFR/NuTeV Collaboration), Phys. Rev. Lett. 86, 2742 (2001). arXiv:hep-ex/0009041

    Article  ADS  Google Scholar 

  52. W. Seligman, C. Arroyo, L. de Barbaro, P. de Barbaro, A. Bazarko et al., Phys. Rev. Lett. 79, 1213 (1997). arXiv:hep-ex/9701017

    Article  ADS  Google Scholar 

  53. M. Goncharov et al. (NuTeV Collaboration), Phys. Rev. D 64, 112006 (2001). arXiv:hep-ex/0102049

    Article  ADS  Google Scholar 

  54. D.A. Mason, Ph. D. Thesis FERMILAB-THESIS-2006-01 UMI-32-11223 (2006)

  55. C. Adloff et al. (H1 Collaboration), Phys. Lett. B 528, 199 (2002). arXiv:hep-ex/0108039

    Article  ADS  Google Scholar 

  56. G. Moreno, C. Brown, W. Cooper, D. Finley, Y. Hsiung et al., Phys. Rev. D 43, 2815 (1991)

    Article  ADS  Google Scholar 

  57. R. Towell et al. (FNAL E866/NuSea Collaboration), Phys. Rev. D 64, 052002 (2001). arXiv:hep-ex/0103030

    Article  ADS  Google Scholar 

  58. J. Webb et al. (NuSea Collaboration), (2003). arXiv:hep-ex/0302019

  59. F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 77, 2616 (1996)

    Article  ADS  Google Scholar 

  60. D. Acosta et al. (CDF Collaboration), Phys. Rev. D 71, 051104 (2005). arXiv:hep-ex/0501023

    Article  ADS  Google Scholar 

  61. V. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 101, 211801 (2008). arXiv:0807.3367

    Article  ADS  Google Scholar 

  62. V. Abazov et al. (D0 Collaboration), Phys. Rev. D 77, 011106 (2008). arXiv:0709.4254

    Article  ADS  Google Scholar 

  63. V. Abazov et al. (D0 Collaboration), Phys. Lett. B 658, 112 (2008). arXiv:hep-ex/0608052

    Article  ADS  Google Scholar 

  64. T.A. Aaltonen et al. (CDF Collaboration), Phys. Lett. B 692, 232 (2010). arXiv:0908.3914

    Article  ADS  Google Scholar 

  65. T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D 78, 052006 (2008). arXiv:0807.2204

    Article  ADS  Google Scholar 

  66. V. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 101, 062001 (2008). arXiv:0802.2400

    Article  ADS  Google Scholar 

  67. G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 85, 072004 (2012). arXiv:1109.5141

    Article  ADS  Google Scholar 

  68. G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 86, 014022 (2012). arXiv:1112.6297

    Article  ADS  Google Scholar 

  69. F. Aaron et al. (H1 Collaboration), Eur. Phys. J. C 71, 1579 (2011). arXiv:1012.4355

    Article  ADS  Google Scholar 

  70. B. Harris, J. Smith, Phys. Rev. D 57, 2806 (1998). arXiv:hep-ph/9706334

    Article  ADS  Google Scholar 

  71. S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 63, 171 (2009). arXiv:0812.3775

    Article  ADS  Google Scholar 

  72. S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 65, 65 (2010). arXiv:0904.3487

    Article  ADS  Google Scholar 

  73. F. Aaron et al. (H1 Collaboration), Eur. Phys. J. C 65, 89 (2010). arXiv:0907.2643

    Article  ADS  Google Scholar 

  74. F. Aaron et al. (H1 Collaboration), Phys. Lett. B 686, 91 (2010). arXiv:0911.3989

    Article  ADS  Google Scholar 

  75. A. Aktas et al. (H1 Collaboration), Eur. Phys. J. C 51, 271 (2007). arXiv:hep-ex/0701023

    Article  ADS  Google Scholar 

  76. J. Breitweg et al. (ZEUS Collaboration), Eur. Phys. J. C 12, 35 (2000). arXiv:hep-ex/9908012

    Article  ADS  Google Scholar 

  77. S. Chekanov et al. (ZEUS Collaboration), Phys. Rev. D 69, 012004 (2004). arXiv:hep-ex/0308068

    Article  ADS  Google Scholar 

  78. F. Aaron et al. (H1 Collaboration), Eur. Phys. J. C 71, 1769 (2011). arXiv:1106.1028

    Article  ADS  Google Scholar 

  79. J. Pumplin, D. Stump, J. Huston, H.-L. Lai, P.M. Nadolsky, W.-K. Tung, J. High Energy Phys. 0207, 012 (2002). arXiv:hep-ph/0201195

    Article  ADS  Google Scholar 

  80. H.-L. Lai, M. Guzzi, J. Huston, Z. Li, P.M. Nadolsky, J. Pumplin, C.-P. Yuan, Phys. Rev. D 82, 074024 (2010). arXiv:1007.2241

    Article  ADS  Google Scholar 

  81. J.C. Collins, J. Pumplin, (2001). arXiv:hep-ph/0105207

  82. P. Bevington, D.K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 2002)

    Google Scholar 

  83. R.D. Ball, V. Bertone, F. Cerutti, L. Del Debbio, S. Forte et al., Nucl. Phys. B 855, 608 (2012). arXiv:1108.1758

    Article  ADS  Google Scholar 

  84. J. Pumplin, Phys. Rev. D 80, 034002 (2009). arXiv:0904.2425

    Article  ADS  Google Scholar 

  85. J. Pumplin, Phys. Rev. D 81, 074010 (2010). arXiv:0909.0268

    Article  ADS  Google Scholar 

  86. R.D. Ball, S. Carrazza, L. Del Debbio, S. Forte, J. Gao et al., (2012). arXiv:1211.5142

  87. R. Gavin, Y. Li, F. Petriello, S. Quackenbush, Comput. Phys. Commun. 182, 2388 (2011). arXiv:1011.3540

    Article  ADS  Google Scholar 

  88. R. Gavin, Y. Li, F. Petriello, S. Quackenbush, (2012). arXiv:1201.5896

  89. C. Anastasiou, S. Buehler, F. Herzog, A. Lazopoulos, J. High Energy Phys. 1112, 058 (2011). arXiv:1107.0683

    Article  ADS  Google Scholar 

  90. P. Baernreuther, M. Czakon, A. Mitov, Phys. Rev. Lett. 109, 132001 (2012). arXiv:1204.5201

    Article  ADS  Google Scholar 

  91. M. Czakon, P. Fiedler, A. Mitov, (2013). arXiv:1303.6254

  92. H.-L. Lai, J. Huston, Z. Li, P. Nadolsky, J. Pumplin, D. Stump, C.-P. Yuan, Phys. Rev. D 82, 054021 (2010). arXiv:1004.4624

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the U.S. DOE Early Career Research Award DE-SC0003870 by Lightner-Sams Foundation. We thank Achim Geiser for the critical reading of the manuscript and appreciate detailed discussions with Karin Daum, Joey Huston, Hung-Liang Lai, Katerina Lipka, Fred Olness, Jon Pumplin, Carl Schmidt, Dan Stump, and C.-P. Yuan. P.N. thanks DESY (Hamburg) for hospitality and financial support of his visit during the work on this project.

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  1. Department of Physics, Southern Methodist University, Dallas, TX, 75275-0181, USA

    Jun Gao & Pavel Nadolsky

  2. Deutsches Elektronen Synchrotron DESY, Notkestrasse 85, 22607, Hamburg, Germany

    Marco Guzzi

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  1. Jun Gao
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Correspondence to Jun Gao.

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Gao, J., Guzzi, M. & Nadolsky, P. Charm quark mass dependence in a global QCD analysis. Eur. Phys. J. C 73, 2541 (2013). https://doi.org/10.1140/epjc/s10052-013-2541-4

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