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Analytic results for \(e^ + e^ - \to \overline {tt} \) and \(\gamma \gamma \to \overline {tt} \) observables near the threshold up to the next-to-next-to-leading order of NRQCD

  • Elementary Particles and Fields
  • Theory
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Abstract

We present an analytic description of top-antitop pair production near the threshold in e + e − annihilation and γγ collisions. A set of basic observables being considered includes total cross sections, forward-backward asymmetry, and top-quark polarization. Threshold effects relevant to the basic observables are described by three universal functions related to S-wave production, P-wave production, and S-P interference. These functions are computed analytically up to the next-to-next-to-leading order of NRQCD. The total \(e^ + e^ - \to \overline {tt} \) cross section near the threshold is obtained in the next-to-next-to-leading order in a closed form including the contribution originating from the axial coupling of top quarks that is mediated by the Z boson. The effects of the running of the strong coupling constant and the finite top-quark width are taken into account analytically for the P-wave production and S-P wave interference.

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References

  1. V. S. Fadin and V. A. Khoze, Pis'ma Zh. Éksp. Teor. Fiz. 46, 417 (1987) [JETP Lett. 46, 525 (1987)]; Yad. Fiz. 48, 487 (1988) [Sov. J. Nucl. Phys. 48, 309 (1988)].

    Google Scholar 

  2. V. S. Fadin and V. A. Khoze, Yad. Fiz. 53, 1118 (1991) [Sov. J. Nucl. Phys. 53, 692 (1991)]; I. I. Bigi, V. S. Fadin, and V. A. Khoze, Nucl. Phys. B 377, 461 (1992); I. I. Bigi, F. Gabbiani, and V. A. Khoze, Nucl. Phys. B 406, 3 (1993); J. H. Kühn, E. Mirkes, and J. Steegborn, Z. Phys. C 57, 615 (1993).

    Google Scholar 

  3. W. Kwong, Phys. Rev. D 43, 1488 (1991); M. J. Strassler and M. E. Peskin, Phys. Rev. D 43, 1500 (1991); M. Jezabek, J. H. Kühh, and T. Teubner, Z. Phys. C 56, 653 (1992); Y. Sumino et al., Phys. Rev. D 47, 56 (1993).

    Article  ADS  Google Scholar 

  4. E. Accomando et al., Phys. Rep. 299, 1 (1998).

    Article  ADS  Google Scholar 

  5. H. Murayama and Y. Sumino, Phys. Rev. D 47, 82 (1993).

    Article  ADS  Google Scholar 

  6. R. Harlander et al., Phys. Lett. B 346, 137 (1995).

    ADS  Google Scholar 

  7. V. S. Fadin, V. A. Khoze, and M. I. Kotsky, Z. Phys. C 64, 45 (1994).

    Article  Google Scholar 

  8. W. E. Caswell and G. E. Lepage, Phys. Lett. B 167, 437 (1986); G. E. Lepage et al., Phys. Rev. D 46, 4052 (1992); G. T. Bodwin, E. Braaten, and G. E. Lepage, Phys. Rev. D 51, 1125 (1995).

    ADS  Google Scholar 

  9. A. V. Manohar, Phys. Rev. D 56, 230 (1997).

    Article  ADS  Google Scholar 

  10. M. Luke and A. V. Manohar, Phys. Rev. D 55, 4129 (1997).

    Article  ADS  Google Scholar 

  11. B. Grinstein and I. Z. Rothstein, Phys. Rev. D 57, 78 (1998).

    ADS  Google Scholar 

  12. M. Luke and M. J. Savage, Phys. Rev. D 57, 413 (1998).

    Article  ADS  Google Scholar 

  13. A. Pineda and J. Soto, Nucl. Phys. B (Proc. Suppl.) 64, 428 (1998).

    Article  ADS  Google Scholar 

  14. M. Beneke and V. A. Smirnov, Nucl. Phys. B 522, 321 (1998).

    Article  ADS  Google Scholar 

  15. P. Labelle, Phys. Rev. D 58, 093013 (1998).

    Google Scholar 

  16. H. W. Griesshammer, Preprint No. UW-98-22 (1998).

  17. A. H. Hoang, Phys. Rev. D 56, 5851 (1997).

    ADS  Google Scholar 

  18. J. H. Kühn, A. A. Penin, and A. A. Pivovarov, Nucl. Phys. B 534, 356 (1998).

    ADS  Google Scholar 

  19. A. A. Penin and A. A. Pivovarov, Phys. Lett. B 435, 413 (1998).

    ADS  Google Scholar 

  20. K. Melnikov and A. Yelkhovsky, Phys. Rev. D 59, 114009 (1999).

    Google Scholar 

  21. A. A. Penin and A. A. Pivovarov, Nucl. Phys. B 549, 217 (1999).

    Article  ADS  Google Scholar 

  22. M. Beneke, A. Singer, and V. A. Smirnov, Phys. Lett. B 454, 137 (1999).

    ADS  Google Scholar 

  23. M. Beneke and A. Singer, Preprint No. CERN-TH/99-163 (1999).

  24. A. H. Hoang, Preprint No. CERN-TH/99-152 (1999).

  25. B. A. Kniehl and A. A. Penin, Preprint No. DESY/99-099 (1999).

  26. A. H. Hoang and T. Teubner, Phys. Rev. D 58, 114023 (1998).

    Google Scholar 

  27. K. Melnikov and A. Yelkhovsky, Nucl. Phys. B 528, 59 (1998).

    Article  ADS  Google Scholar 

  28. J. H. Kühn and T. Teubner, Eur. Phys. J. C 9, 221 (1999).

    ADS  Google Scholar 

  29. T. Nagano, A. Ota, and Y. Sumino, Preprint No. TU-562 (1999).

  30. A. H. Hoang and T. Teubner, Preprint No. CERNTH/99-59 (1999).

  31. A. A. Penin and A. A. Pivovarov, Nucl. Phys. B 550, 375 (1999).

    Article  ADS  Google Scholar 

  32. A. Czarnecky and K. Melnikov, Phys. Rev. Lett. 80, 2531 (1998).

    ADS  Google Scholar 

  33. M. Beneke, A. Signer, and V. A. Smirnov, Phys. Rev. Lett. 80, 2535 (1998).

    Article  ADS  Google Scholar 

  34. A. Pineda and J. Soto, Phys. Lett. B 420, 391 (1998); Phys. Rev. D 59, 016005 (1999).

    MathSciNet  ADS  Google Scholar 

  35. A. Czarnecky, K. Melnikov, and A. Yelkhovsky, Preprint No. BNL-HET-98/44 (1999).

  36. J. H. Kühn, Preprint No. TTP-96-18 (Karlsruhe Univ., 1996); hep-ph/9707321.

  37. R. Karplus and A. Klein, Phys. Rev. 87, 848 (1952); G. Källen and A. Sarby, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 29 (17), 1 (1955); R. Barbieri et al., Phys. Lett. B 57, 535 (1975).

    Article  ADS  Google Scholar 

  38. L. J. Reinders, H. R. Rubinstein, and S. Yazaki, Nucl. Phys. B 181, 109 (1981); J. Jérzak, E. Laemann, and P. M. Zerwas, Phys. Rev. D 25, 1218 (1982).

    ADS  Google Scholar 

  39. I. Harris and L. M. Brown, Phys. Rev. 105, 1656 (1957); R. Barbieri et al., Nucl. Phys. B 154, 535 (1979).

    ADS  Google Scholar 

  40. R. Barbieri et al., Nucl. Phys. B 192, 61 (1981); J. H. Kühn and P. M. Zerwas, Phys. Rep. 167, 321 (1988).

    Article  ADS  Google Scholar 

  41. A. A. Pivovarov, Phys. Rev. D 47, 5183 (1993).

    Article  ADS  Google Scholar 

  42. B. Grzadkowski et al., Nucl. Phys. B 281, 18 (1987); R. J. Guth and J. H. Kühn, Nucl. Phys. B 368, 38 (1992); W. Beenakker et al., Nucl. Phys. B 365, 24 (1991).

    Article  ADS  Google Scholar 

  43. A. Denner, S. Dittmaier, and M. Strobel, Phys. Rev. D 53, 44 (1996).

    Article  ADS  Google Scholar 

  44. B. M. Chibisov and M. V. Voloshin, Mod. Phys. Lett. A 13, 973 (1998).

    ADS  Google Scholar 

  45. V. S. Fadin, V. A. Khoze, and A. D. Martin, Phys. Rev. D 49, 2247 (1994); K. Melnikov and O. Yakovlev, Phys. Lett. B 324, 217 (1994).

    Article  ADS  Google Scholar 

  46. K. Fujii, T. Matsui, and Y. Sumino, Phys. Rev. D 50, 4341 (1994); R. Harlander et al., Z. Phys. C 73, 477 (1997); M. Peter and Y. Sumino, Phys. Rev. D 57, 6912 (1998).

    Article  ADS  Google Scholar 

  47. S. N. Gupta and S. F. Radford, Phys. Rev. D 24, 2309 (1981); Erratum: 25, 3430 (1982); S. N. Gupta, S. F. Radford, and W. W. Repko, Phys. Rev. D 26, 3305 (1982).

    ADS  Google Scholar 

  48. L. D. Landau and E. M. Lifshitz, Relativistic Quantum Theory (Nauka, Moscow, 1968; Pergamon, Oxford, 1974), Part 1.

    Google Scholar 

  49. W. Fisher, Nucl. Phys. B 129, 157 (1977); A. Billoire, Phys. Lett. B 92, 343 (1980).

    ADS  Google Scholar 

  50. M. Peter, Phys. Rev. Lett. 78, 602 (1997); Nucl. Phys. B 501, 471 (1997); Y. Schröder, Phys. Lett. B 447, 321 (1999).

    Article  ADS  Google Scholar 

  51. A. H. Hoang, Phys. Rev. D 56, 7276 (1997).

    ADS  Google Scholar 

  52. K. A. Ispiryan et al., Yad. Fiz. 11, 1278 (1970) [Sov. J. Nucl. Phys. 11, 712 (1970)].

    Google Scholar 

  53. A. Pineda and F. J. Yndurain, Phys. Rev. D 58, 094022 (1998).

    Google Scholar 

  54. M. Beneke and V. M. Braun, Nucl. Phys. B 426, 301 (1994); I. I. Bigi et al., Phys. Rev. D 50, 2234 (1994).

    Article  ADS  Google Scholar 

  55. M. B. Voloshin, Nucl. Phys. B 154, 365 (1979); H. Leutwyler, Phys. Lett. B 98, 447 (1981).

    Article  ADS  Google Scholar 

  56. O. Yakovlev, Phys. Lett. B 457, 170 (1999).

    ADS  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Teilchenphysik, Universität Karlsruhe, D-76128, Karlsruhe, Germany

    A. A. Penin

  2. Institut für Physik, Johannes-Gutenberg-Universität, D-55099, Mainz, Germany

    A. A. Pivovarov

Authors
  1. A. A. Penin
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  2. A. A. Pivovarov
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Additional information

From Yadernaya Fizika, Vol. 64, No. 2, 2001, pp. 323–341.

Original English Text Copyright © 2001 by Penin, Pivovarov.

This article was submitted by authors in English.

on leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, pr. Shestidesyatiletiya Oktyabrya 7a, Moscow, 117312 Russia.

on leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, pr. Shestidesyatiletiya Oktyabrya 7a, Moscow, 117312 Russia.

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Penin, A.A., Pivovarov, A.A. Analytic results for \(e^ + e^ - \to \overline {tt} \) and \(\gamma \gamma \to \overline {tt} \) observables near the threshold up to the next-to-next-to-leading order of NRQCD. Phys. Atom. Nuclei 64, 275–293 (2001). https://doi.org/10.1134/1.1349450

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  • DOI: https://doi.org/10.1134/1.1349450

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