Electroweak two-loop corrections to sin 2θ eff bb and R b using numerical Mellin-Barnes integrals

Journal of High Energy Physics

Volumn 2012, Issue 8, 2012, Pages

  Freitas, Ayres ^a   Huang, Yi Cheng ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Electromagnetic Processes and Properties; LEP HERA and SLC Physics; Standard Model

Indexed keywords

EID: 84865202411     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP08(2012)050     Document Type: Article

References (59)

1. A. Freitas, W. Hollik, W. Walter and G. Weiglein, Complete fermionic two loop results for the M(W)-M(Z) interdependence, Phys. Lett. B 495 (2000) 338 Erratum ibid. B 570 (2003) 260-264 hep-ph/0007091.
2. M. Awramik and M. Czakon, Complete two loop bosonic contributions to the muon lifetime in the standard model, Phys. Rev. Lett. 89 (2002) 241801 hep-ph/0208113.
3. A. Onishchenko and O. Veretin, Two loop bosonic electroweak corrections to the muon lifetime and M(Z)-M(W) interdependence, Phys. Lett. B 551 (2003) 111 hep-ph/0209010.
4. M. Awramik, M. Czakon, A. Onishchenko and O. Veretin, Bosonic corrections to Δr at the two loop level, Phys. Rev. D 68 (2003) 053004 hep-ph/0209084.
5. M. Awramik and M. Czakon, Complete two loop electroweak contributions to the muon lifetime in the standard model, Phys. Lett. B 568 (2003) 48 hep-ph/0305248.
6. A. Freitas, W. Hollik, W. Walter and G. Weiglein, Electroweak two-loop corrections to the M(W)-M(Z) mass correlation in the standard model, Nucl. Phys. B 632 (2002) 189 Erratum ibid. B 666 (2003) 305.
7. M. Awramik, M. Czakon, A. Freitas and G. Weiglein, Precise prediction for the W boson mass in the standard model, Phys. Rev. D 69 (2004) 053006 hep-ph/0311148.
8. pt and indirect determination of the Higgs boson mass, Phys. Rev. Lett. 93 (2004) 201805 hep-ph/0407317.
9. 2), Phys. Lett. B 642 (2006) 563 hep-ph/0605339.
10. M. Awramik, M. Czakon and A. Freitas, Electroweak two-loop corrections to the effective weak mixing angle, JHEP 11 (2006) 048 hep-ph/0608099.
11. eff with two-loop fermionic contributions, Nucl. Phys. B 731 (2005) 213 hep-ph/0507158.
12. eff with two-loop bosonic contributions, Nucl. Phys. B 765 (2007) 154 hep-ph/0610312.
13. s, Nucl. Phys. B 813 (2009) 174 arXiv: 0811.1364.
14. J. van der Bij, K. Chetyrkin, M. Faisst, G. Jikia and T. Seidensticker, Three loop leading top mass contributions to the ρ parameter, Phys. Lett. B 498 (2001) 156 hep-ph/0011373.
15. M. Faisst, J.H. Kühn, T. Seidensticker and O. Veretin, Three loop top quark contributions to the ρ parameter, Nucl. Phys. B 665 (2003) 649 hep-ph/0302275.
16. R. Boughezal, J. Tausk and J. van der Bij, Three-loop electroweak correction to the ρ parameter in the large Higgs mass limit, Nucl. Phys. B 713 (2005) 278 hep-ph/0410216.
17. pt in the large Higgs mass limit, Nucl. Phys. B 725 (2005) 3 hep-ph/0504092.
18. s) correction to the electroweak rho parameter, Phys. Lett. B 336 (1994) 560 Erratum ibid. B 349 (1995) 597-598 hep-ph/9406363.
19. s) to the ρ parameter, Phys. Lett. B 351 (1995) 331 hep-ph/9502291.
20. 2, Phys. Rev. Lett. 75 (1995) 3394 hep-ph/9504413.
21. 2) corrections to the production of heavy quarks, Nucl. Phys. B 482 (1996) 213 hep-ph/9606230.
22. Y. Schr̈oder and M. Steinhauser, Four-loop singlet contribution to the ρ parameter, Phys. Lett. B 622 (2005) 124 hep-ph/0504055.
23. K. Chetyrkin, M. Faisst, J.H. Kuhn, P. Maierhofer and C. Sturm, Four-loop QCD corrections to the ρ parameter, Phys. Rev. Lett. 97 (2006) 102003 hep-ph/0605201.
24. s) corrections to the ρ parameter, Nucl. Phys. B 755 (2006) 221 hep-ph/0606232.
25. A. Arbuzov et al., ZFITTER: a semi-analytical program for fermion pair production in e+e~ annihilation, from version 6.21 to version 642, Comput. Phys. Commun. 174 (2006) 728 hep-ph/0507146.
26. H. Fl̈acher et al., Revisiting the global electroweak fit of the standard model and beyond with Gfitter, Eur. Phys. J. C 60 (2009) 543 Erratum ibid. C 71 (2011) 1718 arXiv: 0811.0009.
27. C. Anastasiou and A. Daleo, Numerical evaluation of loop integrals, JHEP 10 (2006) 031 hep-ph/0511176.
28. M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559 hep-ph/0511200.
29. J. Gluza, K. Kajda, T. Riemann and V. Yundin, Numerical evaluation of tensor Feynman integrals in euclidean kinematics, Eur. Phys. J. C 71 (2011) 1516 arXiv: 1010.1667.
30. A. Freitas and Y.-C. Huang, On the numerical evaluation of loop integrals with Mellin-Barnes representations, JHEP 04 (2010) 074 arXiv: 1001.3243.
31. G. Degrassi and P. Gambino, Two loop heavy top corrections to the Z0 boson partial widths, Nucl. Phys. B 567 (2000) 3 hep-ph/9905472.
32. R. Barbieri, M. Beccaria, P. Ciafaloni, G. Curci and A. Vicere, Radiative correction effects of a very heavy top, Phys. Lett. B 288 (1992) 95 Erratum ibid. B 312 (1993) 511 hep-ph/9205238.
33. R. Barbieri, M. Beccaria, P. Ciafaloni, G. Curci and A. Vicere, Two loop heavy top effects in the standard model, Nucl. Phys. B 409 (1993) 105.
34. J. Fleischer, O. Tarasov and F. Jegerlehner, Two loop heavy top corrections to the ρ parameter: a simple formula valid for arbitrary Higgs mass, Phys. Lett. B 319 (1993) 249.
35. J. Fleischer, O. Tarasov and F. Jegerlehner, Two loop large top mass corrections to electroweak parameters: analytic results valid for arbitrary Higgs mass, Phys. Rev. D 51 (1995) 3820.
36. K. Chetyrkin and F. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159.
37. T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 hep-ph/9912329.
38. S. Bauberger, F.A. Berends, M. B̈ohm and M. Buza, Analytical and numerical methods for massive two loop selfenergy diagrams, Nucl. Phys. B 434 (1995) 383 hep-ph/9409388.
39. S. Bauberger and M. B̈ohm, Simple one-dimensional integral representations for two loop self energies: the master diagram, Nucl. Phys. B 445 (1995) 25 hep-ph/9501201.
40. tot(e+e-+ hadrons) in quantum chromodynamics, Phys. Lett. B 85 (1979) 277.
41. M. Dine and J. Sapirstein, Higher order QCD corrections in e+e-annihilation, Phys. Rev. Lett. 43 (1979) 668.
42. W. Celmaster and R.J. Gonsalves, An analytic calculation of higher order quantum chromodynamic corrections in e+e-annihilation, Phys. Rev. Lett. 44 (1980) 560.
43. S, Phys. Lett. B 212 (1988) 238.
44. K. Chetyrkin and J.H. Kühn, Mass corrections to the Z decay rate, Phys. Lett. B 248 (1990) 359.
45. tot(e+e-hadrons) and Γ(τ-+ τ-neutrino + hadrons) in QCD, Phys. Lett. B 259 (1991) 144.
46. L.R. Surguladze and M.A. Samuel, Total hadronic cross-section in e+e-annihilation at the four loop level of perturbative QCD, Phys. Rev. Lett. 66 (1991) 560 Erratum ibid. 66 (1991) 2416.
47. tot(e+e-hadron) and Z boson decay rate, Phys. Lett. B 287 (1992) 209.
48. K. Chetyrkin, Power suppressed heavy quark mass corrections to the τ lepton and Z boson decay rates, Phys. Lett. B 307 (1993) 169.
49. K.G. Chetyrkin, J. Kühn and A. Kwiatkowski, QCD corrections to the e+e-cross-section and the Z boson decay rate, in Reports of the working group on precision calculations for the Z resonance, D. Bardin, W. Hollik and G. Passarino eds., CERN, Geneva, Switzerland (1995), CERN-95-03.
50. D.Y. Bardin et al., ZFITTER v.6.21: a semianalytical program for fermion pair production ine+e-annihilation, Comput. Phys. Commun. 133 (2001) 229 hep-ph/9908433.
51. Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021.
52. -1 of data, arXiv: 1107.5255.
53. H. Burkhardt and B. Pietrzyk, Recent BES measurements and the hadronic contribution to the QED vacuum polarization, Phys. Rev. D 84 (2011) 037502 arXiv: 1106.2991.
54. D.Yu. Bardin, A. Leike, T. Riemann and M. Sachwitz, Energy dependent width effects in e+e-annihilation near the Z pole, Phys. Lett. B 206 (1988) 539.
55. A. Djouadi and C. Verzegnassi, Virtual very heavy top effects in LEP/SLC precision measurements, Phys. Lett. B 195 (1987) 265.
56. s) vacuum polarization functions of the standard model gauge bosons, Nuovo Cim. A 100 (1988) 357.
57. B.A. Kniehl, Two loop corrections to the vacuum polarizations in perturbative QCD, Nucl. Phys. B 347 (1990) 86.
58. B.A. Kniehl and A. Sirlin, Dispersion relations for vacuum polarization functions in electroweak physics, Nucl. Phys. B 371 (1992) 141.
59. A. Djouadi and P. Gambino, Electroweak gauge bosons selfenergies: complete QCD corrections, Phys. Rev. D 49 (1994) 3499 Erratum ibid. D 53 (1996) 4111 hep-ph/9309298.