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Erratum to: “Electroweak two-loop corrections to the MW–MZ mass correlation in the Standard Model”
Nuclear Physics B 666 (2003) 305–307 www.elsevier.com/locate/npe
Erratum
Erratum to: “Electroweak two-loop corrections to the MW –MZ mass correlation in the Standard Model” [Nucl. Phys. B 632 (2002) 189–218] ✩ A. Freitas a , W. Hollik b,c , W. Walter b , G. Weiglein d a DESY Theorie, Notkestr. 85, D-22603 Hamburg, Germany b Institut für Theoretische Physik, Universität Karlsruhe, D-76128 Karlsruhe, Germany c Max-Planck-Institut für Physik, Föhringer Ring 6, D-80805 München, Germany d IPPP, University of Durham, Durham DH1 3LE, United Kingdom
Received 23 May 2003
PACS: 13.10.+q; 14.70.Fm; 14.80.Bu
We correct an error in the numerical evaluation of a specific vacuum-type integral, which slightly affects our prediction for the W-boson mass by about 1 MeV. As a consequence the values in Tables 1, 2 and 3 should read as given here. In Eq. (62) the 0 = 80.3755 GeV, whereas the first entry in Eq. (64) should read first entry should be MW 0 = 80.3756 GeV. MW We furthermore correct a bug in our computer programs concerning the algebraic treatment of two-loop box diagrams, which affects the Higgs-mass dependence of the bosonic two-loop contributions in Section 7 by up to 0.3 MeV. See Table 4 and Fig. 11 for the correct values. After correcting these errors, there is now perfect agreement between the Higgs-mass dependence of the bosonic two-loop corrections and full result in [1] and between the fermionic corrections and the independent result of [2]. Acknowledgements We are grateful to M. Awramik and M. Czakon for detailed comparisons with their results, which lead to the identification of the errors reported above. ✩
PII of original article: S0550-3213(02)00243-2. E-mail address: [email protected] (A. Freitas).
0550-3213/$ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0550-3213(03)00500-5
306
A. Freitas et al. / Nuclear Physics B 666 (2003) 305–307
Table 1 Two-loop contributions with one closed fermion loop to r for different values of the Higgs mass. Besides the full 2 2 result, r (Nf α ) , also the contributions from the top-bottom doublet, r (Ntb α ) , and the light-fermion doublets, 2 r (Nlf α ) , are given. From the latter the term proportional to α originating from resummation is subtracted
MH /GeV 65 100 300 600 1000
2 r (Nf α ) /10−4
2 r (Ntb α ) /10−4
20.1 20.8 23.3 24.9 24.5
15.7 14.7 11.7 8.9 5.1
2 (α) r (Nlf α ) − 2αrbos /10−4
2.0 2.2 3.1 3.9 4.6
Table 2 The two-loop result for MW based on Eq. (56) in our paper is compared with the results of an expansion in mt expa up to O(G2µ m2t MZ2 ) by Degrassi et al., MW . The last column indicates the difference between the two results expa
MH /GeV
MW /GeV
MW /GeV
MW /MeV
65 100 300 600 1000
80.3985 80.3759 80.3039 80.2509 80.2122
80.4039 80.3805 80.3061 80.2521 80.2129
−5.4 −4.6 −2.2 −1.2 −0.7
Table 3 Investigation of different sources of deviations between the two-loop result for MW based on Eq. (56) in our paper expa ), differences in the QCD implementation and the results of Degrassi et al., MW . In the second column (MW ), in addition and in the resummation of bosonic one-loop terms have been eliminated. In the third column (MW the two-loop contributions from light fermions are excluded MH /GeV
/MeV MW
/MeV MW
65 100 300 600 1000
−5.4 −4.9 −4.0 −4.3 −5.0
−2.3 −1.6 0.0 0.5 0.5
Table 4 Shift in the predicted W mass caused by varying Higgs-boson mass MH when including fermionic two-loop ferm ) and all two-loop corrections (M ferm+bos ). M corrections (MW,sub W,sub gives the difference between these W,sub two contributions, i.e., the effect of the bosonic loops MH /GeV
ferm /MeV MW,sub
ferm+bos MW,sub /MeV
100 200 400 600 1000
0 −43.1 −93.7 −124.7 −163.4
0 −42.6 −93.0 −123.8 −161.7
MW,sub /MeV 0 0.5 0.8 1.0 1.7
A. Freitas et al. / Nuclear Physics B 666 (2003) 305–307
307
Fig. 11. Variation of the Higgs-mass dependence of the MW -prediction due to the inclusion of bosonic two-loop corrections.
References [1] M. Awramik, M. Czakon, Phys. Rev. Lett. 89 (2002) 241801, hep-ph/0208113; A. Onishchenko, O. Veretin, Phys. Lett. B 551 (2003) 111, hep-ph/0209010; M. Awramik, M. Czakon, A. Onishchenko, O. Veretin, hep-ph/0209084. [2] M. Awramik, M. Czakon, hep-ph/0305248.
Erratum
Erratum to: “Electroweak two-loop corrections to the MW –MZ mass correlation in the Standard Model” [Nucl. Phys. B 632 (2002) 189–218] ✩ A. Freitas a , W. Hollik b,c , W. Walter b , G. Weiglein d a DESY Theorie, Notkestr. 85, D-22603 Hamburg, Germany b Institut für Theoretische Physik, Universität Karlsruhe, D-76128 Karlsruhe, Germany c Max-Planck-Institut für Physik, Föhringer Ring 6, D-80805 München, Germany d IPPP, University of Durham, Durham DH1 3LE, United Kingdom
Received 23 May 2003
PACS: 13.10.+q; 14.70.Fm; 14.80.Bu
We correct an error in the numerical evaluation of a specific vacuum-type integral, which slightly affects our prediction for the W-boson mass by about 1 MeV. As a consequence the values in Tables 1, 2 and 3 should read as given here. In Eq. (62) the 0 = 80.3755 GeV, whereas the first entry in Eq. (64) should read first entry should be MW 0 = 80.3756 GeV. MW We furthermore correct a bug in our computer programs concerning the algebraic treatment of two-loop box diagrams, which affects the Higgs-mass dependence of the bosonic two-loop contributions in Section 7 by up to 0.3 MeV. See Table 4 and Fig. 11 for the correct values. After correcting these errors, there is now perfect agreement between the Higgs-mass dependence of the bosonic two-loop corrections and full result in [1] and between the fermionic corrections and the independent result of [2]. Acknowledgements We are grateful to M. Awramik and M. Czakon for detailed comparisons with their results, which lead to the identification of the errors reported above. ✩
PII of original article: S0550-3213(02)00243-2. E-mail address: [email protected] (A. Freitas).
0550-3213/$ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0550-3213(03)00500-5
306
A. Freitas et al. / Nuclear Physics B 666 (2003) 305–307
Table 1 Two-loop contributions with one closed fermion loop to r for different values of the Higgs mass. Besides the full 2 2 result, r (Nf α ) , also the contributions from the top-bottom doublet, r (Ntb α ) , and the light-fermion doublets, 2 r (Nlf α ) , are given. From the latter the term proportional to α originating from resummation is subtracted
MH /GeV 65 100 300 600 1000
2 r (Nf α ) /10−4
2 r (Ntb α ) /10−4
20.1 20.8 23.3 24.9 24.5
15.7 14.7 11.7 8.9 5.1
2 (α) r (Nlf α ) − 2αrbos /10−4
2.0 2.2 3.1 3.9 4.6
Table 2 The two-loop result for MW based on Eq. (56) in our paper is compared with the results of an expansion in mt expa up to O(G2µ m2t MZ2 ) by Degrassi et al., MW . The last column indicates the difference between the two results expa
MH /GeV
MW /GeV
MW /GeV
MW /MeV
65 100 300 600 1000
80.3985 80.3759 80.3039 80.2509 80.2122
80.4039 80.3805 80.3061 80.2521 80.2129
−5.4 −4.6 −2.2 −1.2 −0.7
Table 3 Investigation of different sources of deviations between the two-loop result for MW based on Eq. (56) in our paper expa ), differences in the QCD implementation and the results of Degrassi et al., MW . In the second column (MW ), in addition and in the resummation of bosonic one-loop terms have been eliminated. In the third column (MW the two-loop contributions from light fermions are excluded MH /GeV
/MeV MW
/MeV MW
65 100 300 600 1000
−5.4 −4.9 −4.0 −4.3 −5.0
−2.3 −1.6 0.0 0.5 0.5
Table 4 Shift in the predicted W mass caused by varying Higgs-boson mass MH when including fermionic two-loop ferm ) and all two-loop corrections (M ferm+bos ). M corrections (MW,sub W,sub gives the difference between these W,sub two contributions, i.e., the effect of the bosonic loops MH /GeV
ferm /MeV MW,sub
ferm+bos MW,sub /MeV
100 200 400 600 1000
0 −43.1 −93.7 −124.7 −163.4
0 −42.6 −93.0 −123.8 −161.7
MW,sub /MeV 0 0.5 0.8 1.0 1.7
A. Freitas et al. / Nuclear Physics B 666 (2003) 305–307
307
Fig. 11. Variation of the Higgs-mass dependence of the MW -prediction due to the inclusion of bosonic two-loop corrections.
References [1] M. Awramik, M. Czakon, Phys. Rev. Lett. 89 (2002) 241801, hep-ph/0208113; A. Onishchenko, O. Veretin, Phys. Lett. B 551 (2003) 111, hep-ph/0209010; M. Awramik, M. Czakon, A. Onishchenko, O. Veretin, hep-ph/0209084. [2] M. Awramik, M. Czakon, hep-ph/0305248.