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Erratum to “Z′ bosons in supersymmetric E6 models confront electroweak data” [Nucl. phys. B 531 (1998) 65]
Nuclear Physics B 555 (1999) 651-652
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www.elsevier.nl/locate/npe
Erratum
Erratum to "Z' bosons in supersymmetric E6 models confront electroweak data" [Nucl. Phys. B 531 (1998) 65] * Gi-Chol Cho, Kaoru Hagiwara, Yoshiaki Umeda Eq. (4.13) to obtain the lower mass bound of the Z2 boson is incorrect. We obtained 2 2 the 95% CL upper limit on ge/mz2 and then interpreted it as the 95% CL lower limit of the Z2 boson mass, m95, for a fixed value of ge. Eq. (4.13) should hence read as follows:
0.05
= f~/m~5 d (gZlm2z2) P (gZ/m2z2) 2 2 2 2 f oood (ge/mz2) P (ge/mz2)
(1)
We obtained the bound under the constraint ge/mz2 2 2 ~ O, because in some cases the mean value of the fit resides in the unphysical region, ge/mz2 2 2 < 0. All the numbers given in Table 5 were obtained by using the above equation. In Ref. [ 1], 9 5 % CL lower mass limits of the Z2 boson were obtained from the 2 2 condition AX 2 = 3.84. Using the same approach, we found the constraints on ge/mz2 and corresponding lower mass bounds on mz2 (for gE = gr) as shown in Table 5. Table 5
Model
X ~p "q u
g 2e / m z2e
0.27 1.42 -0.61 0.65
Limits at /I.)(2 = 3.84
[TeV - 2 ]
:k 4+ ±
0.21 2.94 0.87 0.54
2 2 gE/tnZ2
mz2
0.68 7.35 1.08 1.71
431 131 342 273
TeV - 2 TeV - 2 TeV - 2 TeV - 2
GeV GeV GeV GeV
By comparing with the bounds on Table 5 which were obtained by Eq. ( 1 ) under the constraint ge/mz~ 2 2 /> 0, a significantly larger mass bound is found for the r/ model with * PII of original article: S0550-3213(98)00549-5. 0 5 5 0 - 3 2 1 3 / 9 9 / $ - see frontmatter (~) 1999 Published by Elsevier Science B.V. All rights reserved. PI1 S 0 5 5 0 - 3 2 1 3 ( 9 9 ) 0 0 3 8 2 - X
652
G.-C. Cho et aL/Nuclear Physics B 555 (1999) 651-652
the above method. This is because the best fit value of g2/m22 resides in the unphysical region for this model. The bounds obtained by Eq. (1) are more sensible when the best fit is found at a point significantly inside of the unphysical region.
Acknowledgements We would like to thank D. Zeppenfeld for making us aware of the paper by J. Erler and P. Langacker [ 1] which pointed out our mistake in Eq. (4.13).
References [l] J. Erler and P. Langacker, hep-ph/9903476.
ELSEVIER
www.elsevier.nl/locate/npe
Erratum
Erratum to "Z' bosons in supersymmetric E6 models confront electroweak data" [Nucl. Phys. B 531 (1998) 65] * Gi-Chol Cho, Kaoru Hagiwara, Yoshiaki Umeda Eq. (4.13) to obtain the lower mass bound of the Z2 boson is incorrect. We obtained 2 2 the 95% CL upper limit on ge/mz2 and then interpreted it as the 95% CL lower limit of the Z2 boson mass, m95, for a fixed value of ge. Eq. (4.13) should hence read as follows:
0.05
= f~/m~5 d (gZlm2z2) P (gZ/m2z2) 2 2 2 2 f oood (ge/mz2) P (ge/mz2)
(1)
We obtained the bound under the constraint ge/mz2 2 2 ~ O, because in some cases the mean value of the fit resides in the unphysical region, ge/mz2 2 2 < 0. All the numbers given in Table 5 were obtained by using the above equation. In Ref. [ 1], 9 5 % CL lower mass limits of the Z2 boson were obtained from the 2 2 condition AX 2 = 3.84. Using the same approach, we found the constraints on ge/mz2 and corresponding lower mass bounds on mz2 (for gE = gr) as shown in Table 5. Table 5
Model
X ~p "q u
g 2e / m z2e
0.27 1.42 -0.61 0.65
Limits at /I.)(2 = 3.84
[TeV - 2 ]
:k 4+ ±
0.21 2.94 0.87 0.54
2 2 gE/tnZ2
mz2
0.68 7.35 1.08 1.71
431 131 342 273
TeV - 2 TeV - 2 TeV - 2 TeV - 2
GeV GeV GeV GeV
By comparing with the bounds on Table 5 which were obtained by Eq. ( 1 ) under the constraint ge/mz~ 2 2 /> 0, a significantly larger mass bound is found for the r/ model with * PII of original article: S0550-3213(98)00549-5. 0 5 5 0 - 3 2 1 3 / 9 9 / $ - see frontmatter (~) 1999 Published by Elsevier Science B.V. All rights reserved. PI1 S 0 5 5 0 - 3 2 1 3 ( 9 9 ) 0 0 3 8 2 - X
652
G.-C. Cho et aL/Nuclear Physics B 555 (1999) 651-652
the above method. This is because the best fit value of g2/m22 resides in the unphysical region for this model. The bounds obtained by Eq. (1) are more sensible when the best fit is found at a point significantly inside of the unphysical region.
Acknowledgements We would like to thank D. Zeppenfeld for making us aware of the paper by J. Erler and P. Langacker [ 1] which pointed out our mistake in Eq. (4.13).
References [l] J. Erler and P. Langacker, hep-ph/9903476.