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1
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84927884011
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For a recent review, see, for example, H. P. Nilles, in Testing The Standard Model, edited by M. Cvetič and P. Langacker (World Scientific, Singapore, 1991), p. 633, and references therein.
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18
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Langacker and Polonsky citeus513;
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0001017861
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Equivalently, nonminimal gauge kinetic functions were considered by
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(1985)
Phys. Lett.
, vol.155 B
, pp. 381
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Ellis, J.1
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23
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84927884008
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Large dimension six operators (which are not consistent with a perturbative treatment) were considered by A. Datta, S. Pakrasa, and U. Sarkar, Phys. Rev. D (to be published). Implications for b τ unification are studied in Ref. citeus556. For recent discussions, see also Ref. citenath.
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24
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84927884007
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N. Polonsky, ``Unification and low energy supersymmetry at one and two loop orders,'' a University of Pennsylvania dissertation, Report No. UPR 0641T, 1994 (unpublished), and references therein.
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29
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84927884006
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which was used in citeus513. ln mt/MZ corrections to α were treated explicitly in citeus513, leading to the same numerical value of α used here. However, stiny new 2(MZ) - stiny old 2(MZ) approx -0.0002, which is consistent with the 0.0003 residual uncertainty in our s02(MZ).
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30
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0001646107
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The value of (the overline{MS}) α(MZ)-1 = 127.9 pm 0.1 used here employs the estimate of the hadronic correction Δαtiny had in F. Jegerlehner, Renormalizing the Standard Model, in Testing The Standard Model, edited by M. Cvetič and P. Langacker (World Scientific, Singapore, 1991), p. 476. Recently, three new estimates have appeared, which, when translated to the overline{MS} scheme, imply α(MZ)-1 = 128.05 pm 0.10 [M. L. Swartz, SLAC Report No. PUB 6710, (unpublished)], α(MZ)-1 = 127.96 pm 0.06 [, ], and α(MZ)-1 = 127.87 pm 0.10 [S. Eidelman and F. Jegerlehner, PSI Report No. PR 95 1 (unpublished)]. The most extreme deviation, suggested by Swartz, would imply a central value for αs(MZ) of 0.130 rather than 0.129. The change is mainly due to a lower central value of s02(MZ) = 0.2314 pm 0.0003 (for mt0pole = 150 GeV), implying an increase of 0.0009 in αs(MZ). This is partially compensated by the direct effect (-0.0002) of the lower value of α(MZ).
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(1995)
Phys. Lett. B
, vol.345
, pp. 558
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Martin, A.D.1
Zeppenfeld, D.2
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Recent results, some of which are preliminary, are from Ref. citeqcd. Results from the Cern esup +e- collider LEP are from S. Bethke, talk presented at Radiative Corrections: Status and Outlook, Gatlinburg, Tennessee, 1994;
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35
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84927884003
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and from Ref. citefit. Lattice results are from A. X. El Khadra et al., in Lattice '93, Proceedings of the International Symposium, Dallas, Texas, edited by T. Draper et al. [Nucl. Phys. B (Proc. Suppl.) 34, (1994)];
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38
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p. 1297.
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39
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84927884001
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B. R. Webber, in Proceedings of the 27th International Conference on High Energy Physics, Glasgow, Scotland, 1994, edited by P. J. Bussey and I. G. Knowles (IOP, London, in press), and references therein.
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40
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The αs discrepancy and its possible resolutions were discussed recently by M. Shifman, Minnesota Report No. UMN TH 1323 94, 1994 (unpublished).
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43
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We defined the β function coefficients bji equiv a(Si)Ni(j)ti(j), where a(Si) = 1 / 3, 2 / 3,-11 / 3 for a particle i of spin Si = 0, 1 / 2, 1, respectively, Ni(j) is the appropriate multiplicity, and ti(j) = 0, 1 / 2, 2,3, 3 / 5(Y / 2)2 for a singlet, a particle in the fundamental representation of SU(N), an SU(2) triplet, an SU(3) octet, and for j = 1 and a particle with hypercharge Y, respectively.
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Pisa Report, TH 47 94, 1994 (unpublished). After completion of this work we received a paper by
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(1995)
Phys. Lett. B
, vol.348
, pp. 443
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Barbieri, R.1
Ciafaloni, P.2
Strumia, A.3
No., IFUP4
Bagger, J.5
Matchev, K.6
Pierce, D.7
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55
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where similar issues are discussed and large positive corrections to αs(MZ) are also found.
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73
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Tohoku Report No. TU 470, 1994 (unpublished).
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74
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After completion of this work we received the papers by T. Dasgupta, P. Mamales, and P. Nath, Northeastern Report, 1995 and D. Ring, S. Urano, and R. Arnowitt, Texas AM Report No. CTP TAMU 01 95, 1995 (unpublished), where NRO's in the minimal SU(5) model are studied.
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We thank Savas Dimopoulos for stressing this point and for suggesting to plot Fig. 4.
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