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19
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84927343805
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The intricate role of the QCD and electroweak gauge invariance which necessitates a modification of this simple splitting picture for unstable top quarks will be discussed later in Sec. VII.
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21
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84927343803
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The Hamiltonian (3.1) dictates the QCD interaction of t and t bar, which is defined to operate in the subspace of t and t bar. The electroweak interactions responsible for their decays are treated as a perturbation, which may be effectively included as the anti-Hermitian part of the Hamiltonian.
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23
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84927343799
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``The Monte Carlo Program TIPTOP_ for Heavy Fermion Production and Decay at LEP and SLC'', MPI-PAE/Pth
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(1986)
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Jadach, S.1
Kühn, J.H.2
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26
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84927343797
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The use of the Coulombic potential allows us to check our numerical program to calculate the imaginary part of the Green's function G ( x vec = 0 ;E) in Eq. (3.20) against the known analytic expression of Fadin and Khoze [5]. The dashed line in Fig. 4 for the constant toponium width ΓΘ= 2 Γt( mt2) agrees at 1% level with the analytic results, which tests the accuracy of our numerical program to solve the Schrödinger equation.
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27
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84927343796
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Within the general relativistic formalism containing unstable particles, the unitarity relation is preserved only when the running of the particles' self-energies are properly taken into account in the propagators [23].
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28
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0000065089
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Unitarity and causality in a renormalizable field theory with unstable particles
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(1963)
Physica
, vol.29
, pp. 186
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Veltman, M.1
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32
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84927343794
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The angular average of the spin factor F ( n ,n̄) in Eq. (4.18) makes ΓTHETA slightly larger than this naive estimate.
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33
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84927343792
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J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, New York, 1973), Vol. 2, Chap. 5-4.
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48
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84927343790
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If we use the approximate expressions presented by the Particle Data Group [38], the values of Λ {MSbar} (nf) become Λ {MSbar} (5)= (0.068, 0.140, 0.253, 0.416) GeV and Λ {MSbar} (4)= (0.111, 0.212, 0.362, 0.565) GeV for αs( mZ) MS bar = (0.10, 0.11, 0.12, 0.13), respectively. These values are about 6ndash 7 % larger than the values quoted in Table II.
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51
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84927343788
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In order to obtain the perturbative potential where the second coefficient b1 also exhibits the decoupling of heavy quarks, we need to use the two-loop beta function in the momentum subtraction scheme [41], which can only be solved numerically. We used the MS bar_ coupling constant for convenience since the effect of the running of the coefficient b1 has been found to be negligibly small [42].
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56
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84927343784
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G. P. Lepage, in Lattice '91, Proceedings of the International Symposium, Tsukuba, Japan, 1991, edited by M. Fukugita et al. [Nucl. Phys. B (Proc. Suppl.) 26 (1992)].
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62
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84927343779
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edited by, R. Orava, P. Eerola, M. Nordberg, (World Scientific, Singapore, in press).
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Proceedings of the Workshop on Physics and Experiments at Linear Colliders, Saariselkä, Finland, 1991
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Fujii, K.1
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64
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84927343778
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More generally, the true ΓTHETA should vanish above the kinematical cutoff Λkin2= ( mt+ E / 2 )2- mW2, since neither t nor t bar can decay when p vec2> Λkin2. The argument here shows that ΓTHETA becomes negligible well below the kinematical cutoff Λkin.
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