In this paper we present the analytic form of the heavy quark coefficient functions for deep inelastic lepton-hadron scattering in the kinematical regime Q2 >> m 2. Here Q2 and m 2 stand for the masses squared of the virtual photon and heavy quark, respectively. The calculations have been performed up to next-to-leading order in the strong couphng constant a, using operator product expansion techniques. Apart from a check on earlier calculations, which however are only accessible via large computer programs, the asymptotic forms of the coefficient functions are useful for charm production at HERA when the condition Q2 >> mc2 is satisfied. Furthermore, the analytical expressions can also be used when one applies the variable tlavour number scheme up to next-to-leading order in a,.

We discuss Padé-improvement of known four-loop order results based upon an asymptotic threeparameter error formula for Padé-approximants. We derive an explicit formula estimating the nextorder coefficient R 4 from the previous coefficients in a series 1 + R 1 x + R 2 x 2 + R 3 x 3 . We show that such an estimate is within 0.18% of the known five-loop order term in the O(1) β-function, and within 10% of the known five-loop term in the O(1) anomalous mass-dimension function γ m (g). We apply the same formula to generate a [2|2] Padé-summation of the QCD β-function and anomalous mass dimension in order to demonstrate both the relative insensitivity of the evolution of α s (µ) and the running quark masses to higher order corrections, as well as a somewhat increased compatibility of the present empirical range for α s (m τ ) with the range anticipated via evolution from the present empirical range for α s (M z ). For 3 ≤ n f ≤ 6 we demonstrate that positive zeros of any [2|2] Padé-summation estimate of the all-orders β-function which incorporates known two-, three-, and four-loop contributions necessarily correspond to ultraviolet fixed points, regardless of the unknown five-loop term. Padé-improvement of higher-order perturbative expressions is presented for the decay rates of the Higgs into two gluons and into a bb pair, and is used to show the relative insensitivity of these rates to higher order effects. However, Padé-improvement of the purely-perturbative component of scalar/pseudoscalar current correlation functions is indicative of large theoretical uncertainties in QCD sum rules for these channels, particularly if the continuum-threshold parameter s 0 is near 1 GeV

We calculate all radiative corrections to one-loop order for the main decay of the top quark, t-+ b + W y in the standard model, retaining exact dependence on all masses. For m t -150 GeV and MH = 100 GeV we find a -2.9% ( -6.9%) correction with a very weak dependence on the Higgs-boson mass, in renormalization schemes that use a, GF, and Mz (GF, MW, and Mz) as input parameters. Out of the above results, -8.5% is due to QCD. The m t and MH dependence is given up to 300 and 1000 GeV, respectively. The inadequacy of a leading m t calculation is pointed out.PACS numbers: 14.80.Dq, ll.10.Gh, 12.15Ji, 12.38.Bx The top quark, according to recent analyses, is around the corner. From Collider Detector at Fermilab experiments, x m t > 89 GeV, and a maximum-likelihood analysis of recent data 2 has given the most likely value of m t -150 GeV. Other studies 3 prefer m t~~ 130 GeV, while a most recent analysis 4 of some-but not all -higher-order (beyond one-loop) effects shows reasonable probability distributions up to m, --300 GeV. Within the framework of the standard model (SM) discussed here, the main decay of the top quark is t-+ bW, with a tree-level width given byGo s =mb+m l f -2Mjy-\ z , M w and the square of the Weinberg angle is defined as s w = 1 -Mw/Mz.Once the top quark is discovered more accurate experiments will search for radiative corrections to the tree-level width. We present here the full radiative corrections to one-loop order to the main decay mode t-+ bW.The motivation for this work should be clear. Since the top quark has a unique mass scale, being (very likely) the heaviest in the SM, precise tests of its properties against the predictions of the SM represent a unique opportunity to search for the effects of mass scales beyond the SM. Radiative corrections are, of course, powerful tests of gauge theories. Furthermore, the mixing angle V t b must be deduced from experiments by studying the decays of the top quark. At this point we remark that while the quantum chromodynamics (QCD) part of our calculation confirms previous results, 5,6 the electroweak (EW) component of the radiative corrections has not been presented in full. Only leading results valid in the limit ra, ^>A/V,M// have been previously presented. 6 The leading m t calculation fails to describe the correct dependence on the relevant masses, and does not reproduce the exact results even for high m t and low A///, as is shown below.Before the current lower limit on m t was established, a complete first-order calculation of W + -+tb had been presented in Ref. 7. We have independently done that calculation and will adopt the notation of Ref. 7, hereafter referred to as DS (Denner and Sack), and emphasize all the necessary modifications needed for the transformation from W-* tb to t -* Wb, Define the relative correction a-(r-r 0 )/ro,where F is the width including first-order, i.e., one-loop, corrections. Then, the total correction can be separated asThe EW correction is further given aswith contributions from fermion and W-boson wavefunction...

We prove that the coefficient of the longitudinal part of the W-boson propagator close to resonance is equal to 1 /( M& + i e , ), where eL is proportional to squares of masses of those fermions that the W can decay to. Consequently, the full propagator has a non-gGV part that differs from the commonly used form, even in the limit of vanishingly small fermion masses.PACS number(s): 14.70.Fm, 13.38.+BeThe resonance Breit-Wigner propagator of vector bosons has been repeatedly discussed in the literature [I].Most, but not all [2], studies concentrate on the part proportional to -gpv which is Discussions concentrate on renormalization, renormalization schemes, pole position, and whether one should use a 4 2-dependent or 4 2-independent width, E,=T~'/M, or e T = r M W , respectively. We will not dwell upon the above issues here, but rather prove that the commonly written form [3] for the full propagator in the unitary gauge, which is an obvious generalization of the nonresonance W propagator (E,=O), treats the longitudinal part incorrectly. Our main concern is the situation near resonance, where we find that the correct form of the propagator is where the "longitudinal width" is proportional to squares of fermion masses to which the W decays:Eq. (3) differs significantly from Eq. (2). The discussion will also be valid for Z bosons up t o complications due t o y -Z mixing.In most cases one is not sensitive to the qpqv part of the propagator in view of its coupling t o light fermion masses on at least one end, i.e., either at the production or the decay vertex. However, one can encounter a scenario which depends crucially on a knowledge of that part. Let us now describe such a situation, in which an observable is proportional t o ImG,, where the propagator is decomposed into its transverse and longitudinal parts with G, given by Eq. (1). Let us consider [4,5] the CPviolating partial rate asymmetry (PRA) between t +br+v, and i-67-3, with the Weinberg model [6] (WM) of CP violation. A t the lowest order in the weakcoupling constant, and assuming for simplicity that the lowest-mass charged Higgs boson obeys M H + > m , , the P R A is given by the interference between Figs. l(a) and l(b). That interference for t -b T ' V , equals [the integration is from m 2, to ( m, -mb )' I It is interesting t o note that even in the limit E~ <

We show that the charged Higgs sector in Weinberg's model for CP violation can cause a large CP violation effect in t-+brv r . The asymmetry in the partial rate is dominated by contributions such as Z(and y)-H + box diagrams interfering with a (near-resonance) W tree diagram. But far more significant are the asymmetries in the partially integrated rates and in the energy between the r + and the T ~. These stem from (near-resonance) WMree-// + -tree interference.