Radiative corrections to top-quark decay

Abstract

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...

The anatomy of electroweak symmetry breaking Tome II: The Higgs bosons in the Minimal Supersymmetric Model

“…The standard QCD corrections have been calculated up to two loops [266,267] and decrease the partial width by approximately 10%. The one-loop electroweak corrections [267,268], when the naive improved Born approximation is used [that is, when the partial width at the Born level is expressed in terms of G µ as in eq. (2.65)], are positive but small, hardly reaching the level of 2%.…”

Electroweak and finite width corrections to top quark decays into transverse and longitudinalWbosons

“…Relative to the m b = 0 Born term rate they amount to −8.54% (QCD one-loop) [3,4,5,6,7,8], +1.54% (electroweak one-loop) [3,9,10] and −2.05% (−2.16%) (QCD two-loop; approximate) [11] ( [12]). The m b = 0 and finite width corrections reduce the Born width by 0.27% [13,14,15] (for m b = 4.8 GeV [16]) and 1.55% [17], respectively.…”

“…Details of the calculation will be published elsewhere [19]. We use the so-called G F -renormalization scheme for the electroweak corrections where G F , M W and M Z are used as input parameters [3,9]. The G F -scheme is the appropiate renormalization scheme for processes with mass scales which are much larger than M W as in the present case.…”

Probing the top-quark width through ratios of resonance contributions of e + e − → W + W − b b ¯ $$ {\mathrm{e}}^{+}{\mathrm{e}}^{-}\to {\mathrm{W}}^{+}{\mathrm{W}}^{-}\mathrm{b}\overline{\mathrm{b}} $$

“…Apart from NLO QCD corrections [45][46][47] higher order QCD as well as electroweak corrections to Γ(t → W b) are known [48][49][50][51][52][53]. In the SM g tbW can be written as gV tb where V tb is the corresponding CKM matrix element.…”