Helicity fractions ofWbosons from top quark decays at next-to-next-to-leading order in QCD

Abstract

Decay rates of unpolarized top quarks into longitudinally and transversally polarized W bosons are calculated to second order in the strong coupling constant s . Including the finite bottom quark mass and electroweak effects, the standard model predictions for the W-boson helicity fractions are F L ¼ 0:687ð5Þ, F þ ¼ 0:0017ð1Þ, and F À ¼ 0:311ð5Þ.There has been a continuing interest in the measurement of the helicity fractions of the W boson from top quark decays from the CDF Collaboration [1-7] and from the D0 Collaboration [8][9][10][11] at the Tevatron at Fermilab. In the standard model (SM) the top quark decays predominantly into a W þ boson and a bottom quark. Interesting observables, independent of the production rate that is difficult to predict precisely for a hadron collider, are the fractions of the three possible W helicities: F L (longitudinal), F þ (transverse plus) and F À (transverse minus). In the leading order (LO) in the strong coupling constant s (that is, without any gluon corrections), and in the limit of a massless bottom quark one has [12](1) with F L þ F þ þ F À ¼ 1 and x m W =m t . Using m W ¼ 80:401ð43Þ GeV [13] and m t ¼ 172:8ð1:3Þ GeV [14] we get x 2 ¼ m 2 W =m 2 t ¼ 0:216ð3Þ and F L :F þ :F À ' 0:7:0:0:3.The leading order decay t ! bW is a two-body process. With the V À A interaction, a massless b quark is left handed; thus the W can only be left handed or longitudinal due to angular momentum conservation. One therefore has F þ ¼ 0 provided no gluons are emitted.The above LO predictions are only marginally changed by the bottom mass. For a pole mass of m b ¼ 4:8 GeV one finds that the total rate À decreases by about a quarter per cent compared to the massless b limit. The helicity fraction F L slightly decreases while F À increases, by about one per mil. The leakage into the transverse-plus fraction F þ is less than half per mil. Radiative corrections are a more important source of the transverse-plus rate. However, as we shall see, when NLO and NNLO gluon radiation is included, F þ still does not exceed two per mil. Since only hard gluon emission can influence the helicity fractions, this smallness is a reliable prediction of the standard model.For this reason, the transverse-plus fraction F þ is a sensitive probe of new physics effects such as a right chiral admixture to the SM current. The left and right chiral contributions do not interfere for m b ¼ 0 leading to a quadratic dependence on the admixture parameter. The contribution of the right chiral contribution can be obtained from Eq. (1) by exchanging F þ $ F À , whereas F L remains unchanged. We mention that there are some indirect model dependent constraints on a possible right chiral admixture to the SM current from measurements of b ! s þ decays [15][16][17][18].Let us summarize the theoretical prediction for the helicity fractions. In addition to the Oð 2 s Þ effects computed in this paper, we include the lower-order contribution [Born þ Oð s Þ] [19][20][21], the leading electroweak corrections [22], and, for F þ , the m b ...

W helicity, top quark spin and charge

“…The asymmetries can be related to the helicity fractions by a simple system of equations [3]. To measure the asymmetries ATLAS analysis divides cos θ * distribution into four non-uniform bins to count the number of events above and below z. Iterative procedure is used to correct event counts for the acceptance and resolution effects.…”

“…This determines the helicity states in which W bosons are produced in top quark decays. The next-to-next-to-leading-order (NNLO) QCD calculations predict that the fraction of longitudinal helicity W bosons is F 0 = 0.687 ± 0.005, left-handed is F L = 0.311 ± 0.005 and right-handed is F R = 0.0017 ± 0.0001 [3]. These fractions can be extracted from measurements of the angular distribution of the decay products of the top quark:…”

Constraining top-Higgs couplings at high and low energy

“…In addition, the φ distribution is sensitive to the phase of the weak dipole C Wt [24,25]. The SM contribution to the helicity fractions is known at N 2 LO in QCD [26], while the corrections induced by the operators C Wt and C Wb are known at NLO in QCD [27]. As for single top, C Wb is suppressed by the bottom Yukawa, resulting in weak bounds.…”

Measurements of the top quark properties at decay with CMS

“…These helicity fractions are sensitive to the Wtb vertex structure, and in the SM assume the values F 0 = 0.687 ± 0.005, F L = 0.311 ± 0.005 and F R = 0.0017 ± 0.0001 [2], at next-to-next-to-leading order, for a top quark mass of 172.8 ± 1.3 GeV. These fractions are measured recurring to the distributions of the helicity angle θ ⋆ which is defined as the angle between the charged lepton (or down-type quark) and the reversed direction of the top quark, both measured in the W boson rest frame.…”