Weak interaction corrections to hadronic top quark pair production

TL;DR

The study addresses the need for precise Standard Model predictions of hadronic top-quark pair production by incorporating weak corrections at order $\\alpha_s^2\\alpha$ with full spin correlations. The authors compute one-loop weak corrections to $gg\\to t\\bar t$ and mixed electroweak-QCD corrections to $gq$-initiated channels, completing the set when combined with prior results for $q\\bar q$-initiated production, and parameterize these corrections with scaling functions. They find that, while total cross sections receive modest negative corrections, the high-energy tails in $d\\sigma/dp_T$ and $d\\sigma/dM_{t\\bar t}$ exhibit sizable effects at the LHC (up to ~10% and ~6%, respectively). Parity-violating spin observables exist within the SM, related by CP invariance, and the charged-lepton forward-backward asymmetry in semileptonic decays, $A_{PV}$, is predicted to be around 1% under suitable cuts. Together, these results provide essential Standard Model benchmarks for high-precision top-quark studies and for probing potential non-standard CP violation or heavy resonances in future collider data.

Abstract

In this paper we determine the weak-interaction corrections of order $α_s^2α$ to hadronic top-quark pair production. First we compute the one-loop weak corrections to $t \bar t$ production due to gluon fusion and the order $α_s^2α$ corrections to $t \bar t$ production due to (anti)quark gluon scattering in the Standard Model. With our previous result this yields the complete corrections of order $α_s^2α$ to $gg$, $q \bar q$, $q g$, and ${\bar q} g$ induced hadronic $t \bar t$ production with $t$ and $\bar t$ polarizations and spin-correlations fully taken into account. For the Tevatron and the LHC we determine the weak contributions to the transverse top-momentum and to the $t \bar t$ invariant mass distributions. At the LHC these corrections can be of the order of 10 percent compared with the leading-order results, for large $p_T$ and $\mtt$, respectively. Apart from parity-even $t \bar t$ spin correlations we analyze also parity-violating double and single spin asymmetries, and show how they are related if CP invariance holds. For $t$ (and $\bar t$) quarks which decay semileptonically, we compute a resulting charged-lepton forward-backward asymmetry $A_{PV}$ with respect to the $t$ ($\bar t$) direction, which is of the order of one percent at the LHC for suitable invariant-mass cuts.

Figures (27)

• Figure 1: (a) Lowest order QCD diagrams and 1-loop weak corrections to $gg \to t {\bar{t}}$. Crossed diagrams are not drawn. The dotted line in the box diagram and in the vertex and self-energy corrections represents $W,\, Z$ bosons, the corresponding Goldstone bosons, and the Higgs boson $H$. The fermion triangle in the last diagram represents a $t$ and $b$ quark loop, followed by $s$ channel exchange of the $Z$ boson, the associated Goldstone boson, and the Higgs boson. (b) Tree-level diagrams for $q g \to t {\bar{t}} q$. Upper row: QCD diagrams; lower row: mixed electroweak-QCD contributions. The dotted line represents a photon or a $Z$ boson.
• Figure 2: Ratio $r_W^{(0)}$ of the order $\alpha \alpha_s^2$ corrections and the Born cross section for $gg \to t {\bar{t}}$ as a function of $\eta$, for two Higgs masses, $m_H=120$ GeV (solid) and $m_H=200$ GeV (dashed). The dotted curve shows the non-singlet neutral current contribution to $r_W^{(0)}$.
• Figure 3: Ratio $r_W^{(1)}$ of the order $\alpha \alpha_s^2$ corrections (for $m_H=120$ GeV) and the NLO QCD cross section for $gg \to t {\bar{t}}$ (taken from Bernreuther:2001bxBernreuther:2004jv), evaluated for $\mu = m_t/2$ (dotted), $\mu = m_t$ (solid), and $\mu = 2m_t$ (dashed).
• Figure 4: Upper frame: Scaling function $f^{(1W)}_{ug}$ defined in (\ref{['eq:qgsection']}) for u-type quarks. For d-type quarks, $f^{(1W)}_{dg}= -f^{(1W)}_{ug}$. Lower frame: Scaling functions $h^{(1\, W,hel)}_{ug}$ (dotted), $h^{(1\, W,hel)}_{dg}$ (solid), $h^{(1\, W,hel)}_{{\bar{u}} g}$ (dashed), and $h^{(1\, W,hel)}_{{\bar{d}} g}$ (dash-dotted) that determine the expectation value (\ref{['eq:qgbarspin']}) for the helicity axis.
• Figure 5: Scaling function $h^{(1\, W,hel)}_{gg}$ that determines the expectation value (\ref{['eq:sinspin']}) for the helicity axis.