Maximizing Spin Correlations in Top Quark Pair Production at the Tevatron

Abstract

A comparison is made between the off-diagonal and helicity spin bases for top quark pair production at the FNAL Tevatron. In the off-diagonal basis, 92% of the top quark pairs are in the spin configuration up-down plus down-up, whereas in the helicity basis only 70% are left-right plus right-left. The off-diagonal basis maximizes the spin asymmetry and hence the measured angular correlations between the decay products, which are more than twice as big in this basis as compared to the helicity basis. In addition, for the process q qbar --> t tbar, we give a very simple analytic expression for the matrix element squared which includes all spin correlations between the production and subsequent decay of the top quarks.

Figures (4)

• Figure 1: The relevant angles and vectors in the zero momentum frame of the initial $q\bar{q}$ pair for the off-diagonal basis of Parke and Shadmi. The top quark is produced at an angle $\theta^*$ with respect to the beam axis ($\cos\theta^* \equiv c_{qt}$). The spin vector $s$ makes an angle $\psi$ (given by Eq. (\ref{['psidefn']})) with respect to the beam axis. The vectors $(t\pm ms)/2$, where $m$ is the top quark mass, indicate the preferred emission directions for the charged lepton or down-type quark from the decaying $W^{+}$ (see Eq. (\ref{['omegadefn']})). The vectors describing the antitop lie back-to-back with the corresponding top quark vectors.
• Figure 2: The relative importance of the interference terms in the off-diagonal and helicity bases in $q\bar{q}\rightarrow t\bar{t}$ for the Tevatron at $\sqrt{s} = 2 {\rm \enspace TeV}$. Plotted is the differential distribution in ${\widehat{\cal I}}\equiv {\cal I}/\sum\vert{\cal M}\vert^2$, the value of the interference term (Eq. (\ref{['Iusb']}) or (\ref{['Ihel']})) normalized to the square of the total matrix element (Eq. (\ref{['Fullmsq']})). In the off-diagonal basis, 90% of the cross section comes from phase space points where $\vert {\widehat{\cal I}} \vert < 0.15$, whereas in the helicity basis only 50% of the cross section comes from this region.
• Figure 3: Differential cross section for $t\bar{t}$ production as a function of the $t\bar{t}$ invariant mass $M_{t\bar{t}}$ for the Tevatron with center-of-mass energy 2.0 TeV, decomposed into UD+DU and UU+DD spins of the $t\bar{t}$ pair using the off-diagonal basis for both $q\bar{q}$ and $gg$ components.
• Figure 4: Angular correlations in Tevatron $t\bar{t}$ events at $\sqrt{s} = 2 {\rm \enspace TeV}$ using the off-diagonal basis. The data in each plot are divided into spin-"up" (solid) and spin-"down" (dashed) top quark components, determined by using the charged lepton from the $t$ decay in (a)--(c), and the $b$-quark in (d). Plotted are the angular distributions with respect to the $\bar{t}$ spin axis in the $\bar{t}$ rest frame for the following $\bar{t}$ decay products: (a) the charged lepton, (b) the "d"-type quark, (c) and (d) the $\bar{b}$-quark.