Energy correlation and asymmetry of secondary leptons ine+e−→tt¯

Top quarks produced in the reaction ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$→tt¯ are predicted to have a strong spin-spin correlation. We show that this correlation reflects itself in a strong energy correlation of the charged leptons produced in the decays t→${\mathit{bl}}^{+}$ ${\nu }_{\mathit{l}}$ (t¯→b¯${\mathit{l}}^{\mathrm{-}}$ν${\mathrm{¯}}_{\mathit{l}}$). Analytical expressions are given for the two-dimensional distribution dσ/dxdx’ where x and x’ are scaled energy variables of ${\mathit{l}}^{+}$ and ${\mathit{l}}^{\mathrm{-}}$. In the presence of a CP-violating term in the ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$→tt¯ amplitude, this correlation acquires an antisymmetric component which is also calculated. Our formalism yields compact expressions for the single-particle energy spectra of ${\mathit{l}}^{+}$ and ${\mathit{l}}^{\mathrm{-}}$ and the asymmetry between them.