# Longitudinal quark polarization in \(e^+e^- \to t\overline{t}\) and chromoelectric and chromomagnetic dipole couplings of the top quark

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## Abstract.

The effect of anomalous chromomagnetic (\(\mu\)) and chromoelectric couplings (*d*) of the gluon to the top quark is considered in \(e^+e^- \to t\overline{t}\), with unpolarized and longitudinally polarized electron beams. The total cross section, as well as *t* and \(\overline{t}\) polarizations, are calculated to order \(\alpha_s\) in the presence of the anomalous couplings. One of the two linear combinations of *t* and \(\overline{t}\) polarizations is CP even, while the other is CP odd. The limits that could be obtained at a typical future linear collider with an integrated luminosity of 50 fb\(^{-1}\) and a total c.m. energy of 500 GeV on the most sensitive CP-even combination of anomalous couplings, are estimated as \(-3 < {\rm Re}(\mu) < 2\), for \({\rm Im}(\mu)=0=d\), and \(\sqrt{{\rm Im}(\mu)^2 + \vert d \vert ^2} < 2.25\), for \({\rm Re}(\mu)=0\). There is an improvement by roughly a factor of 2 at 1000 GeV. On the other hand, from the CP-odd combination, we derive the possible complementary bounds as \(-3.6 < {\rm Im} (\mu^* d) < 3.6\), for \({\rm Im} (d) = 0\), and \(-10 < {\rm Im} (d) < 10\), for \({\rm Im} (\mu^* d) = 0\), for a c.m. energy of 500 GeV. The corresponding limit for 1000 GeV is almost an order of magnitude better for \({\rm Im} (\mu^* d)\), though somewhat worse for \({\rm Im} (d)\). Results for the c.m. energies 500 GeV and 1000 GeV, if combined, would yield *independent* limits on the two CP-violating parameters of \(-0.8 < {\rm Im} (\mu^* d) < 0.8\) and \(-11 <{\rm Im} (d) < 11\).

## Keywords

Linear Combination Electron Beam Total Cross Section Dipole Coupling Linear Collider## Preview

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