Spin correlations, using a generic spin basis, are investigated to leading order in QCD for top quark production at lepton colliders. Even though, these radiative corrections induce an anomalous γ/Z magnetic moment for the top quarks and allow for single, real gluon emission, their effects on the top quark spin orientation are very small. The final results are that the top (or anti-top) quarks are produced in an essentially unique spin configuration in polarized lepton collisions even after including the O(α s ) QCD corrections. PACS number(s): 12.38. Bx, 13.88.+e, 14.65.Ha

The complete set of twist-3 flavor singlet operators which contribute to the structure function g2(X, Q2) is constructed. We develop a covariant approach to derive the anomalous dimension of these operators. We clarify the role played by the operators proportional to the equations of motion and the "alien" operators.The structure function 92(X, Q2) plays a distinguished role in spin physics 1) because it contains information inaccessible by the more familiar spin structure function 91 (x, Q2). 2), 3) In the framework of the operator product expansion (OPE), not only the twist-2 but also the twist-3 operators contribute to 92(X, Q2) to leading order of .)

We discuss top quark production and its subsequent decay at lepton colliders including both QCD corrections and anomalous γ/Z − tt couplings. The off-diagonal spin basis for the top and anti-top quarks is shown to be useful to probe the anomalous couplings.

We analyze the spin correlations of the top quark pairs produced at Photon Linear Colliders. We employ the circular polarized photon beams and general spin basis for the top quark pair. We consider general spin bases to find a strong spin correlation between produced top quark and anti-top quark. We show the cross-section in these bases and discuss the characteristics of results.We have been progressing in our understanding of nature step by step. LEP and Tevatron experiments provided us with the precision measurement of the top quark mass [1,2], W boson mass, the bound for the Higgs boson mass and many other electro-weak parameters. With these numerous data, the standard electro-weak theory are enjoying the nature without any discrepancies at least in current experiments.In 1994, the last fundamental quark of the "Standard Model", the top was discovered at the Fermi-Lab Tevatron. The discovery of this very heavy fundamental particle is remarkable, which brought us some good chance to probe the electro-weak symmetry breaking mechanism. The top quark sector is not yet well established and many authors are discussing related problems. For instance, T or CP violation in the top quark sector and the possibility of the presence of anomalous couplings have been discussed in many papers [3]. A very heavy top quark arouse our interests in trying to understand the nature deeply and we expect to investigate the top quark sector of the Standard Model at the Next Linear Collider (NLC) [4,5] in the near future.The top quark physics at NLC is attractive and will give us some new information to understand the Standard Model and clue to physics beyond the Standard Model.On the other hand, the Photon Linear Colliders [6] may be the best alternatives to the electron positron colliders. Physics opportunities in the Photon Linear Colliders are as rich as those in the e + e − colliders and furthermore we have an unique opportunity in the case of the Photon Linear Colliders, namely, we can control the initial photon polarization by the inverse Compton scattering of the polarized laser by the electron/positron beams at NLC. Handling the polarized photon beams, we have the total angular momentum J = 0, 2, · · · states in the s-channel. Using these polarized high energy photon beams, we will have attractive channels for Higgs particle production [6], top quark pair production [7] and other interesting processes.It was discussed in the papers [8][9][10] that the spin of the top quark can be determined from the angular distribution of the electro-weak decay products of the top quark. So, it is interesting to investigate the spin correlations of the top quark pairs at the Photon Linear Colliders. We discuss in this paper the top quark pair production at the Photon Linear Colliders with the circular polarized photon beams and the general spin basis for the top and anti-top quarks.This paper is organized as follows. In Sec.II we explain our notation and convention to calculate the cross-section. We show the cross-section of the top quark pair...