We investigate the chiral-odd generalized parton distributions for nonzero skewness in transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer, respectively. We present overlap formulas for the chiral-odd generalized parton distributions in terms of light-front wave functions (LFWFs) of the proton both in the EfremovRadyushkin-Brodsky-Lepage and Dokshitzer-Gribov-Lipatov-Altarelli-Parisi regions. We calculate them in a field theory inspired model of a relativistic spin-1=2 composite state with the correct correlation between the different LFWFs in Fock space, namely, that of the quantum fluctuations of an electron in a generalized form of QED. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.

We investigate the generalized parton distributions (GPDs) for u and d quarks in a proton in transverse and longitudinal position space using a recent phenomenological parametrization. We take nonzero skewness ζ and consider the region x > ζ. Impact parameter space representation of the GPD E is found to depend sharply on the parameters used within the model, in particular in the low x region. In longitudinal position space a diffraction pattern is observed, as seen before in several other models.

Basis Light-front Quantization (BLFQ) has recently been developed as a promising nonperturbative technique. Using BLFQ, we investigate the Generalized Parton Distributions (GPDs) in a nonperturbative framework for a dressed electron in QED. We evaluate light-front wave functions and carry out overlap calculations to obtain GPDs. We also perform perturbative calculations in the corresponding basis spaces to demonstrate that they compare reasonably with the BLFQ results.

We present a study of the parton distributions in transverse position or impact parameter space using a recent parametrization of u and d quark generalized parton distributions (GPDs) H(x, t) andE(x, t) at zero skewness. We make a comparative study between different parametrizations and discuss the region of validity of the positivity condition.

The forward–backward asymmetry observed in the top quark pair production at the Fermilab Tevatron points toward the existence of beyond the standard model physics. We have studied the top quark pair production [Formula: see text] in the TeV energy electron–positron linear collider to the leading order of the noncommutative parameter Θμν in the noncommutative standard model. We have made a detailed laboratory frame analysis of the time-averaged cross-section, polar, azimuthal angular distributions, transverse momentum and rapidity distributions, polar (forward–backward) and azimuthal asymmetries of the top-quark pair production in the presence of earth's rotation. We investigated their dependence on the orientation angle of the noncommutative vector η and the noncommutative scale Λ and found that those deviates from the standard model distributions significantly. The azimuthal distribution which is flat in the standard model deviates largely for η = π/2 and Λ = 700 GeV at the fixed machine energy E com = 1000 GeV . We found that the polar distribution deviates largely from the standard model distribution for η = π/2 and Λ = 500 GeV . The azimuthal asymmetry Aϕ which is zero in the standard model can be as large as 4% for Λ = 500 GeV and η = π/2 at the fixed machine energy E com = 1000 GeV . Assuming that the future TeV linear collider will observe Aϕ = ±0.01 we find Λ≤750(860) GeV corresponding to η = π/2. Similarly, corresponding to polar asymmetry A FBz = 0.5078 (which deviates from the standard model prediction by 1%), we find Λ≤760 GeV at the fixed machine energy E com = 1000 GeV for η = π/2.