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Symbolic expressions for fully differential single top quark production cross section and decay width of polarized top quark in the presence of anomalous Wtb couplings

Spin correlations in the t-channel single top quark production and its subsequent decay are investigated for the case of contributions involving anomalous Wtb couplings. We obtain analytical expressions for the differential widths for the three-particle decay of a polarized t quark in its rest frame and also expressions for the differential cross sections of the full process of production and decay of the t quark ($2\to 4$) as a function of the energy of a charged lepton and two angles of orientation of the quantization axis of the t-quark spin. The expression is presented in the most general form for the case of real and imaginary vector and tensor anomalous Wtb couplings. We show that shapes of certain multidimensional kinematic distributions of final state particles are significantly different for the contributions proportional to different combinations of the anomalous couplings. The most noticeable differences appear in the shape of the surfaces of two-dimensional distributions, where one of the variables is the energy of a charged lepton and the other is one of the t-quark spin orientation angles. Observed properties are confirmed by two methods of computations either from the obtained symbolic expression for the differential cross sections of the full process of the polarized single top quark production with its subsequent decay or by means of the CompHEP program for the complete process involving the t-channel single top. In addition, using the obtained analytical expressions, we estimate the statistical accuracy of extracting values of the anomalous Wtb couplings for different levels of the expected integral luminosity at the LHC.