We analyse the semileptonic decay of a polarised top-quark with a large velocity based on the perturbative QCD factorisation framework. Thanks to the factorisation and the spin decomposition, the production part and the decay part can be factorised a
nd the spin dependence is introduced in the decay part. The decay part is converted to the top-jet function which describes the distribution of jet observables and the spin is translated to the helicity of the boosted top. Using this top-jet function, the energy profile of b-jet is investigated and it is turned out that the sub-jet energy for the helicity-minus top is accumulated faster than that for the helicity-plus top. This behaviour for the boosted top can be understood with the negative spin-analysing-power of b-quark in the polarised-top decay.
We study jet substructures of a boosted polarized top quark, which undergoes the semileptonic decay $tto bell u$, in the perturbative QCD framework. The jet mass distribution (energy profile) is factorized into the convolution of a hard top-quark dec
ay kernel with the bottom-quark jet function (jet energy function). Computing the hard kernel to leading order in QCD and inputting the latter functions from the resummation formalism, we observe that the jet mass distribution is not sensitive to the helicity of the top quark, but the energy profile is: energy is accumulated faster within a left-handed top jet than within a right-handed one, a feature related to the $V-A$ structure of weak interaction. It is pointed out that the energy profile is a simple and useful jet observable for helicity discrimination of a boosted top quark, which helps identification of physics beyond the Standard Model at the Large Hadron Collider. The extension of our analysis to other jet substructures, including those associated with a hadronically decaying polarized top quark, is proposed.
We perform perturbative QCD factorization of infrared radiations associated with an energetic $b$ quark from a polarized top quark decay, taking the semi-leptonic channel as an example. The resultant formula is expressed as a convolution of an infrar
ed-finite heavy-quark kernel with a $b$-quark jet function. Evaluating the heavy-quark kernel up to leading order in the coupling constant and adopting the jet function from QCD resummation, we predict the dependence of the spin analyzing power for a polarized top quark on the invariant mass of the $b$-quark jet. It is observed that the spin analyzing power could be enhanced by a factor 2 compared to the inclusive case with the jet mass being integrated over. It is worthwhile to test experimentally the enhancement of the spin analyzing power due to the inclusion of jet dynamics.
We investigated top quark effects on virtual photon structure functions by pQCD. We include the top quark mass effects on the virtual photon structure function with the quark parton model and with the operator product expansion up to the next-to-lead
ing order in QCD. We also consider the threshold effect on the running coupling constant in the calculation to the effective photon structure function with a matching condition. The numerical calculations are investigated in the kinematical region expected at the future international linear collider.
We discuss the resummation of the large logarithmic terms appearing in the heavy quark effects on parton distribution functions inside the virtual photon. We incorporate heavy quark mass effects by changing the initial condition of the leading-order
DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and discuss the property of the resummed heavy quark effects.
