Abstract
We present the analytical expressions for the next-to-leading order corrections to the partial decay width $t(\uparrow) \rightarrow bW^+$, followed by $b\rightarrow H_bX$, for nonzero b-quark mass ($m_b\neq 0$) in the fixed-flavor-number scheme (FFNs). To make the predictions for the energy distribution of outgoing hadrons $H_b$, as a function of the normalized $H_b$-energy fraction $x_H$, we apply the general-mass variable-flavor-number scheme (GM-VFNs) in a specific helicity coordinate system where the polarization of top quark is evaluated relative to the b-quark momentum. We also study the effects of gluon fragmentation and finite hadron mass on the hadron energy spectrum so that hadron masses are responsible for the low-$x_H$ threshold. In order to describe both the b-quark and the gluon hadronizations in top decays we apply realistic and nonperturbative fragmentation functions extracted through a global fit to $e^+e^-$ annihilation data from CERN LEP1 and SLAC SLC by relying on their universality and scaling violations.
Highlights
Among other things, the CERN LHC is a genuine top factory, in particular in Run II, producing about 90 million top-quark pairs per year of running at design energy 14 TeV
Being manifestly based on Collin’s QCD factorization theorem [12] convenient for massive quarks, this factorization scheme allows us to resum the large logarithms in mb, to retain the finite-mb effects and to preserve the universality of the fragmentation functions (FFs), whose scaling violations remain to be subject to DGLAP evolution [13,14,15,16,17]
We briefly review the various interactions of the top quark field t in the standard model (SM) Lagrangian; a topic needed for the calculation of top decay widths
Summary
The CERN LHC is a genuine top factory, in particular in Run II, producing about 90 million top-quark pairs per year of running at design energy 14 TeV. Using the same frame, we revisit B-hadron production from polarized top decays by working at NLO in the general-mass variable-flavor-number scheme (GM-VFNs), where b-quark masses are preserved from the beginning. Being manifestly based on Collin’s QCD factorization theorem [12] convenient for massive quarks, this factorization scheme allows us to resum the large logarithms in mb, to retain the finite-mb effects and to preserve the universality of the FFs, whose scaling violations remain to be subject to DGLAP evolution [13,14,15,16,17] In this way, it combines the virtues of the fixed-flavor-number scheme (FFNs) and the ZM-VFN scheme and avoids their flaws.
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