By Alexander Mitov
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Extra info for Applications of perturbative quantum chromodynamics to processes with heavy quarks
2) the differential top width with respect to the b-energy fraction in NLO QCD taking full account of the mass of the b quark. 3) we resum with NLL accuracy the large quasi-collinear logs ln(m2b /m2t ). 4) we improve the prediction for the b-energy spectrum at large xb → 1. Then we discuss the improvement to the fixed order calculation due to the various resummations. 5) we extract the non-perturbative fragmentation function using e+ e− data to make predictions for the energy spectrum of b-flavored hadrons in top decay.
We will return to that point later when we consider our applications. 74). 76) where the function A(αS ) can be expanded as follows: ∞ A(αS ) = n=1 αS π n A(n) . 78) 5 − nf . 79) A numerical estimate for A(3) is known too  (see also ). 36). CHAPTER 2. 74) contains all NLL contributions. Its explicit evaluation would, however, contain subleading terms as well. One can evaluate explicitly the integrals and extract only the LL and NLL terms. 80) where we have specified all arguments, restored the separate dependence on the renormalization and factorization scales, and introduced: λ = b0 αS (µ2 ) ln N.
E. 1 0 dz z N −1 (F ⊗ G)(z) = F (N)G(N). 40) CHAPTER 2. 38) and omitting the summation over the partons (as in the NS case for example), one has: d d Q2 2 µ ln f (N, µ ) = −µ ln C N, 2 , αS (µ2 ) = 2γ(N, αS (µ2 )). 28). 41) it is clear that the function γ(N, αS (µ2 )) plays the role of a “separation constant” that depends on the common variables of the functions f and C. Therefore, that equation is of importance only if the function γ is known. 42) if the value of the fragmentation function at some initial scale µ0 is known.
Applications of perturbative quantum chromodynamics to processes with heavy quarks by Alexander Mitov