Abstract
We compute the fragmentation functions for the production of a Higgs boson at mathcal{O} ( {y}_t^2 αs). As part of this calculation, the relevant splitting functions are also derived at the same perturbative order. Our results can be used to compute differential cross sections with arbitrary top-quark and Higgs-boson masses from massless calculations. They can also be used to resum logarithms of the form ln(pT/m) at large transverse momentum pT to next-to-leading-logarithmic accuracy by solving the DGLAP equations.
Highlights
Been known for a long time [6,7,8,9,10,11] and have since been extended to incorporate the decay of the top quarks, including off-shell effects [12]
Soft-gluon resummation has been performed, first at next-to-leading-logarithmic accuracy (NLL) [13] and at NNLL [14,15,16], and NNLO corrections have been computed in the soft-gluon limit [17]
In analogy to the initial state factorisation theorem, which states that hadron-collision cross sections can be described, up to power corrections, by a convolution of non-perturbative parton distribution functions and perturbative hard scattering matrix elements, the production of hadrons can be factorised into non-perturbative fragmentation functions Di→h, which describe the transition from the parton i to the hadron h, and perturbative hard scattering matrix elements: dσh dEh (Eh) dσi dEi (Eh) ≡
Summary
Fragmentation functions were initially introduced to describe the production of hadrons at high pT [26]. The main benefit of factorising the production of the massive quark into fragmentation functions is that this allows one to use the DGLAP equations to resum mass logarithms: whereas the fully massive calculation contains logarithms of the type ln Q2/m2 , the perturbative fragmentation function (PFF) formalism splits the calculation into fragmentation functions, which contain the logarithm ln μ2F r/m2 , and massless cross sections, which contain the logarithm ln Q2/μ2F r. [23] involved comparing the massive and massless cross sections, the derivation of the NNLO heavy-quark FFs in refs. There, the LO FF and splitting function for the transition t → H, and of several other transitions, was derived by directly employing the definition of FFs given in ref. Where the sum is over all QCD partons (including the top quark) and the Higgs boson, assuming only QCD corrections are considered
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