Theoretical aspects of inclusive light-hadron production

We study the fragmentation of the b quark in top decay in NLO QCD, within the framework of perturbative fragmentation, which allows one to resum large logarithms ∼ log(m 2 t /m 2 b ). We show the b-energy distribution, which we compare with the exact O(α S ) result for a massive b quark. We use data from e + e − machines in order to describe the b-quark hadronization and make predictions for the energy spectrum of b-flavoured hadrons in top decay. We also investigate the effect of NLL soft-gluon resummation in the initial condition of the perturbative fragmentation function on parton-and hadron-level energy distributions.

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“…For an explicit expression of the normalization factor A and of the Mellin transform of Eq. (22), see [32]. The N-space transforms of Eqs.…”

Section: Perturbative Fragmentation and Parton-level Resultsmentioning

confidence: 99%

Bottom-quark fragmentation in top-quark decay

2002

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“…Finally we note that our numerical procedures are also applicable to the evaluation of other relativistic corrections like the velocity-dependent potentials [55,56,11] and the potential at O(1/m) [14,15,11,57,58,59,60,61], which are also represented as the field strength correlators on the quark-antiquark source with different combination of the field strength operators from the spindependent potentials. The first lattice result on the potential at O(1/m) was published in Ref.…”

Section: Discussionmentioning

confidence: 99%

Spin-dependent potentials from lattice QCD

2007

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The spin-dependent corrections to the static inter-quark potential are phenomenologically relevant to describing the fine and hyperfine spin splitting of the heavy quarkonium spectra. We investigate these corrections, which are represented as the field strength correlators on the quark-antiquark source, in SU(3) lattice gauge theory. We use the Polyakov loop correlation function as the quark-antiquark source, and by employing the multi-level algorithm, we obtain remarkably clean signals for these corrections up to intermediate distances of around 0.6 fm. Our observation suggests several new features of the corrections.Comment: 36 pages, 22 figures, version to appear in Nucl. Phys.

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“…As opposed to the massive case, where only a limited set of NNLO virtual corrections have been calculated [30][31][32][33][34][35][36][37], both the one-loop times one-loop and two-loop times Born interference terms are known for the case of massless two-to-two scattering [14,[38][39][40]. These results are implicitly summed over colors and cannot be used to extract the hard matrix directly, on the other hand they can be used to extract the contribution of the NNLO hard function to the approximate NNLO formulas covered below.…”

Section: Hard Functionmentioning

confidence: 99%

“…where Z [q] is the object given to NNLO in Eqs. (37) and (38) of [27]. Here and in the remainder of the section we have neglected terms which vanish in the limit m t → 0.…”

Section: A Small-mass Limits Of Massive Hard and Soft Functionsmentioning

confidence: 99%

Soft-gluon resummation for boosted top-quark production at hadron colliders

2012

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We investigate the production of highly energetic top-quark pairs at hadron colliders, focusing on the case where the invariant mass of the pair is much larger than the mass of the top quark. In particular, we set up a factorization formalism appropriate for describing the differential partonic cross section in the double soft and small-mass limit, and explain how to resum simultaneously logarithmic corrections arising from soft gluon emission and from the ratio of the pair-invariant mass to that of the top quark to next-to-next-to-leading logarithmic accuracy. We explore the implications of our results on approximate next-to-next-to-leading order formulas for the differential cross section in the soft limit, pointing out that they offer a simplified calculational procedure for determining the currently unknown delta-function terms in the limit of high invariant mass.using the results of [9][10][11][12]. A fully resummed cross section appropriate for both limits is then obtained by deriving and solving the renormalization-group (RG) evolution equations for the different functions separately. The anomalous dimensions appearing in the RG equations are known to the level sufficient for resummation of both mass and soft logarithms to NNLL accuracy. As simple and obvious as this approach is, it has yet to be fully worked out for any particular observable in top-quark pair production at hadron collider experiments.This formalism for the simultaneous resummation of soft and mass logarithms in the invariant-mass distribution is interesting in its own right. Moreover, with use of a proper matching procedure, it provides supplemental information to the current state-of-the-art predictions based on soft-gluon resummation with the counting m t ∼ M [5]. Particularly important in this regard is its use as a tool to calculate, up to easily quantifiable power corrections in m t /M, the full NNLO corrections to the massive hard and soft functions. Together, these pieces determine the coefficient of the delta-function coefficient in the fixed-order expansion at NNLO, a missing piece in currently available "approximate NNLO" formulas for generic values of the top-quark mass. Using our factorization formula for the double soft and smallmass limit, we can calculate the pieces of the NNLO delta-function correction enhanced by logarithms of the ratio m t /M. Furthermore, using the explicit NNLO results for the heavyquark fragmentation function [13] and the virtual corrections to massless qq → q ′q′ [14] and gg → qq [15] scattering, we can very nearly determine the piece of the delta-function coefficients which is constant in the limit m t /M → 0. The missing piece is the NNLO soft function for massless partons, related to double real emission for gg → qq and qq → qq scattering in the soft limit. We do not calculate this function here, but plan to return to it in future work. While these delta-function pieces of the NNLO partonic cross section are of N 3 LL in the counting of soft-gluon resummation, including them can only make the pred...

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Theoretical aspects of inclusive light-hadron production

Cited by 6 publications

References 66 publications

Bottom-quark fragmentation in top-quark decay

Bottom-quark fragmentation in top-quark decay

Spin-dependent potentials from lattice QCD

Soft-gluon resummation for boosted top-quark production at hadron colliders

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