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On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays

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I.I.Bigi, M.A.Shifman, N.G.Uraltsev, A.I.Vainshtein

High Energy Physics - Phenomenology · Submitted 31 Dec 1993

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We derive a model-independent {\em lower} bound on the kinetic energy of the heavy quark inside the hadron.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-ph/9312359 (version 2)
Pith IDZ5BVLRBQ, Pith's permanent record of this paper and its review
CitationA.I.Vainshtein, I.I.Bigi, M.A.Shifman, N.G.Uraltsev. "On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays." arXiv:hep-ph/9312359 (1993). https://pith.science/paper/Z5BVLRBQ
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,183 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.64 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.75 · compares with prior results 0.86 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In previous papers we have pointed out that there exists a QCD analog of the phenomenological concept of the so called Fermi motion for the heavy quark inside a hadron. Here we show in a more detailed way how this comes about and we analyze the limitations of this concept. Non-perturbative as well as perturbative aspects are included. We emphasize both the similarities and the differences to the well-known treatment of deep inelastic lepton-nucleon scattering. We derive a model-independent {\em lower} bound on the kinetic energy of the heavy quark inside the hadron.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In previous papers we have pointed out that there exists a QCD analog of the phenomenological concept of the so called Fermi motion for the heavy quark inside a hadron. background 0.99 0.44 0.07 asserted 0.99
s1 Here we show in a more detailed way how this comes about and we analyze the limitations of this concept. contribution 1.00 0.92 0.11 asserted 1.00
s2 Non-perturbative as well as perturbative aspects are included. method 0.57 0.71 0.03 asserted 0.87
s3 We emphasize both the similarities and the differences to the well-known treatment of deep inelastic lepton-nucleon scattering. contribution 0.80 0.77 0.04 asserted 0.87
s4 We derive a model-independent {\em lower} bound on the kinetic energy of the heavy quark inside the hadron. result 0.97 0.96 0.40 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In previous papers we have pointed out that there exists a QCD analog of the phenomenological concept of the so called Fermi motion for the heavy quark inside a hadron. Here we show in a more detailed way how this comes about and we analyze the limitations of this concept. Non-perturbative as well as perturbative aspects are included. We emphasize both the similarities and the differences to the well-known treatment of deep inelastic lepton-nucleon scattering. We derive a model-independent {\em lower} bound on the kinetic energy of the heavy quark inside the hadron.

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References
How the literature uses it

48 arXiv papers cite this in 65 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 35 sentences without a confident label

Builds on it 1 paper
  • For the charmed baryons, the same expression [ref] is rewritten in terms of the operators [ref] in the baryon basis: [equation] In [ref] and [ref], $g_s^2 = 4π$ represents a non-perturbative scale; following eg [ref] , we set $= 1$.

    Lifetimes of singly charmed hadrons · Darwin parameter $(H)$ · 0.87

Uses its method or tool 3 papers
  • Within the diquark picture, the Darwin matrix element receives two separate contributions, one from the diquark-light interaction and one from the interaction of the two heavy quarks inside the diquark: [equation] The diquark-light quark contribution can be obtained by relating the Darwin operator to four-quark operators using the equation of motion for the gluon field [ref] resulting with [equation] For the remaining $ρ̂_D^3|_Q-Q'$ piece, arising from the interactions between two heavy quarks within the heavy diquark, the leading nonrelativistic term reads [equation] and in the NRCQM we obtain [equation]

    New Predictions for the Lifetimes of Doubly Heavy Baryons and the $B_c$ Meson · Darwin rhoD3 terms · 0.84

  • An alternative approach [ref] is to relate the Darwin parameter to the matrix elements of the dimension-six spectator contributions by applying the equations of motion for a gluon field, $[D^μ, G_μν] = -i g_s^2 t_a q̅_f t_aγ_νq_f$, where all the repeated indices are summed over, including the index $f$ that denotes the light quark flavours, and the gluon field strength is $G^μν≡[iD^μ,iD^ν]$.

    Lifetimes of singly charmed hadrons · Darwin parameter $(H)$ · 0.92

  • This Heavy Quark Expansion [ref] (see [ref] for reviews) allows to effectively compute the matrix elements in perturbation theory.

    Rare $B$ Decays as Tests of the Standard Model · Theoretical framework · 0.86

Compares with it 1 paper
  • It is instructive to compare the Wilson line definition of the heavy quark jet function with the corresponding definitions for the heavy quark shape function that appears in $B$-decays [ref] , and with the heavy quark fragmentation function [ref] .

    Two-loop Jet-Function and Jet-Mass for Top Quarks · Wilson Loop Representations, and Comparison with the Heavy Quark Shape Function and Fragmentation Function · 0.99

Cites it as support 1 paper
  • our confidence in the model is also based on phenomenological grounds; we have checked it in beauty fragmentation [ref] , where soft contributions are similar to those in $b$ decay[ The soft effects are contained in the initial condition of the $b$ fragmentation function $D^ini$, which has the same resummed expression as the shape function in $b$ decays [ref] . ].

    Inclusive Measure of |V_ub| with the Analytic Coupling Model · Conclusions · 0.98

Cites it as background 23 papers

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