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Re-study on the contribution of scalar potential and spectra of $c\bar c$, $b\bar b$ and $b\bar c(\bar b c)$ families
High Energy Physics - Phenomenology · Submitted 2 Dec 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim But the situation is different for QCD, one reason is that the loop effects are more significant because $\alpha_s$ is much larger than $\alpha$, and secondly the non-perturbative QCD effects may induce a sizable scalar potential.
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The abstract, sentence by sentence
We indicated in our previous work that for QED the role of the scalar potential which appears at the loop level is much smaller than that of the vector potential and in fact negligible. But the situation is different for QCD, one reason is that the loop effects are more significant because $\alpha_s$ is much larger than $\alpha$, and secondly the non-perturbative QCD effects may induce a sizable scalar potential. In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia, bottomonia and $b\bar c(\bar b c)$ family. Taking into account both vector and scalar potentials, by fitting the well measured charmonia and bottomonia spectra, we re-fix the relevant parameters and test them by calculating other states of not only the charmonia, bottomonia, but also further the $b\bar c$ family. We also consider the Lamb shift of the spectra.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We indicated in our previous work that for QED the role of the scalar potential which appears at the loop level is much smaller than that of the vector potential and in fact negligible. | background 0.99 | 0.31 | 0.06 | asserted 0.67 |
| s1 | But the situation is different for QCD, one reason is that the loop effects are more significant because $\alpha_s$ is much larger than $\alpha$, and secondly the non-perturbative QCD effects may induce a sizable scalar potential. | background 0.95 | 0.14 | 0.09 | asserted 0.83 |
| s2 | In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia, bottomonia and $b\bar c(\bar b c)$ family. | contribution 1.00 | 0.88 | 0.07 | asserted 0.88 |
| s3 | Taking into account both vector and scalar potentials, by fitting the well measured charmonia and bottomonia spectra, we re-fix the relevant parameters and test them by calculating other states of not only the charmonia, bottomonia, but also further the $b\bar c$ family. | method 0.91 | 0.93 | 0.14 | asserted 0.98 |
| s4 | We also consider the Lamb shift of the spectra. | contribution 0.95 | 0.79 | 0.04 | asserted 0.90 |
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The paper
Original abstract
We indicated in our previous work that for QED the role of the scalar potential which appears at the loop level is much smaller than that of the vector potential and in fact negligible. But the situation is different for QCD, one reason is that the loop effects are more significant because $\alpha_s$ is much larger than $\alpha$, and secondly the non-perturbative QCD effects may induce a sizable scalar potential. In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia, bottomonia and $b\bar c(\bar b c)$ family. Taking into account both vector and scalar potentials, by fitting the well measured charmonia and bottomonia spectra, we re-fix the relevant parameters and test them by calculating other states of not only the charmonia, bottomonia, but also further the $b\bar c$ family. We also consider the Lamb shift of the spectra.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 18 sentences without a confident label
Uses the method or tool of 2 papers
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The authors of [ref] suggest an effective method to deal with the divergence and meanwhile fix the value of $α_s$ (see the text, where we introduce the method in some details for the readers' convenience).
Rigourous QCD Evaluation of Spectrum and Ground State Properties of Heavy Quarkonium Systems; with a Precision Determination of the bottom quark mass and of the eta-b mass · Introduction · 0.99
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The radial equation ([ref]) can be solved in terms of the method so-called “The iterative numerical process” which is introduced in literatures (for example, see [ref] ).
Solving the radial Dirac equations: a numerical odyssey · The Energy Gap Function for The $bb̅$ bottomonia and The numerical Results without taking into account the Lamb shift · 0.99
Uses data or values from 4 papers
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Thus we adopt the value given in [ref] .
Search for $B_c(ns)$ via the $B_c(ns)\to B_c(ms)\pi^+\pi^-$ transition at LHCb and $Z_0$ factory · Introduction · 1.00
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All the constants as $a_1$, $a_2$, $b_1$, $β_i (i=1,2,3)$ are given in Ref. [ref] (also see [ref] ).
The static potential in QCD to two loops · The mass spectra of the bottomonia as the Lamb shift is taken into account · 0.90
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All the constants as $a_1$, $a_2$, $b_1$, $β_i (i=1,2,3)$ are given in Ref. [ref] (also see [ref] ).
Rigourous QCD Evaluation of Spectrum and Ground State Properties of Heavy Quarkonium Systems; with a Precision Determination of the bottom quark mass and of the eta-b mass · The mass spectra of the bottomonia as the Lamb shift is taken into account · 0.90
Compares with 2 papers
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For readers' convenience and a clear comparison, we also list the results for the charmonia which were obtained in our previous work [ref] .
Phenomenological study on the significance of the scalar potential and Lamb shift · The Energy Gap Function for The $bb̅$ bottomonia and The numerical Results without taking into account the Lamb shift · 0.96
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Here we set $α_s=0.284$ and $κ=0.42$ GeV which seem somehow different from the values given in literature [ref] .
Search for $B_c(ns)$ via the $B_c(ns)\to B_c(ms)\pi^+\pi^-$ transition at LHCb and $Z_0$ factory · The Energy Gap Function for The $bb̅$ bottomonia and The numerical Results without taking into account the Lamb shift · 0.86
Cites as support 3 papers
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First because the strong coupling $α_s$ is much larger than $α$, the loop suppression is not as much as for the QED and sometimes the NLO effect of QCD can even exceed the leading order [ref] .
Next-to-Leading-Order QCD Corrections to e^ + e^- -> J/\psi+gg at the B Factories · Introduction · 0.99
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First because the strong coupling $α_s$ is much larger than $α$, the loop suppression is not as much as for the QED and sometimes the NLO effect of QCD can even exceed the leading order [ref] .
Double charm production e^+ e^- \to J/\psi + c \bar{c} at B factories with next-to-leading order QCD corrections · Introduction · 0.99
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That was also suggested by some authors [ref] .
Supersymmetric Patterns in the Pseudospin Spin and Coulomb Limits of the Dirac Equation with Scalar and Vector Potentials · Introduction · 1.00
Cites as background 1 paper
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The subject on heavy quarkonia was thoroughly discussed in an enlightening paper [ref] .
Heavy Quarkonium Physics · Introduction · 1.00
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