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Charm and Bottom Quark Masses from Perturbative QCD
High Energy Physics - Phenomenology · Submitted 1 May 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using a new result for the first moment of the hadronic production cross section at order ${\cal O}(\alpha_s^3)$, and new data on the $J/\psi$ and $\psi'$ resonances for the charm quark, we determine the \msb masses of the charm and bottom quarks to be $\bar{m}_c(\bar{m}_c) = 1.295 \pm 0.015$ GeV and $\bar{m}_b(\bar{m}_b) = 4.205 \pm 0.058$ GeV.
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The abstract, sentence by sentence
Using a new result for the first moment of the hadronic production cross section at order ${\cal O}(\alpha_s^3)$, and new data on the $J/\psi$ and $\psi'$ resonances for the charm quark, we determine the \msb masses of the charm and bottom quarks to be $\bar{m}_c(\bar{m}_c) = 1.295 \pm 0.015$ GeV and $\bar{m}_b(\bar{m}_b) = 4.205 \pm 0.058$ GeV. We assume that the continuum contribution to the sum rules is adequately described by pQCD. While we observe a large reduction of the perturbative error, the shifts induced by the theoretical input are very small. The main change in the central value of $m_c$ is related to the experimental data. On the other hand, the value of $m_b$ is not changed by our calculation to the assumed precision.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Using a new result for the first moment of the hadronic production cross section at order ${\cal O}(\alpha_s^3)$, and new data on the $J/\psi$ and $\psi'$ resonances for the charm quark, we determine the \msb masses of the charm and bottom quarks to be $\bar{m}_c(\bar{m}_c) = 1.295 \pm 0.015$ GeV and $\bar{m}_b(\bar{m}_b) = 4.205 \pm 0.058$ GeV. | result 1.00 | 0.96 | 0.94 | asserted 1.00 |
| s1 | We assume that the continuum contribution to the sum rules is adequately described by pQCD. | method 0.80 | 0.40 | 0.02 | asserted 0.50 |
| s2 | While we observe a large reduction of the perturbative error, the shifts induced by the theoretical input are very small. | interpretation 0.80 | 0.89 | 0.08 | asserted 1.00 |
| s3 | The main change in the central value of $m_c$ is related to the experimental data. | interpretation 0.94 | 0.89 | 0.10 | asserted 1.00 |
| s4 | On the other hand, the value of $m_b$ is not changed by our calculation to the assumed precision. | result 0.78 | 0.90 | 0.10 | asserted 0.99 |
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The paper
Original abstract
Using a new result for the first moment of the hadronic production cross section at order ${\cal O}(\alpha_s^3)$, and new data on the $J/\psi$ and $\psi'$ resonances for the charm quark, we determine the \msb masses of the charm and bottom quarks to be $\bar{m}_c(\bar{m}_c) = 1.295 \pm 0.015$ GeV and $\bar{m}_b(\bar{m}_b) = 4.205 \pm 0.058$ GeV. We assume that the continuum contribution to the sum rules is adequately described by pQCD. While we observe a large reduction of the perturbative error, the shifts induced by the theoretical input are very small. The main change in the central value of $m_c$ is related to the experimental data. On the other hand, the value of $m_b$ is not changed by our calculation to the assumed precision.
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References
How the literature uses it
35 arXiv papers cite this in 52 sentences
Papers citing it · 41 sentences without a confident label
Uses its method or tool 1 paper
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The reduction of hundreds of integrals to master integrals has been achieved, originally for $C_0$ and $C_1$ [ref] , subsequently for $C_2$ and $C_3$, using the program Crusher [ref] .
Massive Tadpoles: Techniques and Applications · SVZ sum rules, moments and tadpoles · 0.91
Uses its data or values 4 papers
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We present coefficients $r_nj$ through $j=3$ in Table [ref] [ref] ; the values for $n=4$–10 are exact, while $r_n3$ is estimated for the others.
High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD · Truncated Perturbation Theory · 0.89
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The coefficients $Ĉ_n$ are known [ref] up to $O(α̂_s^3)$ for $n ≤3$, and up to $O(α̂_s^2)$ for the rest [ref] .
Bottom Quark Mass with Calibrated Uncertainty · Moment sum rules · 0.87
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The four-loop coefficients $C̅_1^(30)$ and $C̅_2^(30)$ for the pseudoscalar correlator are new [ref] ; and $C̅_1^(30)$ for the vector correlator comes from [ref] .
High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD · Appendix A: Continuum perturbation theory · 0.92
Compares with it 1 paper
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Combining in quadrature the three errors in the conversion we obtain for the $MS$ mass [equation] This value is in good agreement with the world average $m = 1.27^+0.07_-0.11$ [ref] but has a larger error than recent determinations using low-$n$ moments [ref] .
The charm quark mass from non-relativistic sum rules · Results · 0.96
Cites it as background 5 papers
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Low moments of heavy-quark correlators are perturbative and several are now known through $(α_s^3)$ in perturbation theory (that is, four-loop order) [ref] .
High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD · Introduction · 0.92
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Previous results: In a number of recent low-$n$ sum rule analyses [ref] based on $O(α_s^3)$ perturbation theory [ref] the constraint $μ_m=μ_α$ was employed.
Charm and Bottom Masses from Sum Rules with a Convergence Test · Introduction · 0.94
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On the other hand, in the limit of small external momentum the so-called moments have been obtained also up to four-loop order [ref] and both $α_s$ and the charm and bottom quark masses could be extracted by comparing to experimental data or lattice simulations [ref] .
Moments of heavy quark correlators with two masses: exact mass dependence to three loops · QCD corrections to current correlators · 0.93
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