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Three-quark ground-state potential in the SU(3) lattice QCD
High Energy Physics - Lattice · Submitted 31 May 2002
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim With accuracy better than a few %, $V_{\rm 3Q}$ is well described by a sum of a constant $C_{\rm 3Q}$, the two-body Coulomb part $-A_{\rm 3Q}\sum_{i<j} \frac1{|{\bf r}_i-{\bf r}_j|}$ and the three-body linear confinement part $\sigma_{\rm 3Q} L_{\rm min}$, where $L_{\rm min}$ denotes the minimal length of the color flux tube linking the three quarks.
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The abstract, sentence by sentence
With the smearing technique, the three-quark (3Q) ground-state potential $V_{\rm 3Q}$ is numerically extracted in the SU(3)$_c$ lattice QCD Monte Carlo simulation with $12^3 \times 24$ and $\beta=5.7$ at the quenched level. With accuracy better than a few %, $V_{\rm 3Q}$ is well described by a sum of a constant $C_{\rm 3Q}$, the two-body Coulomb part $-A_{\rm 3Q}\sum_{i<j} \frac1{|{\bf r}_i-{\bf r}_j|}$ and the three-body linear confinement part $\sigma_{\rm 3Q} L_{\rm min}$, where $L_{\rm min}$ denotes the minimal length of the color flux tube linking the three quarks. By comparing with the Q-$\bar {\rm Q}$ potential, we find a universal feature of the string tension as $\sigma_{\rm 3Q} \simeq \sigma_{\rm Q \bar Q}$ and the one-gluon-exchange result for the Coulomb coefficient as $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$. All our results including the constant term are consistent with the requirement on the diquark limit in the lattice regularization.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | With the smearing technique, the three-quark (3Q) ground-state potential $V_{\rm 3Q}$ is numerically extracted in the SU(3)$_c$ lattice QCD Monte Carlo simulation with $12^3 \times 24$ and $\beta=5.7$ at the quenched level. | method 0.80 | 0.96 | 0.05 | asserted 1.00 |
| s1 | With accuracy better than a few %, $V_{\rm 3Q}$ is well described by a sum of a constant $C_{\rm 3Q}$, the two-body Coulomb part $-A_{\rm 3Q}\sum_{i<j} \frac1{|{\bf r}_i-{\bf r}_j|}$ and the three-body linear confinement part $\sigma_{\rm 3Q} L_{\rm min}$, where $L_{\rm min}$ denotes the minimal length of the color flux tube linking the three quarks. | result 1.00 | 0.94 | 0.57 | asserted 1.00 |
| s2 | By comparing with the Q-$\bar {\rm Q}$ potential, we find a universal feature of the string tension as $\sigma_{\rm 3Q} \simeq \sigma_{\rm Q \bar Q}$ and the one-gluon-exchange result for the Coulomb coefficient as $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$. | result 0.89 | 0.94 | 0.45 | asserted 1.00 |
| s3 | All our results including the constant term are consistent with the requirement on the diquark limit in the lattice regularization. | interpretation 0.67 | 0.85 | 0.10 | hedged possibility 0.63 |
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Original abstract
With the smearing technique, the three-quark (3Q) ground-state potential $V_{\rm 3Q}$ is numerically extracted in the SU(3)$_c$ lattice QCD Monte Carlo simulation with $12^3 \times 24$ and $\beta=5.7$ at the quenched level. With accuracy better than a few %, $V_{\rm 3Q}$ is well described by a sum of a constant $C_{\rm 3Q}$, the two-body Coulomb part $-A_{\rm 3Q}\sum_{i<j} \frac1{|{\bf r}_i-{\bf r}_j|}$ and the three-body linear confinement part $\sigma_{\rm 3Q} L_{\rm min}$, where $L_{\rm min}$ denotes the minimal length of the color flux tube linking the three quarks. By comparing with the Q-$\bar {\rm Q}$ potential, we find a universal feature of the string tension as $\sigma_{\rm 3Q} \simeq \sigma_{\rm Q \bar Q}$ and the one-gluon-exchange result for the Coulomb coefficient as $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$. All our results including the constant term are consistent with the requirement on the diquark limit in the lattice regularization.
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States the same result 1 paper
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The lattice QCD data of $V_{3Q}$ are well reproduced within a few % deviation by a sum of a constant, the two-body Coulomb term and the three-body linear confinement term $\sigma_{3Q} L_{min}$, with $L_{min}$ the minimal value of total length of color flux tubes linking the three quarks.
SU(3) Lattice QCD Study for Static Three-Quark Potential · 0.97
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