Noncommutative probability, matrix models, and quantum orbifold geometry

Lee, C.-W. H.

doi:10.1088/1126-6708/2003/06/044

Cited by 4 publications

(9 citation statements)

References 32 publications

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“…The b = 1/2 renormalon of m q [14] has a residue that has been determined with a reasonably high precision [15,16], due to a good convergence behaviour of the series for the residue. First the calculation of this residue will be re-done, focusing on the resulting uncertainties.…”

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confidence: 99%

Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation

Cvetič¹

2004

J. Phys. G: Nucl. Part. Phys.

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It had been known that the Borel transforms of the twice quark pole mass 2mq and of the QCD q-q static potential V (r) have leading infrared renormalons at b = 1/2 such that they cancel in the sum. The renormalon residue of 2mq had been determined with reasonably high precision from the known perturbative coefficients of the ratio mq/mq, where mq is the MS renormalon-free mass of the quark q. These values of the residues are used here to estimate the hitherto unknown part of the three-loop coefficient of the static potential V (r). Further, the method takes into account the fact that the ultrasoft energy regime contributions must be excluded from the analysis. In the bb quarkonium, aforementioned estimated part of the three-loop term turns out to give a contribution to the binding energy comparable to the nonpertubative contribution. This is the version v3 as it will appear in J. Phys. G. The changes in comparison to the previous version: the first paragraph is new; the paragraph containing Eqs. (31)-(32) is new, as is Table I; the last paragraph (before Acknowledgments) is new; some new references were added. Numerical results are unchanged.

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confidence: 99%

Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation

Cvetič¹

2004

J. Phys. G: Nucl. Part. Phys.

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“…Like the models we studied in Ref. [8], the dual of the Feynman diagrams of this model in the double large-N limit in which we take N v to infinity first and N m to infinity afterwards may be identified as quadrangulated surfaces of the orbifold R 2 /Z 2 × Z 2 . Note that the expression…”

Section: Introductionmentioning

confidence: 94%

“…The worldsheets involved are orbifolded and respect a Z 2 symmetry which interchanges left-and right-movers. Recently, we have discovered a family of matrix-vector models which not only serve as examples of noncommutative probability of type B [7] but also may be used to study models of orbifolded string worldsheets [8]. The basic ingredients of these models are vectors of square matrices of Grassmann numbers.…”

Section: Introductionmentioning

confidence: 99%

Multicritical matrix-vector models of quantum orbifold geometry

Lee¹

2003

J. High Energy Phys.

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We construct bosonic and fermionic matrix-vector models which describe orbifolded string worldsheets at a limit in which the dimension of the vector space and the matrix order are taken to infinity. We evaluate tree-level one-loop or multiloop amplitudes of these string worldsheets by means of Schwinger-Dyson equations and derive their expressions at the multicritical points. Some of these amplitudes resemble or are closely related to those of ordinary multicritical Hermitian matrix models by a constant factor, whereas some differ significantly.

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“…The difference between the quark mass and the pole mass is considered as an imaginary part (which is a multiple of QCD ) [7]:…”

Section: Ms and Pole Massmentioning

confidence: 99%

“…One of the results of analyzing the heavy quark spectrum is that the position of the pole in the propagator is considered as the pole mass [4]. The difference between the quark mass and the pole mass is considered as an imaginary part (which is a multiple of Λ QCD ) [6]:…”

Section: Introductionmentioning

confidence: 99%

Description of Heavy Quark $\overline{MS}$ Mass by Lippmann-Schwinger Equation

2012

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Quark masses are of great prominence in high-energy physics. In this paper, we have studied the heavy meson systems via solving the Lippmann-Schwinger equation by using the Martin potential for heavy quark masses. We have also attempted to use Martin potential to find an acceptable mass spectrum for heavy quarkonia. We obtained this spectrum via minimal phenomenological model (Melles in Phys. Rev. D. 62:074019, 2000).The mass spectra for bb and cc are calculated without taking into account the relativistic corrections and spin-dependent effects. The obtained mass spectra turn out to fit the experimental findings. By using the conventional spectrum, we extract the pole mass of heavy quarks and use it along with the relation between MS mass (modified minimal subtraction scheme) and the on-shell quark mass to find MS mass for these quarks. The obtained results for MS mass are in good agreement with corresponding values reported in the literature.

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Noncommutative probability, matrix models, and quantum orbifold geometry

Cited by 4 publications

References 32 publications

Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation

Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation

Multicritical matrix-vector models of quantum orbifold geometry

Description of Heavy Quark $\overline{MS}$ Mass by Lippmann-Schwinger Equation

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