Ground-water hydrology

Broadhurst, W.L.

doi:10.3133/ofr5219

Cited by 17 publications

(57 citation statements)

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“…All-order results, from large-N analyses [9] and DysonSchwinger methods [10], have further strengthened the connection of knot theory and number theory, via field theory. A striking feature of this connection is that the first irreducible MZV of depth 2 occurs at weight 8 [4,11], in accord with the appearance of the first positive 3-braid knot at crossing number 8. Likewise the first irreducible MZV of depth 3 occurs at weight 11 [12], matching the appearance of the first positive 4-braid at 11 crossings, obtained from skeining link diagrams that encode momentum flow in 7-loop counterterms [5].…”

Section: Introductionmentioning

confidence: 77%

“…We follow the economical notation of [3,4,5], referring to a vacuum diagram by a so-called angular diagram [3], which results from choosing one vertex as origin, and indicating all vertices that are connected to this origin by dots, after removing the origin and the propagators connected to it. From such an angular diagram one may uniquely reconstruct the original Feynman diagram.…”

Section: Knot-numbers From Evaluations Of Feynman Diagramsmentioning

confidence: 99%

“…The connection of positive knots with transcendental numbers, via the counterterms of quantum field theory, proposed in [1] and developed in [2], and has been vigorously tested against previous [3,4] and new [5] calculations, entailing knots with up to 11 crossings, related by counterterms with up to 7 loops to numbers that are irreducible multiple zeta values (MZVs) [6,7]. Cancellations of transcendentals in gauge theories have been illuminated by knot theory [8].…”

Section: Introductionmentioning

confidence: 99%

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Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops

Broadhurst¹,

Kreimer²

1997

Physics Letters B

261

321

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It is found that the number, M n , of irreducible multiple zeta values (MZVs) of weight n, is generated by 1 − x 2 − x 3 = n (1 − x n ) Mn . For 9 ≥ n ≥ 3, M n enumerates positive knots with n crossings. Positive knots to which field theory assigns knot-numbers that are not MZVs first appear at 10 crossings. We identify all the positive knots, up to 15 crossings, that are in correspondence with irreducible MZVs, by virtue of the connection between knots and numbers realized by Feynman diagrams with up to 9 loops. * ) Work supported in part by grant CHRX-CT94-0579, from HUCAM.

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Section: Introductionmentioning

confidence: 77%

Section: Knot-numbers From Evaluations Of Feynman Diagramsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops

Broadhurst¹,

Kreimer²

1997

Physics Letters B

261

321

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“…The (pseudo)vector correlator was found in [13], where the results of calculations of absorptive parts [21] were compared and corrected. (See also [16].) The pseudoscalar and pseudovector results were obtained in the scheme with γ 5 anticommuting with all γ µ , by changing the sign of a quark mass in scalar and vector results.…”

Section: Two-loop Perturbative Contributionmentioning

confidence: 99%

“…Mesons with a single heavy quark have been considered in applications of nonrelativistic [10,11], relativistic Borel-transform [12,13,14], and moment-method [15,16,17] QCD sum rules. (A comparison is made in [18].)…”

Section: Introductionmentioning

confidence: 99%

Operator product expansion in static-quark effective field theory. Large perturbative correction

Broadhurst

Grozin²

1992

Physics Letters B

114

113

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We calculate the coefficients of operators with dimensions d ≤ 7 in the operator product expansion of correlators ofqΓQ currents, for the effective field theory of an infinite-mass quark, Q. Exact two-loop results are obtained, with an arbitrary gauge group and spacetime dimension, for the perturbative (d = 0) and quark-condensate (d = 3) contributions, confirming our previous result for the anomalous dimension of the current. Leading-order results are given for light-quark operators with d = 5, 6, 7 and gluon operators with d = 4, 6. The existence of a perturbative correction of order 100% precludes a reliable determination of f B from non-relativistic sum rules.

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The strange quark mass from QCD sum rules

Jamin¹,

Münz

1995

Z. Phys. C - Particles and Fields

127

240

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The strange quark mass is calculated from QCD sum rules for the divergence of the vector as well as axial-vector current in the next-next-to-leading logarithmic approximation. The determination for the divergence of the axial-vector current is found to be unreliable due to large uncertainties in the hadronic parametrisation of the two-point function.From the sum rule for the divergence of the vector current, we obtain a value of m s ≡ m s (1 GeV) = 189 ± 32 MeV, where the error is dominated by the unknown perturbative O(α 3 s ) correction. Assuming a continued geometric growth of the perturbation series, we find m s = 178 ± 18 MeV. Using both determinations of m s , together with quark-mass ratios from chiral perturbation theory, we also give estimates of the light quark masses m u and m d .

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Ground-water hydrology

Cited by 17 publications

References 0 publications

Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops

Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops

Operator product expansion in static-quark effective field theory. Large perturbative correction

The strange quark mass from QCD sum rules

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