2005
DOI: 10.1103/physrevlett.94.072001
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Precise Quark-Mass Dependence of the Instanton Determinant

Abstract: The fermion determinant in an instanton background for a quark field of arbitrary mass is determined exactly using an efficient numerical method to evaluate the determinant of a partial-wave radial differential operator. The bare sum over partial waves is divergent but can be renormalized in the minimal subtraction scheme using the result of WKB analysis of the large partial-wave contribution. Previously, only a few leading terms in the extreme small and large mass limits were known for the corresponding effec… Show more

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Cited by 51 publications
(138 citation statements)
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“…[17,18,19]. Leaving the somewhat involved details of this derivation elsewhere [20], we shall here only report the results for X (2) l,j (s) and X (3) l,j (s) (which are related to the phase shift contributions of respective order by the integral relation of (3.5)):…”
Section: Systematic Wkb Phase-shift Analysismentioning
confidence: 99%
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“…[17,18,19]. Leaving the somewhat involved details of this derivation elsewhere [20], we shall here only report the results for X (2) l,j (s) and X (3) l,j (s) (which are related to the phase shift contributions of respective order by the integral relation of (3.5)):…”
Section: Systematic Wkb Phase-shift Analysismentioning
confidence: 99%
“…This rule regarding what operations should be done first follows [20] by adopting a definition of F (s) as given by the infinite 'energy' cutoff limit (see the remark at the end of Sec. II).…”
Section: Systematic Wkb Phase-shift Analysismentioning
confidence: 99%
“…Recently similar computations have been presented in Ref. [12] using ζ function regularization. A different technique for computing the fluctuation determinant has been used in [13,14,15].…”
Section: Introductionmentioning
confidence: 79%
“…Its normalization, defined by η 0i = N 0 ∇ i φ, and the condition that η 0i is normalized to unity, is given by 12) where there is no summation over i and where T is the kinetic part of the action. Quantization of the collective coordinates yields the prefactor (N −2 0 /2π) 2 = (T /4π) 2 .…”
Section: Basic Relationsmentioning
confidence: 99%
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