Mathematical aspects of the asymptotic expansion in contour improved perturbation theory for hadronic tau decays

Gracia, Néstor G.; Hoang, André H.; Mateu, Vicent

doi:10.1103/physrevd.108.034013

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…In the resummed expression, on the third line, Γ(0, iy g ) is the incomplete gamma function, whose integral expression for a complex second argument can be found in ref. [33]. Using Cauchy's root test is simple to check that the series converges in the entire complex y g plane.…”

Section: Jhep05(2024)146mentioning

confidence: 99%

Secondary massive quarks with the Mellin-Barnes expansion

Bris,

Mateu

2024

J. High Energ. Phys.

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Processes involving only massless or massive quarks at tree-level get corrections from massive (lighter, heavier, or equal-mass) secondary quarks starting at two-loop order, generated by a virtual gluon splitting into a massive quark anti-quark pair. One convenient approach to compute such two-loop corrections is starting with the one-loop diagram considering the virtual gluon massive. Carrying out a dispersive integral with a suitable kernel over the gluon mass yields the desired two-loop result. On the other hand, the Mellin-Barnes representation can be used to compute the expansion of Feynman integrals in powers of a small parameter. In this article we show how to combine these two ideas to obtain the corresponding expansions for large and small secondary quark masses to arbitrarily high orders in a straightforward manner. Furthermore, the convergence radius of both expansions can be shown to overlap, being each series rapidly convergent. The advantage of our method is that the Mellin representation is obtained directly for the full matrix element from the same one-loop computation one needs in large-β0 computations, therefore many existing results can be recycled. With minimal modifications, the strategy can be applied to compute the expansion of the one-loop correction coming from a massive gauge boson. We apply this method to a plethora of examples, in particular those relevant for factorized cross sections involving massless and massive jets, recovering known results and obtaining new ones. Another bonus of our approach is that, postponing the Mellin inversion, one can obtain the small- and large-mas expansions for the RG-evolved jet functions. In many cases, the series can be summed up yielding closed expressions.

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Section: Jhep05(2024)146mentioning

confidence: 99%

Secondary massive quarks with the Mellin-Barnes expansion

Bris,

Mateu

2024

J. High Energ. Phys.

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“…Based on a plausible ansatz for the Borel transform of the series expansion, it was shown that the FOPT series approaches the Borel sum within its ambiguity, while CIPT does not, with the conclusion that CIPT should be abandoned. (A mathematical analysis that explains this behaviour of CIPT has appeared shortly before this talk [8].) Further analysis [9] showed that the numerical difference between FOPT and CIPT is caused by the infrared (IR) renormalon pole related to the gluon condensate in the OPE despite the fact that its contribution to the 𝜏 decay width is suppressed by the weight function that relates the 𝜏 width to the Adler function.…”

Section: Introductionmentioning

confidence: 99%

Gradient-flow renormalon subtraction and the hadronic tau decay series

Beneke,

Takaura

2023

Proceedings of 16th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology — P

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The inconsistency between the fixed-order (FO) and contour-improved (CI) representation of the QCD corrections to the inclusive hadronic tau decay width limits the precision to which the strong coupling can be determined from this process. It has recently been shown that subtracting the infrared renormalon divergence related to the gluon condensate resolves the discrepancy. Here we suggest to employ the gradient flow to define gauge-invariant regularized operators and to use the corresponding condensates in the operator product expansion. The associated rearrangement of the perturbative series results in automatic renormalon subtraction without the need to determine explicitly the Stokes constants that normalize the divergent asymptotic series. Applying this method to the gluon condensate, we find that the CI series is modified and now agrees with the (unmodified) FO series. This conclusively demonstrates the preference for the fixed-order approach, as has been advocated long ago.

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Renormalization group improved determination of light quark masses from Borel-Laplace sum rules

Khan

2023

Phys. Rev. D

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Mathematical aspects of the asymptotic expansion in contour improved perturbation theory for hadronic tau decays

Cited by 4 publications

References 22 publications

Secondary massive quarks with the Mellin-Barnes expansion

Secondary massive quarks with the Mellin-Barnes expansion

Gradient-flow renormalon subtraction and the hadronic tau decay series

Renormalization group improved determination of light quark masses from Borel-Laplace sum rules

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