Cross-Moment Consistency and the Fifth Adler Coefficient in Hadronic Tau Decays
Abstract
The unknown coefficient c5,1 controls the first omitted fifth-order term in fixed-order analyses of inclusive hadronic τ decays. We determine what the four known Adler coefficients can actually test. For any normalized polynomial weight, the fixed-order Adler-to-moment map is triangular with unit diagonal. Hence one common Adler-coefficient error reaches every moment with the same absolute size, and a multi-weight relative test reduces to one absolute tolerance. For three representative weights, a ten-percent test resolves c5,1 only to about ±24; the closest contour-improved test is weaker by more than an order of magnitude. Moreover, any continuation that preserves the observed sign of the direct Padé/Shanks defects gives c5,1≥378.03, so values near $280$ require additional structure. A calibration-and-falsification protocol applied to a simplified Beneke--Jamin-type pure-power ansatz gives the conditional estimate c5,1=248±30 (struct)±74 (method)=248±80. At the physical order its central value coincides algebraically with the exact four-parameter fit; the protocol adds a falsifiable admissibility test and a method uncertainty, not new coefficient information. We also clarify that the often-quoted Beneke--Jamin value $283$ is a linear extrapolation of total-width FOPT te
Related
BibTeX
@misc{abbas2026crossmoment,
title = {{Cross-Moment Consistency and the Fifth Adler Coefficient in Hadronic Tau Decays}},
author = {Gauhar Abbas and Debabina Biswas and Pratham Dadhich and Vartika Singh},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06824},
eprint = {2611.06824},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06824},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cross-Moment Consistency and the Fifth Adler Coefficient in Hadronic Tau Decays
AU - Gauhar Abbas
AU - Debabina Biswas
AU - Pratham Dadhich
AU - Vartika Singh
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06824
UR - https://arxiv.org/abs/2611.06824
AB - The unknown coefficient c_5,1 controls the first omitted fifth-order term in fixed-order analyses of inclusive hadronic τ decays. We determine what the four known Adler coefficients can actually test. For any normalized polynomial weight, the fixed-order Adler-to-moment map is triangular with unit diagonal. Hence one common Adler-coefficient error reaches every moment with the same absolute size, and a multi-weight relative test reduces to one absolute tolerance. For three representative weights, a ten-percent test resolves c_5,1 only to about ±24; the closest contour-improved test is weaker by more than an order of magnitude. Moreover, any continuation that preserves the observed sign of the direct Padé/Shanks defects gives c_5,1≥378.03, so values near $280$ require additional structure. A calibration-and-falsification protocol applied to a simplified Beneke--Jamin-type pure-power ansatz gives the conditional estimate c_5,1=248±30 (struct)±74 (method)=248±80. At the physical order its central value coincides algebraically with the exact four-parameter fit; the protocol adds a falsifiable admissibility test and a method uncertainty, not new coefficient information. We also clarify that the often-quoted Beneke--Jamin value $283$ is a linear extrapolation of total-width FOPT te
ER -