Bounds on hadronic contributions to the anomalous magnetic moment of the τ lepton from QCD Sum Rules
Abstract
A QCD sum-rule study is performed to place bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the τ lepton (aτHVP, LO, aτ= (g−2)τ/2). The QCD contributions to aτHVP, LO are modeled as a combination of Laplace QCD sum rules (LSRs) and finite-energy QCD sum rules (FESRs) of various weights, which are bounded by Hölder and related fundamental inequalities. The light-quark (u, d, s) contributions are evaluated up to five-loop order in perturbative contributions in the chiral limit, LO in light quark mass corrections, next-to-leading order (NLO) in dimension-four QCD condensates and to LO in dimension-six QCD condensates. Extending previous work on aμHVP, LO, we present a robust methodology for using QCD sum rules to constrain aτHVP, LO, and more generally any lepton g−2. A criterion is developed to extract from the bounds analysis a final result of aτQCD = ( 3.385± 0.048 ) × 10−6, which after inclusion of charmonium and bottomonium contributions gives a final result aτHVP, LO = ( 3.501±0.048) × 10−6, comparable to data-driven and lattice predictions. Lattice QCD results along with our value for aτHVP, LO are used to obtain a combined QCD determination from lattice and sum-rule methods of aμHVP, LO = (7.217±0.233)×10−8. Our analysis provides fundamental QCD sum-rule inputs into the theoretical determinations of aτ, and establishes new methodologies for QCD sum-rule determinations of low-energy observables.
Related
- The hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment in isospin-symmetric lattice QCD with twisted-mass fermions
- The anomalous magnetic moment of the muon in the Standard Model: an update
- Neutral Pseudoscalar Mesons, Hadron Light-by-Light Scattering, and the Muon Anomalous Magnetic Moment
- Measurement of the γγ→ ττ cross section and constraints on the anomalous magnetic moment of the τ lepton in ultraperipheral PbPb collisions at √(sNN) = 5.02 TeV
- Implications of the muon anomalous magnetic moment in a doublet left-right symmetric model
BibTeX
@misc{li2026bounds,
title = {{Bounds on hadronic contributions to the anomalous magnetic moment of the $τ$ lepton from QCD Sum Rules}},
author = {Siyuan Li and J. Ho and R. T. Kleiv and D. Leighton and E. J. Obbink and T. G. Steele},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20945},
eprint = {2610.20945},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20945},
}
RIS
TY - UNPB
TI - Bounds on hadronic contributions to the anomalous magnetic moment of the τ lepton from QCD Sum Rules
AU - Siyuan Li
AU - J. Ho
AU - R. T. Kleiv
AU - D. Leighton
AU - E. J. Obbink
AU - T. G. Steele
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20945
UR - https://arxiv.org/abs/2610.20945
AB - A QCD sum-rule study is performed to place bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the τ lepton (a_τ^HVP, LO, a_τ= (g−2)_τ/2). The QCD contributions to a_τ^HVP, LO are modeled as a combination of Laplace QCD sum rules (LSRs) and finite-energy QCD sum rules (FESRs) of various weights, which are bounded by Hölder and related fundamental inequalities. The light-quark (u, d, s) contributions are evaluated up to five-loop order in perturbative contributions in the chiral limit, LO in light quark mass corrections, next-to-leading order (NLO) in dimension-four QCD condensates and to LO in dimension-six QCD condensates. Extending previous work on a_μ^HVP, LO, we present a robust methodology for using QCD sum rules to constrain a_τ^HVP, LO, and more generally any lepton g−2. A criterion is developed to extract from the bounds analysis a final result of a_τ^QCD = ( 3.385± 0.048 ) × 10^−6, which after inclusion of charmonium and bottomonium contributions gives a final result a_τ^HVP, LO = ( 3.501±0.048) × 10^−6, comparable to data-driven and lattice predictions. Lattice QCD results along with our value for a_τ^HVP, LO are used to obtain a combined QCD determination from lattice and sum-rule methods of a_μ^HVP, LO = (7.217±0.233)×10^−8. Our analysis provides fundamental QCD sum-rule inputs into the theoretical determinations of a_τ, and establishes new methodologies for QCD sum-rule determinations of low-energy observables.
ER -