Relativistic corrections to Υ(1S,2S)→γη(′) in perturbative QCD
Abstract
We calculate the radiative decays Υ(1S),Υ(2S)→γη(′) in perturbative quantum chromodynamics through order q2 in the relativistic expansion, including the quark-content, two-gluon, and electromagnetic contributions. The quark contribution dominates, with substantial constructive electromagnetic interference and a strongly suppressed gluon contribution. The annihilation rates depend weakly on the tested light-cone distribution amplitudes and light-quark masses. Relativistic corrections reduce the Υ(1S) rates by a few percent but enhance the Υ(2S) rates by approximately 17%--30%. The ratio of the γη′ and γη branching fractions is sensitive to the light-meson mixing parameters, with predictions differing by about a factor of $5$ between two representative schemes. At a scale of half the quarkonium mass, however, the Υ(1S)→γη′ central predictions in the two mixing schemes exceed the experimental upper limit by factors of approximately $5$ and $7$. We also examine the heavy-pseudoscalar admixtures in the light mesons. The ηc contribution is small, whereas ηb mixing can substantially modify the rates through interference. Destructive interference alleviates the discrepancy. With the scale set to the quarkonium mass, the prediction in the mixing scheme inferred from transition form factors is compatible with the upper limit within the input uncertainty.
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BibTeX
@misc{wang2026relativistic,
title = {{Relativistic corrections to $Υ(1S,2S)\rightarrowγη^(\prime)$ in perturbative QCD}},
author = {Cong Wang and Chao-Jie Fan and Jun-Kang He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33662},
eprint = {2610.33662},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33662},
}
RIS
TY - UNPB
TI - Relativistic corrections to Υ(1S,2S)→γη^(′) in perturbative QCD
AU - Cong Wang
AU - Chao-Jie Fan
AU - Jun-Kang He
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33662
UR - https://arxiv.org/abs/2610.33662
AB - We calculate the radiative decays Υ(1S),Υ(2S)→γη^(′) in perturbative quantum chromodynamics through order q^2 in the relativistic expansion, including the quark-content, two-gluon, and electromagnetic contributions. The quark contribution dominates, with substantial constructive electromagnetic interference and a strongly suppressed gluon contribution. The annihilation rates depend weakly on the tested light-cone distribution amplitudes and light-quark masses. Relativistic corrections reduce the Υ(1S) rates by a few percent but enhance the Υ(2S) rates by approximately 17%--30%. The ratio of the γη^′ and γη branching fractions is sensitive to the light-meson mixing parameters, with predictions differing by about a factor of $5$ between two representative schemes. At a scale of half the quarkonium mass, however, the Υ(1S)→γη^′ central predictions in the two mixing schemes exceed the experimental upper limit by factors of approximately $5$ and $7$. We also examine the heavy-pseudoscalar admixtures in the light mesons. The η_c contribution is small, whereas η_b mixing can substantially modify the rates through interference. Destructive interference alleviates the discrepancy. With the scale set to the quarkonium mass, the prediction in the mixing scheme inferred from transition form factors is compatible with the upper limit within the input uncertainty.
ER -