Next-to-leading-order QCD corrections to the radiative decays χbJ→ J/ψ+γ
Abstract
Within nonrelativistic QCD (NRQCD) factorization, we calculate the next-to-leading-order (NLO) QCD corrections to χbJ→ J/ψ+γ with J=0,1,2. We determine all six independent helicity amplitudes, including the one-loop corrections to the QED amplitude and the two-loop corrections to the QCD amplitude, and retain the interference between the QED and QCD amplitudes in the decay widths. The NLO corrections substantially enhance the χb0 and χb1 decay widths, while reducing the χb2 decay width by approximately 36%. Including the QED amplitude leads to sizable destructive interference for χb0 and an enhancement for χb2, but has only a small effect on the χb1 decay width. Two treatments of photon fragmentation, based on the NRQCD matrix element and the experimentally determined J/ψ decay constant, yield NLO unpolarized decay widths that agree at the few percent level or better. Using the decay constant scheme at μR=mb, we obtain NLO central branching fractions of 1.03×10−6, 1.45×10−5, and 1.99×10−6 for the three channels, respectively. The NLO corrections reduce the renormalization scale dependence, particularly for χb2, although a sizable dependence remains for χb0. At fixed mb, the branching fractions decrease with increasing r=mc/mb, more strongly for χb1 and χb2 than for χb0. For pp collisions at √s=14 TeV and an integrated luminosity of 100 fb−1, we estimate about 1.9×104 and 4.8×104 ℓ+ℓ-γ events from χb0 and χb2 decays, respectively. Measurements with the existing Belle Υ(2S) sample remain challenging because of the small expected yields. A larger Υ(2S) sample at Belle II would improve the prospects for observing these radiative decays.
Versions
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BibTeX
@misc{zhang2026nexttoleadingorder,
title = {{Next-to-leading-order QCD corrections to the radiative decays $χ_bJ\to J/ψ+γ$}},
author = {Yu-Dong Zhang and Zai-Fu Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29181},
eprint = {2610.29181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29181},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Next-to-leading-order QCD corrections to the radiative decays χ_bJ→ J/ψ+γ
AU - Yu-Dong Zhang
AU - Zai-Fu Jiang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29181
UR - https://arxiv.org/abs/2610.29181
AB - Within nonrelativistic QCD (NRQCD) factorization, we calculate the next-to-leading-order (NLO) QCD corrections to χ_bJ→ J/ψ+γ with J=0,1,2. We determine all six independent helicity amplitudes, including the one-loop corrections to the QED amplitude and the two-loop corrections to the QCD amplitude, and retain the interference between the QED and QCD amplitudes in the decay widths. The NLO corrections substantially enhance the χ_b0 and χ_b1 decay widths, while reducing the χ_b2 decay width by approximately 36%. Including the QED amplitude leads to sizable destructive interference for χ_b0 and an enhancement for χ_b2, but has only a small effect on the χ_b1 decay width. Two treatments of photon fragmentation, based on the NRQCD matrix element and the experimentally determined J/ψ decay constant, yield NLO unpolarized decay widths that agree at the few percent level or better. Using the decay constant scheme at μ_R=m_b, we obtain NLO central branching fractions of 1.03×10^−6, 1.45×10^−5, and 1.99×10^−6 for the three channels, respectively. The NLO corrections reduce the renormalization scale dependence, particularly for χ_b2, although a sizable dependence remains for χ_b0. At fixed m_b, the branching fractions decrease with increasing r=m_c/m_b, more strongly for χ_b1 and χ_b2 than for χ_b0. For pp collisions at √s=14 TeV and an integrated luminosity of 100 fb^−1, we estimate about 1.9×10^4 and 4.8×10^4 ℓ^+ℓ^-γ events from χ_b0 and χ_b2 decays, respectively. Measurements with the existing Belle Υ(2S) sample remain challenging because of the small expected yields. A larger Υ(2S) sample at Belle II would improve the prospects for observing these radiative decays.
ER -