$\bar{B}_{s,d}^{0} \to J/ψμ^{+}μ^{-}$ Decays in QCD Factorization
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| Format: | Preprint |
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2025
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| _version_ | 1866917470281924608 |
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| author | Li, Xin-Qiang Shi, Yan Yang, Ya-Dong Yuan, Xing-Bo Zhao, Chun-Yang |
| author_facet | Li, Xin-Qiang Shi, Yan Yang, Ya-Dong Yuan, Xing-Bo Zhao, Chun-Yang |
| contents | Motivated by the first LHCb searches for the rare $\bar{B}_{s,d}^{0} \to J/ψμ^{+}μ^{-}$ decays, we perform a detailed study of these processes within the QCD factorization formalism. Since the transverse size of the $J/ψ$ meson is small in the heavy quark mass limit, this formalism is generally expected to hold for these decays. We include both the leading- and next-to-leading-order QCD corrections to the hard-scattering kernels, which are convoluted with the light-cone distribution amplitudes (LCDAs) of the initial- and final-state hadrons. It is numerically found that, depending on the model parameters for the leading-twist $B$-meson LCDA, the maximum branching ratios of $\bar{B}_{s}^{0}\to J/ψμ^{+}μ^{-}$ and $\bar{B}_{d}^{0} \to J/ψμ^{+}μ^{-}$, integrated over the dimuon invariant mass squared $q^2$ from $1\,\mathrm{GeV}^2$ to $(m_{B_{s,d}}-m_{J/ψ})^2$, can reach up to $2.21\times10^{-9}$ and $7.69\times10^{-11}$ at the leading order in $α_s$, respectively. After incorporating the non-factorizable one-loop vertex corrections, these branching ratios are further reduced by about one order of magnitude, with $\mathcal{B}(\bar{B}_{s}^{0} \to J/ψμ^{+}μ^{-})|_{q^2 \geq 1\,\mathrm{GeV}^2}=2.88\times10^{-10}$ and $\mathcal{B}(\bar{B}_{d}^{0} \to J/ψμ^{+}μ^{-})|_{q^2 \geq 1\,\mathrm{GeV}^2}=1.07\times10^{-11}$. In addition, we have presented the dimuon invariant mass distributions of the individual and total helicity amplitudes squared, as well as the differential and integrated longitudinal polarization fractions of the $J/ψ$ meson, which could be probed by the future LHCb and Belle II experiments with more accumulated data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\bar{B}_{s,d}^{0} \to J/ψμ^{+}μ^{-}$ Decays in QCD Factorization Li, Xin-Qiang Shi, Yan Yang, Ya-Dong Yuan, Xing-Bo Zhao, Chun-Yang High Energy Physics - Phenomenology High Energy Physics - Experiment Motivated by the first LHCb searches for the rare $\bar{B}_{s,d}^{0} \to J/ψμ^{+}μ^{-}$ decays, we perform a detailed study of these processes within the QCD factorization formalism. Since the transverse size of the $J/ψ$ meson is small in the heavy quark mass limit, this formalism is generally expected to hold for these decays. We include both the leading- and next-to-leading-order QCD corrections to the hard-scattering kernels, which are convoluted with the light-cone distribution amplitudes (LCDAs) of the initial- and final-state hadrons. It is numerically found that, depending on the model parameters for the leading-twist $B$-meson LCDA, the maximum branching ratios of $\bar{B}_{s}^{0}\to J/ψμ^{+}μ^{-}$ and $\bar{B}_{d}^{0} \to J/ψμ^{+}μ^{-}$, integrated over the dimuon invariant mass squared $q^2$ from $1\,\mathrm{GeV}^2$ to $(m_{B_{s,d}}-m_{J/ψ})^2$, can reach up to $2.21\times10^{-9}$ and $7.69\times10^{-11}$ at the leading order in $α_s$, respectively. After incorporating the non-factorizable one-loop vertex corrections, these branching ratios are further reduced by about one order of magnitude, with $\mathcal{B}(\bar{B}_{s}^{0} \to J/ψμ^{+}μ^{-})|_{q^2 \geq 1\,\mathrm{GeV}^2}=2.88\times10^{-10}$ and $\mathcal{B}(\bar{B}_{d}^{0} \to J/ψμ^{+}μ^{-})|_{q^2 \geq 1\,\mathrm{GeV}^2}=1.07\times10^{-11}$. In addition, we have presented the dimuon invariant mass distributions of the individual and total helicity amplitudes squared, as well as the differential and integrated longitudinal polarization fractions of the $J/ψ$ meson, which could be probed by the future LHCb and Belle II experiments with more accumulated data. |
| title | $\bar{B}_{s,d}^{0} \to J/ψμ^{+}μ^{-}$ Decays in QCD Factorization |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2510.00378 |