$CP$-violating observables of four-body $B_{(s)} \to (ππ)(K\bar{K})$ decays in perturbative QCD
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| Format: | Preprint |
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2024
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| _version_ | 1866911869419126784 |
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| author | Yan, Da-Cheng Yan, Yan Rui, Zhou |
| author_facet | Yan, Da-Cheng Yan, Yan Rui, Zhou |
| contents | In this work, we investigate six helicity amplitudes of the four-body $B_{(s)} \to (ππ)(K\bar{K})$ decays in the perturbative QCD (PQCD) approach. The $ππ$ invariant mass spectrum is dominated by the vector resonance $ρ(770)$ together with scalar resonance $f_0(980)$, while the vector resonance $ϕ(1020)$ and scalar resonance $f_0(980)$ are expected to contribute in the $K\bar{K}$ invariant mass range. We extract the two-body branching ratios ${\cal B}(B_{(s)}\to ρϕ)$ from the corresponding four-body decays $B_{(s)}\to ρϕ\to (ππ)(K \bar K)$. The predicted ${\cal B}(B^0_{s}\to ρϕ)$ agrees well with the current experimental data within errors. The longitudinal polarization fractions of the $B_{(s)}\to ρϕ$ decays are found to be as large as $90\%$, basically consistent with the previous two-body predictions within uncertainties. In addition, the triple-product asymmetries (TPAs) of the considered decays are also presented for the first time. Since the $B_s^0\to ρ^0ϕ\to(π^+π^-)(K^+K^-)$ decay is induced by both tree and penguin operators, the values of the ${\cal A}^{\rm CP}_{\rm dir}$ and ${\cal A}^{1}_{\text{T-true}}$ are calculated to be $(21.8^{+2.7}_{-3.3})\%$ and $(-10.23^{+1.73}_{-1.56})\%$ respectively. While for pure penguin decays $B^0\to ρ^0ϕ\to(π^+π^-)(K^+K^-)$ and $B^+\to ρ^+ϕ\to(π^+π^0)(K^+K^-)$, both the direct $CP$ asymmetries and ``true" TPAs are naturally expected to be zero in the standard model (SM). The ``fake" TPAs requiring no weak phase difference are usually none zero for all considered decay channels. The sizable ``fake" ${\cal A}^{1}_{\text{T-fake}}=(-20.92^{+6.26}_{-2.80})\%$ of the $B^0\to ρ^0ϕ\to(π^+π^-)(K^+K^-)$ decay is predicted in the PQCD approach, which provides valuable information on the final-state interactions.Our predictions can be tested by the future experiments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_19198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $CP$-violating observables of four-body $B_{(s)} \to (ππ)(K\bar{K})$ decays in perturbative QCD Yan, Da-Cheng Yan, Yan Rui, Zhou High Energy Physics - Phenomenology In this work, we investigate six helicity amplitudes of the four-body $B_{(s)} \to (ππ)(K\bar{K})$ decays in the perturbative QCD (PQCD) approach. The $ππ$ invariant mass spectrum is dominated by the vector resonance $ρ(770)$ together with scalar resonance $f_0(980)$, while the vector resonance $ϕ(1020)$ and scalar resonance $f_0(980)$ are expected to contribute in the $K\bar{K}$ invariant mass range. We extract the two-body branching ratios ${\cal B}(B_{(s)}\to ρϕ)$ from the corresponding four-body decays $B_{(s)}\to ρϕ\to (ππ)(K \bar K)$. The predicted ${\cal B}(B^0_{s}\to ρϕ)$ agrees well with the current experimental data within errors. The longitudinal polarization fractions of the $B_{(s)}\to ρϕ$ decays are found to be as large as $90\%$, basically consistent with the previous two-body predictions within uncertainties. In addition, the triple-product asymmetries (TPAs) of the considered decays are also presented for the first time. Since the $B_s^0\to ρ^0ϕ\to(π^+π^-)(K^+K^-)$ decay is induced by both tree and penguin operators, the values of the ${\cal A}^{\rm CP}_{\rm dir}$ and ${\cal A}^{1}_{\text{T-true}}$ are calculated to be $(21.8^{+2.7}_{-3.3})\%$ and $(-10.23^{+1.73}_{-1.56})\%$ respectively. While for pure penguin decays $B^0\to ρ^0ϕ\to(π^+π^-)(K^+K^-)$ and $B^+\to ρ^+ϕ\to(π^+π^0)(K^+K^-)$, both the direct $CP$ asymmetries and ``true" TPAs are naturally expected to be zero in the standard model (SM). The ``fake" TPAs requiring no weak phase difference are usually none zero for all considered decay channels. The sizable ``fake" ${\cal A}^{1}_{\text{T-fake}}=(-20.92^{+6.26}_{-2.80})\%$ of the $B^0\to ρ^0ϕ\to(π^+π^-)(K^+K^-)$ decay is predicted in the PQCD approach, which provides valuable information on the final-state interactions.Our predictions can be tested by the future experiments. |
| title | $CP$-violating observables of four-body $B_{(s)} \to (ππ)(K\bar{K})$ decays in perturbative QCD |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2404.19198 |