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We study the $CP$ asymmetry of $B^\pm\to ��K^\pm$ with the inclusion of the $��-��$ mixing mechanism. It is shown that the $CP$ asymmetry of $B^\pm\to��K^\pm$ experimentally measured ($A_{CP}^{\text{exp}}$) and conventionally defined ($A_{CP}^{\text{con}}$) are in fact different, which relation can be illustrated as $A_{CP}^{\text{exp}}=A_{CP}^{\text{con}}+��A_{CP}^{����}$, with $��A_{CP}^{����}$ the $��-��$ mixing contribution to $A_{CP}^{\text{exp}}$. $A_{CP}^{\text{exp}}$ is in fact the regional $CP$ asymmetry of $B^\pm\to��^+��^-��^0 K^\pm$ when the invariant mass of the three pions lies in the vicinity of the $��$ resonance. The numerical value of $��A_{CP}^{����}$ is extracted from the experimental data of $B^\pm\to��^+��^-K^\pm$ and is found to be comparable with $A_{CP}^{\text{exp}}$, hence, nonnegligible. The conventionally defined $CP$ asymmetry, $A_{CP}^{\text{con}}$, is obtained from the values of $A_{CP}^{\text{exp}}$ and $��A_{CP}^{����}$, and is compared with the theoretical calculations in the literature., 8 pages, version accepted by JHEP

In this work, within the QCD factorization approach, we study the localized integrated CP violation in the B−→π−π+π− decay and the branching fraction of the B−→σπ− decay. Both the resonance and nonresonance contributions are included when we study the localized CP asymmetry in the B−→π−π+π− decay. The resonance contributions from the scalar σ(600) and vector ρ0(770) mesons are included. For the σ(600) meson, we apply both the Breit-Wigner and Bugg models to deal with its propagator, and obtain B(B−→σ(600)π−)<1.67×10−6 and B(B−→σ(600)π−)<1.946×10−5 in these two models, respectively. We find that there is no allowed divergence parameters ρS and ϕS to satisfy the experimental data ACP(π−π+π−)=0.584±0.082±0.027±0.007 in the region mπ+π−high2>15 GeV2 and mπ+π−low2<0.4 GeV2 and the upper limit of B(B−→σ(600)π−) in the Breit-Wigner model, however, there exists the region ρS∈[1.70,3.34] and ϕS∈[0.50,4.50] satisfying the data for ACP(π−π+π−) and the upper limit of B(B−→σ(600)π−) in the Bugg model. This reveals that the Bugg model is more plausible than the Breit-Wigner model to describe the propagator of the σ(600) meson even though the finite width effects are considered in both models. The large values of ρS indicate that the contributions from weak annihilation and hard spectator scattering processes are both large, especially, the weak annihilation contribution should not be neglected for B decays to final states including a scalar meson.

In this work, we study the localized CP violation in B−→K−π+π− and B−→K−σ(600) decays by employing the quasi-two-body QCD factorization approach. Both the resonance and the nonresonance contributions are studied for the B−→K−π+π− decay. The resonance contributions include those not only from [ππ] channels including σ(600), ρ0(770) and ω(782) but also from [Kπ] channels including K0*(700)(κ), K*(892), K0*(1430), K*(1410), K*(1680) and K2*(1430). By fitting the four experimental data ACP(K−π+π−)=0.678±0.078±0.0323±0.007 for mK−π+2<15 GeV2 and 0.08

The $��_K$ has been re-evaluated via mass relations and latest experimental results, meanwhile, the $M_{K_{1B}}$ also be obtained. Based on the singlet-octet mixing model and quark-flavor mixing model, the $��_{h_1}$ has been recalculated with a modified formula, by inputting $M_{K_{1B}}$ instead of $��_K$. The values are calculated to be $|{��_K}| = {(42.6 \pm 2.2)^ \circ }$, $M_{K_{1B}} = 1333.9 \pm 4.6\ {\rm{MeV}}/c^{2}$ and $��_{h_1} = 29.5\pm 2.0^\circ$. Using these calculations as input, we predict that the branching fraction of $J/��\to ��'(��)h_1(1170)$ is about one order higher than that of $J/��\to ��'(��)h_1(1415)$, which can be measured in future experiments to test the validity of these two models., 6 pages, with no figure

We study the CP violation induced by the interference between two intermediate resonances K⁎(892)+ and K⁎(892)- in the phase space of singly-Cabibbo-suppressed decay D0→K+K-π0. We adopt the factorization-assisted topological approach in dealing with the decay amplitudes of D0→K±K⁎(892)∓. The CP asymmetries of two-body decays are predicted to be very tiny, which are (-1.27±0.25)×10-5 and (3.86±0.26)×10-5, respectively, for D0→K+K⁎(892)- and D0→K-K⁎(892)+, while the differential CP asymmetry of D0→K+K-π0 is enhanced because of the interference between the two intermediate resonances, which can reach as large as 3×10-4. For some NPs which have considerable impacts on the chromomagnetic dipole operator O8g, the global CP asymmetries of D0→K+K⁎(892)- and D0→K-K⁎(892)+ can be then increased to (0.56±0.08)×10-3 and (-0.50±0.04)×10-3, respectively. The regional CP asymmetry in the overlapped region of the phase space can be as large as (1.3±0.3)×10-3.

Within the QCD factorization approach, we study the CP violations in $$B^-\rightarrow K^-\pi ^+\pi ^-$$ B-→K-π+π- and $$B^-\rightarrow K^- f_0(500)$$ B-→K-f0(500) decays. We find the experimental data of the localized CP asymmetry in $$B^-\rightarrow K^-\pi ^+\pi ^-$$ B-→K-π+π- decays in the region $$m_{K^-\pi ^+}^2mK-π+2<15 $$\mathrm {GeV}^2$$ GeV2 and $$0.080.08

Within the QCD factorization approach, we study the $CP$ violations in $B^-\rightarrow K^-\pi^+\pi^-$ and $B^-\rightarrow K^- f_0(500)$ decays. We find the experimental data of the localized $CP$ asymmetry in $B^-\rightarrow K^-\pi^+\pi^-$ decays in the region $m_{K^-\pi^+}^2, Comment: 13 pages, 4 figures

Figure S1. Grains of NILZS97 and NILMY46 for qGS1-35.2. Scale bar, 20Â mm. (PDF 1936 kb)

Table S1. Gene-specific Primers used for qRT-PCR assays in this study. Table S2. Overview of the high-throughput RNA-seq data of the short-term and long-term nitrogen limitation experiments. Table S3. Evolutionary selection pressure analysis of the BnaNLA family genes. Table S4. Molecular characterization of the BnaNLA family proteins in Brassica napus. Table S5. Molecular characterization of the BnaNRT1.7/BnaNPF2.13 family proteins in Brassica napus. Figure S1. Copy number of the NLA1 and NLA2 family genes in diverse plants species. Figure S2. Hypothetical evolutionary processes and expansion events of the NLA family genes in A. thaliana and Brassica crops. Figure S3. Analysis of phylogenetic relationships and functional divergence of the NLA proteins. Figure S4. Molecular characterization of the expression pattern of BnaNLA2s under different N supply. Figure S5. Hypothetical evolutionary processes and expansion events of the NRT1.7 family genes in A. thaliana and Brassica crops. Figure S6. Analysis of phylogenetic relationships and conserved motifs of the NRT1.7 proteins. (DOCX 855 kb)

We study the $\mathit{CP}$ violation induced by the interference between two intermediate resonances $K^*(892)^+$ and $K^*(892)^-$ in the phase space of singly-Cabibbo-suppressed decay $D^0 \to K^+K^-��^0$. We adopt the factorization-assisted topological approach in dealing with the decay amplitudes of $D^0 \to K^\pm K^*(892)^\mp$. The $\mathit{CP}$ asymmetries of two-body decays are predicted to be very tiny, which are $(-1.27 \pm 0.25) \times 10^{-5}$ and $(3.86 \pm 0.26) \times 10^{-5}$ respectively for $D^0 \to K^+ K^*(892)^-$ and $D^0 \to K^- K^*(892)^+$. While the differential $\mathit{CP}$ asymmetry of $D^0 \to K^+K^-��^0$ is enhanced because of the interference between the two intermediate resonances, which can reach as large as $3\times10^{-4}$. For some NPs which have considerable impacts on the chromomagnetic dipole operator $O_{8g}$, the global $\mathit{CP}$ asymmetries of $D^0 \to K^+ K^*(892)^- $ and $D^0 \to K^- K^*(892)^+ $ can be then increased to $(0.56\pm0.08)\times10^{-3}$ and $(-0.50\pm0.04)\times10^{-3}$, respectively. The regional $\mathit{CP}$ asymmetry in the overlapped region of the phase space can be as large as $( 1.3\pm 0.3)\times10^{-3}$., 24 pages

Table S1. Primers used for population development and QTL mapping. Table S2. Primers used for sequence analysis. Table S3. Primers used for quantitative real-time PCR. Table S4. Nucleotide and amino acid differences between Zhenshan 97 and Milyang 46. (DOCX 23 kb)