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1. Dispersive analysis of $$\eta \rightarrow 3 \pi $$η→3π

   https://doi.org/10.1140/epjc/s10052-018-6377-9  

   Colangelo, Gilberto; Lanz, Stefan; Leutwyler, Heinrich; Passemar, Emilie (November 2018, The European Physical Journal C)
2. Search for CP violation in $$ {D}_{(s)}^{+}\to {h}^{+}{\pi}^0 $$ and $$ {D}_{(s)}^{+}\to {h}^{+}\eta $$ decays

   https://doi.org/10.1007/JHEP06(2021)019  

   Aaij, R.; Abellán Beteta, C.; Ackernley, T.; Adeva, B.; Adinolfi, M.; Afsharnia, H.; Aidala, C. A.; Aiola, S.; Ajaltouni, Z.; Akar, S.; et al (June 2021, Journal of High Energy Physics)

   A bstract Searches for CP violation in the two-body decays $$ {D}_{(s)}^{+}\to {h}^{+}{\pi}^0 $$ D s + → h + π 0 and $$ {D}_{(s)}^{+}\to {h}^{+}\eta $$ D s + → h + η (where h + denotes a π + or K + meson) are performed using pp collision data collected by the LHCb experiment corresponding to either 9 fb − 1 or 6 fb − 1 of integrated luminosity. The π 0 and η mesons are reconstructed using the e + e − γ final state, which can proceed as three-body decays π 0 → e + e − γ and η → e + e − γ , or via the two-body decays π 0 → γγ and η → γγ followed by a photon conversion. The measurements are made relative to the control modes $$ {D}_{(s)}^{+}\to {K}_{\mathrm{S}}^0{h}^{+} $$ D s + → K S 0 h + to cancel the production and detection asymmetries. The CP asymmetries are measured to be $$ {\displaystyle \begin{array}{c}{\mathcal{A}}_{CP}\left({D}^{+}\to {\pi}^{+}{\pi}^0\right)=\left(-1.3\pm 0.9\pm 0.6\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}^{+}\to {K}^{+}{\pi}^0\right)=\left(-3.2\pm 4.7\pm 2.1\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}^{+}\to {\pi}^{+}\eta \right)=\left(-0.2\pm 0.8\pm 0.4\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}^{+}\to {K}^{+}\eta \right)=\left(-6\pm 10\pm 4\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {K}^{+}{\pi}^0\right)=\left(-0.8\pm 3.9\pm 1.2\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {\pi}^{+}\eta \right)=\left(0.8\pm 0.7\pm 0.5\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {K}^{+}\eta \right)=\left(0.9\pm 3.7\pm 1.1\right)\%,\end{array}\end{array}\end{array}\end{array}} $$ A CP D + → π + π 0 = − 1.3 ± 0.9 ± 0.6 % , A CP D + → K + π 0 = − 3.2 ± 4.7 ± 2.1 % , A CP D + → π + η = − 0.2 ± 0.8 ± 0.4 % , A CP D + → K + η = − 6 ± 10 ± 4 % , A CP D s + → K + π 0 = − 0.8 ± 3.9 ± 1.2 % , A CP D s + → π + η = 0.8 ± 0.7 ± 0.5 % , A CP D s + → K + η = 0.9 ± 3.7 ± 1.1 % , where the first uncertainties are statistical and the second systematic. These results are consistent with no CP violation and mostly constitute the most precise measurements of $$ {\mathcal{A}}_{CP} $$ A CP in these decay modes to date. 

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3. Measurements of the branching fractions of $$ {\Xi}_c^0\to {\Xi}^0{\pi}^0 $$, $$ {\Xi}_c^0\to {\Xi}^0\eta $$, and $$ {\Xi}_c^0\to {\Xi}^0{\eta}^{\prime } $$ and asymmetry parameter of $$ {\Xi}_c^0\to {\Xi}^0{\pi}^0 $$

   https://doi.org/10.1007/JHEP10(2024)045  

   Adachi, I; Aggarwal, L; Aihara, H; Akopov, N; Aloisio, A; Althubiti, N; Anh_Ky, N; Asner, D M; Atmacan, H; Aushev, T; et al (October 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We present a study of$$ {\Xi}_c^0\to {\Xi}^0{\pi}^0 $$ ${\Xi }_c^0\to {\Xi }^0{\pi }^0$,$$ {\Xi}_c^0\to {\Xi}^0\eta $$ ${\Xi }_c^0\to {\Xi }^0\eta$, and$$ {\Xi}_c^0\to {\Xi}^0{\eta}^{\prime } $$ ${\Xi }_c^0\to {\Xi }^0{\eta }^{\prime }$decays using the Belle and Belle II data samples, which have integrated luminosities of 980 fb⁻¹and 426 fb⁻¹, respectively. We measure the following relative branching fractions$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0{\pi}^0\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.48\pm 0.02\left(\textrm{stat}\right)\pm 0.03\left(\textrm{syst}\right),\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0\eta \right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.11\pm 0.01\left(\textrm{stat}\right)\pm 0.01\left(\textrm{syst}\right),\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0{\eta}^{\prime}\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.08\pm 0.02\left(\textrm{stat}\right)\pm 0.01\left(\textrm{syst}\right)\end{array}} $$ $\begin{array}{c}B\left({\Xi }_c^0\to {\Xi }^0{\pi }^0\right)/B\left({\Xi }_c^0\to {\Xi }^{-}{\pi }^{+}\right)=0.48\pm 0.02\left(\text{stat}\right)\pm 0.03\left(\text{syst}\right),\\ B\left({\Xi }_c^0\to {\Xi }^0\eta \right)/B\left({\Xi }_c^0\to {\Xi }^{-}{\pi }^{+}\right)=0.11\pm 0.01\left(\text{stat}\right)\pm 0.01\left(\text{syst}\right),\\ B\left({\Xi }_c^0\to {\Xi }^0{\eta }^{\prime }\right)/B\left({\Xi }_c^0\to {\Xi }^{-}{\pi }^{+}\right)=0.08\pm 0.02\left(\text{stat}\right)\pm 0.01\left(\text{syst}\right)\end{array}$ for the first time, where the uncertainties are statistical (stat) and systematic (syst). By multiplying by the branching fraction of the normalization mode,$$ \mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right) $$ $B\left({\Xi }_c^0\to {\Xi }^{-}{\pi }^{+}\right)$, we obtain the following absolute branching fraction results$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0{\pi}^0\right)=\left(6.9\pm 0.3\left(\textrm{stat}\right)\pm 0.5\left(\textrm{syst}\right)\pm 1.3\left(\operatorname{norm}\right)\right)\times {10}^{-3},\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0\eta \right)=\left(1.6\pm 0.2\left(\textrm{stat}\right)\pm 0.2\left(\textrm{syst}\right)\pm 0.3\left(\operatorname{norm}\right)\right)\times {10}^{-3},\\ {}\mathcal{B}\left({\varXi}_c^0\to {\Xi}^0{\eta}^{\prime}\right)=\left(1.2\pm 0.3\left(\textrm{stat}\right)\pm 0.1\left(\textrm{syst}\right)\pm 0.2\left(\operatorname{norm}\right)\right)\times {10}^{-3},\end{array}} $$ $\begin{array}{c}B\left({\Xi }_c^0\to {\Xi }^0{\pi }^0\right)=\left(6.9\pm 0.3\left(\text{stat}\right)\pm 0.5\left(\text{syst}\right)\pm 1.3\left(norm\right)\right)\times {10}^{-3},\\ B\left({\Xi }_c^0\to {\Xi }^0\eta \right)=\left(1.6\pm 0.2\left(\text{stat}\right)\pm 0.2\left(\text{syst}\right)\pm 0.3\left(norm\right)\right)\times {10}^{-3},\\ B\left({\Xi }_c^0\to {\Xi }^0{\eta }^{\prime }\right)=\left(1.2\pm 0.3\left(\text{stat}\right)\pm 0.1\left(\text{syst}\right)\pm 0.2\left(norm\right)\right)\times {10}^{-3},\end{array}$ where the third uncertainties are from$$ \mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right) $$ $B\left({\Xi }_c^0\to {\Xi }^{-}{\pi }^{+}\right)$. The asymmetry parameter for$$ {\Xi}_c^0\to {\Xi}^0{\pi}^0 $$ ${\Xi }_c^0\to {\Xi }^0{\pi }^0$is measured to be$$ \alpha \left({\Xi}_c^0\to {\Xi}^0{\pi}^0\right)=-0.90\pm 0.15\left(\textrm{stat}\right)\pm 0.23\left(\textrm{syst}\right) $$ $\alpha \left({\Xi }_c^0\to {\Xi }^0{\pi }^0\right)=-0.90\pm 0.15\left(\text{stat}\right)\pm 0.23\left(\text{syst}\right)$. 

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4. $$\pi ^{0}$$π0 and $$\eta $$η meson production in proton-proton collisions at $$\sqrt{s}=8$$s=8 TeV

   https://doi.org/10.1140/epjc/s10052-018-5612-8  

   Acharya, S.; Adam, J.; Adamová, D.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, N.; et al (March 2018, The European Physical Journal C)
5. Almost PI algebras are PI

   https://doi.org/10.1090/proc/15818  

   Larsen, Michael; Shalev, Aner (April 2022, Proceedings of the American Mathematical Society)

   We define the notion of an almost polynomial identity of an associative algebra R R , and show that its existence implies the existence of an actual polynomial identity of R R . A similar result is also obtained for Lie algebras and Jordan algebras. We also prove related quantitative results for simple and semisimple algebras. 

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