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1. 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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2. The branching fraction of $$ {B}_s^0\to {K}^0{\overline{K}}^0 $$: three puzzles

   https://doi.org/10.1007/JHEP02(2023)113  

   Amhis, Yasmine; Grossman, Yuval; Nir, Yosef (February 2023, Journal of High Energy Physics)

   A bstract The branching fraction of the $$ {B}_s\to {K}^0{\overline{K}}^0 $$ B s → K 0 K ¯ 0 decay has been recently measured by the LHCb and Belle experiments. We study the consistency of the measured value with three relations to other decay rates and CP asymmetries which follow from the Standard Model, and from the approximate flavor SU(3) symmetry of the strong interactions. We find that each of these relations is violated at a level of above 3 σ . We argue that various subleading effects — rescattering, electroweak penguins and SU(3) breaking — if larger than theoretically expected, can account for some of these puzzles, but not for all of them simultaneously. 

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3. Measurements of branching fractions and asymmetry parameters of $$ {\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0} $$, $$ {\Xi}_c^0\to {\Sigma}^0{\overline{K}}^{\ast 0} $$, and $$ {\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast -} $$ decays at Belle

   https://doi.org/10.1007/JHEP06(2021)160  

   Jia, S.; Tang, S. S.; Shen, C. P.; Adachi, I.; Aihara, H.; Al Said, S.; Asner, D. M.; Aulchenko, V.; Aushev, T.; Ayad, R.; et al (June 2021, Journal of High Energy Physics)

   A bstract Using a data sample of 980 fb − 1 collected with the Belle detector at the KEKB asymmetric-energy e + e − collider, we study the processes of $$ {\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0} $$ Ξ c 0 → Λ K ¯ ∗ 0 , $$ {\Xi}_c^0\to {\Sigma}^0{\overline{K}}^{\ast 0} $$ Ξ c 0 → Σ 0 K ¯ ∗ 0 , and $$ {\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast -} $$ Ξ c 0 → Σ + K ∗ − for the first time. The relative branching ratios to the normalization mode of $$ {\Xi}_c^0\to {\Xi}^{-}{\pi}^{+} $$ Ξ c 0 → Ξ − π + are measured to be $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0}\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.18\pm 0.02\left(\mathrm{stat}.\right)\pm 0.01\left(\mathrm{syst}.\right),\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Sigma}^0{\overline{K}}^{\ast 0}\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.69\pm 0.03\left(\mathrm{stat}.\right)\pm 0.03\left(\mathrm{syst}.\right),\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast -}\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.34\pm 0.06\left(\mathrm{stat}.\right)\pm 0.02\left(\mathrm{syst}.\right),\end{array}} $$ B Ξ c 0 → Λ K ¯ ∗ 0 / B Ξ c 0 → Ξ − π + = 0.18 ± 0.02 stat . ± 0.01 syst . , B Ξ c 0 → Σ 0 K ¯ ∗ 0 / B Ξ c 0 → Ξ − π + = 0.69 ± 0.03 stat . ± 0.03 syst . , B Ξ c 0 → Σ + K ∗ − / B Ξ c 0 → Ξ − π + = 0.34 ± 0.06 stat . ± 0.02 syst . , where the uncertainties are statistical and systematic, respectively. We obtain $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0}\right)=\left(3.3\pm 0.3\left(\mathrm{stat}.\right)\pm 0.2\left(\mathrm{syst}.\right)\pm 1.0\left(\mathrm{ref}.\right)\right)\times {10}^{-3},\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Sigma}^0{\overline{K}}^{\ast 0}\right)=\left(12.4\pm 0.5\left(\mathrm{stat}.\right)\pm 0.5\left(\mathrm{syst}.\right)\pm 3.6\left(\mathrm{ref}.\right)\right)\times {10}^{-3},\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast 0}\right)=\left(6.1\pm 1.0\left(\mathrm{stat}.\right)\pm 0.4\left(\mathrm{syst}.\right)\pm 1.8\left(\mathrm{ref}.\right)\right)\times {10}^{-3},\end{array}} $$ B Ξ c 0 → Λ K ¯ ∗ 0 = 3.3 ± 0.3 stat . ± 0.2 syst . ± 1.0 ref . × 10 − 3 , B Ξ c 0 → Σ 0 K ¯ ∗ 0 = 12.4 ± 0.5 stat . ± 0.5 syst . ± 3.6 ref . × 10 − 3 , B Ξ c 0 → Σ + K ∗ 0 = 6.1 ± 1.0 stat . ± 0.4 syst . ± 1.8 ref . × 10 − 3 , where the uncertainties are statistical, systematic, and from $$ \mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right) $$ B Ξ c 0 → Ξ − π + , respectively. The asymmetry parameters $$ \alpha \left({\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0}\right) $$ α Ξ c 0 → Λ K ¯ ∗ 0 and $$ \alpha \left({\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast -}\right) $$ α Ξ c 0 → Σ + K ∗ − are 0 . 15 ± 0 . 22(stat . ) ± 0 . 04(syst . ) and − 0 . 52 ± 0 . 30(stat . ) ± 0 . 02(syst . ), respectively, where the uncertainties are statistical followed by systematic. 

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4. Rationality of forms of M¯0,n$$\overline{{\mathcal {M}}}_{0,n}$$

   https://doi.org/10.1112/jlms.70097  

   Hassett, Brendan; Tschinkel, Yuri; Zhang, Zhijia (February 2025, Journal of the London Mathematical Society)

   Abstract We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points. 

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5. A Proof of the Delta Conjecture When $$\varvec{q=0}$$ q = 0

   https://doi.org/10.1007/s00026-019-00426-x  

   Garsia, Adriano; Haglund, Jim; Remmel, Jeffrey B.; Yoo, Meesue (June 2019, Annals of Combinatorics)