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1. Experimental study of the $$ \gamma p \rightarrow K^{0}\Sigma^{+}$$, $$ \gamma n \rightarrow K^{0} \Lambda$$, and $$ \gamma n \rightarrow K^{0} \Sigma^{0}$$ reactions at the Mainz Microtron

   https://doi.org/10.1140/epja/i2019-12924-x  

   Akondi, C. S.; Bantawa, K.; Manley, D. M.; Abt, S.; Achenbach, P.; Afzal, F.; Aguar-Bartolomé, P.; Ahmed, Z.; Annand, J. R.; Arends, H. J.; et al (November 2019, The European Physical Journal A)

   null (Ed.)

   Abstract. This work measured $$ \mathrm{d}\sigma/\mathrm{d}\Omega$$ d σ / d Ω for neutral kaon photoproduction reactions from threshold up to a c.m. energy of 1855MeV, focussing specifically on the $$ \gamma p\rightarrow K^0\Sigma^+$$ γ p → K 0 Σ + , $$ \gamma n\rightarrow K^0\Lambda$$ γ n → K 0 Λ , and $$ \gamma n\rightarrow K^0 \Sigma^0$$ γ n → K 0 Σ 0 reactions. Our results for $$ \gamma n\rightarrow K^0 \Sigma^0$$ γ n → K 0 Σ 0 are the first-ever measurements for that reaction. These data will provide insight into the properties of $$ N^{\ast}$$ N * resonances and, in particular, will lead to an improved knowledge about those states that couple only weakly to the $$ \pi N$$ π N channel. Integrated cross sections were extracted by fitting the differential cross sections for each reaction as a series of Legendre polynomials and our results are compared with prior experimental results and theoretical predictions. 

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2. 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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3. Limiting Betti distributions of Hilbert schemes on n points

   https://doi.org/10.4153/S0008439522000261  

   Griffin, Michael; Ono, Ken; Rolen, Larry; Tsai, Wei-Lun (March 2023, Canadian Mathematical Bulletin)

   Abstract Hausel and Rodriguez-Villegas (2015, Astérisque 370, 113–156) recently observed that work of Göttsche, combined with a classical result of Erdös and Lehner on integer partitions, implies that the limiting Betti distribution for the Hilbert schemes $$(\mathbb {C}^{2})^{[n]}$$ on $$n$$ points, as $$n\rightarrow +\infty ,$$ is a Gumbel distribution . In view of this example, they ask for further such Betti distributions. We answer this question for the quasihomogeneous Hilbert schemes $$((\mathbb {C}^{2})^{[n]})^{T_{\alpha ,\beta }}$$ that are cut out by torus actions. We prove that their limiting distributions are also of Gumbel type. To obtain this result, we combine work of Buryak, Feigin, and Nakajima on these Hilbert schemes with our generalization of the result of Erdös and Lehner, which gives the distribution of the number of parts in partitions that are multiples of a fixed integer $$A\geq 2.$$ Furthermore, if $$p_{k}(A;n)$$ denotes the number of partitions of $$n$$ with exactly $$k$$ parts that are multiples of $$A$$ , then we obtain the asymptotic $$ \begin{align*} p_{k}(A,n)\sim \frac{24^{\frac k2-\frac14}(n-Ak)^{\frac k2-\frac34}}{\sqrt2\left(1-\frac1A\right)^{\frac k2-\frac14}k!A^{k+\frac12}(2\pi)^{k}}e^{2\pi\sqrt{\frac1{6}\left(1-\frac1A\right)(n-Ak)}}, \end{align*} $$ a result which is of independent interest. 

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4. Universality for 1d Random Band Matrices: Sigma-Model Approximation

   https://doi.org/10.1007/s10955-018-1969-1  

   Shcherbina, Mariya; Shcherbina, Tatyana (January 2018, Journal of Statistical Physics)

   The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233–1260, 2016; Commun Math Phys 351:1009–1044, 2017). We consider random Hermitian block band matrices consisting of $$W\times W$$ random Gaussian blocks (parametrized by $$j,k \in\Lambda=[1,n]^d\cap \mathbb{Z}^d$$) with a fixed entry's variance $$J_{jk}=\delta_{j,k}W^{-1}+\beta\Delta_{j,k}W^{-2}$$, $$\beta>0$$ in each block. Taking the limit $$W\to\infty$$ with fixed $$n$$ and $$\beta$$, we derive the sigma-model approximation of the second correlation function similar to Efetov's one. Then, considering the limit $$\beta, n\to\infty$$, we prove that in the dimension $d=1$ the behaviour of the sigma-model approximation in the bulk of the spectrum, as $$\beta\gg n$$, is determined by the classical Wigner -- Dyson statistics. 

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5. Observation of B$$^0$$ $$\rightarrow $$ $$\uppsi $$(2S)K$$^0_\mathrm {S}\uppi ^+\uppi ^-$$ and B$$^0_\mathrm {s}$$ $$\rightarrow $$ $$\uppsi $$(2S)K$$^0_\mathrm {S}$$ decays

   https://doi.org/10.1140/epjc/s10052-022-10315-y  

   Tumasyan, A.; Adam, W.; Andrejkovic, J. W.; Bergauer, T.; Chatterjee, S.; Damanakis, K.; Dragicevic, M.; Valle, A. Escalante; Frühwirth, R.; Jeitler, M.; et al (May 2022, The European Physical Journal C)

   Abstract Using a data sample of $$\sqrt{s}=13\,\text {TeV}$$ s = 13 TeV proton-proton collisions collected by the CMS experiment at the LHC in 2017 and 2018 with an integrated luminosity of $$103\text {~fb}^{-1}$$ 103 fb - 1 , the $$\text {B}^{0}_{\mathrm{s}} \rightarrow \uppsi (\text {2S})\text {K}_\mathrm{S}^{0}$$ B s 0 → ψ ( 2S ) K S 0 and $$\text {B}^{0} \rightarrow \uppsi (\text {2S})\text {K}_\mathrm{S}^{0} \uppi ^+\uppi ^-$$ B 0 → ψ ( 2S ) K S 0 π + π - decays are observed with significances exceeding 5 standard deviations. The resulting branching fraction ratios, measured for the first time, correspond to $${\mathcal {B}}(\text {B}^{0}_{\mathrm{s}} \rightarrow \uppsi (\text {2S})K_\mathrm{S}^{0})/{\mathcal {B}}(\text {B}^{0}\rightarrow \uppsi (\text {2S})K_\mathrm{S}^{0}) = (3.33 \pm 0.69 (\text {stat})\, \pm 0.11\,(\text {syst}) \pm 0.34\,(f_{\mathrm{s}}/f_{\mathrm{d}})) \times 10^{-2}$$ B ( B s 0 → ψ ( 2S ) K S 0 ) / B ( B 0 → ψ ( 2S ) K S 0 ) = ( 3.33 ± 0.69 ( stat ) ± 0.11 ( syst ) ± 0.34 ( f s / f d ) ) × 10 - 2 and $${\mathcal {B}}(\text {B}^{0} \rightarrow \uppsi (\text {2S})\text {K}_\mathrm{S}^{0} \uppi ^{+} \uppi ^{-})/ {\mathcal {B}}(\text {B}^{0} \rightarrow \uppsi (\text {2S})\text {K}^{0}_{\mathrm{S}}) = 0.480 \pm 0.013\,(\text {stat}) \pm 0.032\,(\text {syst})$$ B ( B 0 → ψ ( 2S ) K S 0 π + π - ) / B ( B 0 → ψ ( 2S ) K S 0 ) = 0.480 ± 0.013 ( stat ) ± 0.032 ( syst ) , where the last uncertainty in the first ratio is related to the uncertainty in the ratio of production cross sections of $$\hbox {B}^{0}_{\mathrm{s}}$$ B s 0 and $$\hbox {B}^{0}$$ B 0 mesons, $$f_{\mathrm{s}}/f_{\mathrm{d}}$$ f s / f d . 

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