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1. 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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2. Evidence for the singly Cabibbo-suppressed decay $$ {\Omega}_c^0\to {\Xi}^{-}{\pi}^{+} $$ and search for $$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$ and Ω−K+ decays at Belle

   https://doi.org/10.1007/JHEP01(2023)055  

   Han, X.; Jia, S.; Yuan, L.; Shen, C. P.; Adachi, I.; Ahn, J. K.; Aihara, H.; Asner, D. M.; Aushev, T.; Ayad, R.; et al (January 2023, 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 for the first time the singly Cabibbo-suppressed decays $$ {\Omega}_c^0\to {\Xi}^{-}{\pi}^{+} $$ Ω c 0 → Ξ − π + and Ω − K + and the doubly Cabibbo-suppressed decay $$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$ Ω c 0 → Ξ − K + . Evidence for an $$ {\Omega}_c^0 $$ Ω c 0 signal in the $$ {\Omega}_c^0 $$ Ω c 0 → Ξ − π + mode is reported with a significance of 4 . 5 σ including systematic uncertainties. The ratio of branching fractions to the normalization mode $$ {\Omega}_c^0 $$ Ω c 0 → Ω − π + is measured to be $$ \mathcal{B}\left({\Omega}_c^0\to {\Xi}^{-}{\pi}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)=0.253\pm 0.052\left(\textrm{stat}.\right)\pm 0.030\left(\textrm{syst}.\right). $$ B Ω c 0 → Ξ − π + / B Ω c 0 → Ω − π + = 0.253 ± 0.052 stat . ± 0.030 syst . . No significant signals of $$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$ Ω c 0 → Ξ − K + and Ω − K + modes are found. The upper limits at 90% confidence level on ratios of branching fractions are determined to be $$ \mathcal{B}\left({\Omega}_c^0\to {\Xi}^{-}{K}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)<0.070 $$ B Ω c 0 → Ξ − K + / B Ω c 0 → Ω − π + < 0.070 and $$ \mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{K}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)<0.29. $$ B Ω c 0 → Ω − K + / B Ω c 0 → Ω − π + < 0.29 . 

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3. Azimuthal correlations of prompt D mesons with charged particles in pp and p–Pb collisions at $$\varvec{\sqrt{s_\mathrm{NN}}} = 5.02\ \hbox {TeV}$$

   https://doi.org/10.1140/epjc/s10052-020-8118-0  

   Acharya, S.; Adamová, D.; Adler, A.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; et al (October 2020, The European Physical Journal C)

   null (Ed.)

   Abstract The measurement of the azimuthal-correlation function of prompt D mesons with charged particles in pp collisions at $$\sqrt{s} =5.02\ \hbox {TeV}$$ s = 5.02 TeV and p–Pb collisions at $$\sqrt{s_{\mathrm{NN}}} = 5.02\ \hbox {TeV}$$ s NN = 5.02 TeV with the ALICE detector at the LHC is reported. The $$\mathrm{D}^{0}$$ D 0 , $$\mathrm{D}^{+} $$ D + , and $$\mathrm{D}^{*+} $$ D ∗ + mesons, together with their charge conjugates, were reconstructed at midrapidity in the transverse momentum interval $$3< p_\mathrm{T} < 24\ \hbox {GeV}/c$$ 3 < p T < 24 GeV / c and correlated with charged particles having $$p_\mathrm{T} > 0.3\ \hbox {GeV}/c$$ p T > 0.3 GeV / c and pseudorapidity $$|\eta | < 0.8$$ | η | < 0.8 . The properties of the correlation peaks appearing in the near- and away-side regions (for $$\Delta \varphi \approx 0$$ Δ φ ≈ 0 and $$\Delta \varphi \approx \pi $$ Δ φ ≈ π , respectively) were extracted via a fit to the azimuthal correlation functions. The shape of the correlation functions and the near- and away-side peak features are found to be consistent in pp and p–Pb collisions, showing no modifications due to nuclear effects within uncertainties. The results are compared with predictions from Monte Carlo simulations performed with the PYTHIA, POWHEG+PYTHIA, HERWIG, and EPOS 3 event generators. 

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4. Large-time behavior of solutions of parabolic equations on the real line with convergent initial data III: unstable limit at infinity

   Pauthier, Antoine; Poláčik, Peter (August 2022, Partial Differential Equations and Applications)

   Abstract This is a continuation, and conclusion, of our study of bounded solutions u of the semilinear parabolic equation $$u_t=u_{xx}+f(u)$$ u t = u xx + f ( u ) on the real line whose initial data $$u_0=u(\cdot ,0)$$ u 0 = u ( · , 0 ) have finite limits $$\theta ^\pm $$ θ ± as $$x\rightarrow \pm \infty $$ x → ± ∞ . We assume that f is a locally Lipschitz function on $$\mathbb {R}$$ R satisfying minor nondegeneracy conditions. Our goal is to describe the asymptotic behavior of u ( x ,  t ) as $$t\rightarrow \infty $$ t → ∞ . In the first two parts of this series we mainly considered the cases where either $$\theta ^-\ne \theta ^+$$ θ - ≠ θ + ; or $$\theta ^\pm =\theta _0$$ θ ± = θ 0 and $$f(\theta _0)\ne 0$$ f ( θ 0 ) ≠ 0 ; or else $$\theta ^\pm =\theta _0$$ θ ± = θ 0 , $$f(\theta _0)=0$$ f ( θ 0 ) = 0 , and $$\theta _0$$ θ 0 is a stable equilibrium of the equation $${{\dot{\xi }}}=f(\xi )$$ ξ ˙ = f ( ξ ) . In all these cases we proved that the corresponding solution u is quasiconvergent—if bounded—which is to say that all limit profiles of $$u(\cdot ,t)$$ u ( · , t ) as $$t\rightarrow \infty $$ t → ∞ are steady states. The limit profiles, or accumulation points, are taken in $$L^\infty _{loc}(\mathbb {R})$$ L loc ∞ ( R ) . In the present paper, we take on the case that $$\theta ^\pm =\theta _0$$ θ ± = θ 0 , $$f(\theta _0)=0$$ f ( θ 0 ) = 0 , and $$\theta _0$$ θ 0 is an unstable equilibrium of the equation $${{\dot{\xi }}}=f(\xi )$$ ξ ˙ = f ( ξ ) . Our earlier quasiconvergence theorem in this case involved some restrictive technical conditions on the solution, which we now remove. Our sole condition on $$u(\cdot ,t)$$ u ( · , t ) is that it is nonoscillatory (has only finitely many critical points) at some $$t\ge 0$$ t ≥ 0 . Since it is known that oscillatory bounded solutions are not always quasiconvergent, our result is nearly optimal. 

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5. Observations of the singly Cabibbo-suppressed decays $$ {\Xi}_c^{+}\to p{K}_S^0 $$, $$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$, and $$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ at Belle and Belle II

   https://doi.org/10.1007/JHEP03(2025)061  

   Adachi, I; Aggarwal, L; Akopov, N; Alhakami, M; Aloisio, A; Althubiti, N; Anh_Ky, N; Asner, D M; Atmacan, H; Aushev, T; et al (March 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> Using data samples of 983.0 fb⁻¹and 427.9 fb⁻¹accumulated with the Belle and Belle II detectors operating at the KEKB and SuperKEKB asymmetric-energye⁺e⁻colliders, singly Cabibbo-suppressed decays$$ {\Xi}_c^{+}\to p{K}_S^0 $$ ${\Xi }_c^{+}\to p{K}_S^0$,$$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$ ${\Xi }_c^{+}\to \Lambda {\pi }^{+}$, and$$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}$are observed for the first time. The ratios of branching fractions of$$ {\Xi}_c^{+}\to p{K}_S^0 $$ ${\Xi }_c^{+}\to p{K}_S^0$,$$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$ ${\Xi }_c^{+}\to \Lambda {\pi }^{+}$, and$$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}$relative to that of$$ {\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}$are measured to be$$ {\displaystyle \begin{array}{c}\frac{\mathcal{B}\left({\Xi}_c^{+}\to p{K}_S^0\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(2.47\pm 0.16\pm 0.07\right)\%,\\ {}\frac{\mathcal{B}\left({\Xi}_c^{+}\to \Lambda {\pi}^{+}\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(1.56\pm 0.14\pm 0.09\right)\%,\\ {}\frac{\mathcal{B}\left({\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+}\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(4.13\pm 0.26\pm 0.22\right)\%.\end{array}} $$ $\begin{array}{c}\frac{B\left({\Xi }_c^{+}\to p{K}_S^0\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(2.47\pm 0.16\pm 0.07\right)\%,\\ \frac{B\left({\Xi }_c^{+}\to \Lambda {\pi }^{+}\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(1.56\pm 0.14\pm 0.09\right)\%,\\ \frac{B\left({\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(4.13\pm 0.26\pm 0.22\right)\%.\end{array}$ Multiplying these values by the branching fraction of the normalization channel,$$ \mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)=\left(2.9\pm 1.3\right)\% $$ $B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)=\left(2.9\pm 1.3\right)\%$, the absolute branching fractions are determined to be$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^{+}\to p{K}_S^0\right)=\left(7.16\pm 0.46\pm 0.20\pm 3.21\right)\times {10}^{-4},\\ {}\mathcal{B}\left({\Xi}_c^{+}\to \Lambda {\pi}^{+}\right)=\left(4.52\pm 0.41\pm 0.26\pm 2.03\right)\times {10}^{-4},\\ {}\mathcal{B}\left({\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+}\right)=\left(1.20\pm 0.08\pm 0.07\pm 0.54\right)\times {10}^{-3}.\end{array}} $$ $\begin{array}{c}B\left({\Xi }_c^{+}\to p{K}_S^0\right)=\left(7.16\pm 0.46\pm 0.20\pm 3.21\right)\times {10}^{-4},\\ B\left({\Xi }_c^{+}\to \Lambda {\pi }^{+}\right)=\left(4.52\pm 0.41\pm 0.26\pm 2.03\right)\times {10}^{-4},\\ B\left({\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}\right)=\left(1.20\pm 0.08\pm 0.07\pm 0.54\right)\times {10}^{-3}.\end{array}$ The first and second uncertainties above are statistical and systematic, respectively, while the third ones arise from the uncertainty in$$ \mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right) $$ $B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)$. 

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