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1. Well-Posedness for Ohkitani Model and Long-Time Existence for Surface Quasi-geostrophic Equations

   https://doi.org/10.1007/s00220-025-05257-x  

   Chae, Dongho; Jeong, In-Jee; Na, Jungkyoung; Oh, Sung-Jin (April 2025, Communications in Mathematical Physics)

   Abstract We consider the Cauchy problem for the logarithmically singular surface quasi-geostrophic (SQG) equation, introduced by Ohkitani,$$\begin{aligned} \begin{aligned} \partial _t \theta - \nabla ^\perp \log (10+(-\Delta )^{\frac{1}{2}})\theta \cdot \nabla \theta = 0, \end{aligned} \end{aligned}$$ $\begin{array}{c}\begin{array}{c}{\partial }_t\theta -{\nabla }^{\perp }log(10+{(-\Delta )}^{\frac{1}{2}})\theta ·\nabla \theta =0,\end{array}\end{array}$and establish local existence and uniqueness of smooth solutions in the scale of Sobolev spaces with exponent decreasing with time. Such a decrease of the Sobolev exponent is necessary, as we have shown in the companion paper (Chae et al. in Illposedness via degenerate dispersion for generalized surface quasi-geostrophic equations with singular velocities,arXiv:2308.02120) that the problem is strongly ill-posed in any fixed Sobolev spaces. The time dependence of the Sobolev exponent can be removed when there is a dissipation term strictly stronger than log. These results improve wellposedness statements by Chae et al. (Comm Pure Appl Math 65(8):1037–1066, 2012). This well-posedness result can be applied to describe the long-time dynamics of the$$\delta $$ $\delta$-SQG equations, defined by$$\begin{aligned} \begin{aligned} \partial _t \theta + \nabla ^\perp (10+(-\Delta )^{\frac{1}{2}})^{-\delta }\theta \cdot \nabla \theta = 0, \end{aligned} \end{aligned}$$ $\begin{array}{c}\begin{array}{c}{\partial }_t\theta +{\nabla }^{\perp }{(10+{(-\Delta )}^{\frac{1}{2}})}^{-\delta }\theta ·\nabla \theta =0,\end{array}\end{array}$for all sufficiently small$$\delta >0$$ $\delta >0$depending on the size of the initial data. For the same range of$$\delta $$ $\delta$, we establish global well-posedness of smooth solutions to the dissipative SQG equations. 

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2. Global well-posedness for 2D generalized parabolic Anderson model via paracontrolled calculus

   https://doi.org/10.1007/s40072-025-00358-z  

   Shen, Hao; Zhu, Rongchan; Zhu, Xiangchan (May 2025, Stochastics and Partial Differential Equations: Analysis and Computations)

   Abstract This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on$$\mathbb {R}^+\times \mathbb {T}^2$$ $R^{+}\times T^2$within the framework of paracontrolled calculus (Gubinelli et al. in Forum Math, 2015). The model is given by the equation:$$\begin{aligned} (\partial _t-\Delta ) u=F(u)\eta \end{aligned}$$ $\begin{array}{c}({\partial }_t-\Delta )u=F\left(u\right)\eta \end{array}$where$$\eta \in C^{-1-\kappa }$$ $\eta \in C^{-1-\kappa }$with$$1/6>\kappa >0$$ $1/6>\kappa >0$, and$$F\in C_b^2(\mathbb {R})$$ $F\in C_b^2\left(R\right)$. Assume that$$\eta \in C^{-1-\kappa }$$ $\eta \in C^{-1-\kappa }$and can be lifted to enhanced noise, we derive new a priori bounds. The key idea follows from the recent work by Chandra et al. (A priori bounds for 2-d generalised Parabolic Anderson Model,,2024), to represent the leading error term as a transport type term, and our techniques encompass the paracontrolled calculus, the maximum principle, and the localization approach (i.e. high-low frequency argument). 

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3. 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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4. Search for the $$ {B}_s^0 $$ → μ+μ−γ decay

   https://doi.org/10.1007/JHEP07(2024)101  

   Aaij, R; Abdelmotteleb, A_S W; Abellan_Beteta, C; Abudinén, F; Ackernley, T; Adefisoye, A A; Adeva, B; Adinolfi, M; Adlarson, P; Agapopoulou, C; et al (July 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> A search for the fully reconstructed$$ {B}_s^0 $$ $B_s^0$→ μ⁺μ⁻γdecay is performed at the LHCb experiment using proton-proton collisions at$$ \sqrt{s} $$ $\sqrt{s}$= 13 TeV corresponding to an integrated luminosity of 5.4 fb⁻¹. No significant signal is found and upper limits on the branching fraction in intervals of the dimuon mass are set$$ {\displaystyle \begin{array}{cc}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[2{m}_{\mu },1.70\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<7.7\times {10}^{-8},&\ m\left({\mu}^{+}{\mu}^{-}\right)\in \left[\textrm{1.70,2.88}\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[3.92,{m}_{B_s^0}\right]\textrm{GeV}/{c}^2,\end{array}} $$ $\begin{array}{cc}B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(2m_{\mu },1.70\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<7.7\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(\mathrm{1.70,\; 2.88}\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(3.92,m_{B_s^0}\right)\mathrm{GeV}/c^2,\end{array}$ at 95% confidence level. Additionally, upper limits are set on the branching fraction in the [2m_μ,1.70] GeV/c²dimuon mass region excluding the contribution from the intermediateϕ(1020) meson, and in the region combining all dimuon-mass intervals. 

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5. 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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