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1. 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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2. Search for the $$ {B}_c^{+} $$ → χc1(3872)π+ decay

   https://doi.org/10.1007/JHEP06(2025)013  

   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 (June 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> A search for the decay$$ {B}_c^{+} $$ $B_c^{+}$→ χ_c1(3872)π⁺is reported using proton-proton collision data collected with the LHCb detector between 2011 and 2018 at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb⁻¹. No significant signal is observed. Using the decay$$ {B}_c^{+} $$ $B_c^{+}$→ψ(2S)π⁺as a normalisation channel, an upper limit for the ratio of branching fractions$$ {\mathcal{R}}_{\psi (2S)}^{\chi_{c1}(3872)}=\frac{{\mathcal{B}}_{B_c^{+}\to {\chi}_{c1}(3872){\pi}^{+}}}{{\mathcal{B}}_{B_c^{+}\to \psi (2S){\pi}^{+}}}\times \frac{{\mathcal{B}}_{\chi_{c1}(3872)\to J/\psi {\pi}^{+}{\pi}^{-}}}{{\mathcal{B}}_{\psi (2S)\to J/\psi {\pi}^{+}{\pi}^{-}}}<0.05(0.06), $$ $R_{\psi \left(2S\right)}^{{\chi }_{c1}\left(3872\right)}=\frac{B_{B_c^{+}\to {\chi }_{c1}\left(3872\right){\pi }^{+}}}{B_{B_c^{+}\to \psi \left(2S\right){\pi }^{+}}}\times \frac{B_{{\chi }_{c1}\left(3872\right)\to J/\psi {\pi }^{+}{\pi }^{-}}}{B_{\psi \left(2S\right)\to J/\psi {\pi }^{+}{\pi }^{-}}}<0.05\left(0.06\right),$ is set at the 90 (95)% confidence level. 

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3. On a Traveling Salesman Problem for Points in the Unit Cube

   https://doi.org/10.1007/s00453-024-01257-w  

   Balogh, József; Clemen, Felix Christian; Dumitrescu, Adrian (September 2024, Algorithmica)

   Abstract LetXbe ann-element point set in thek-dimensional unit cube$$[0,1]^k$$ ${[0,1]}^k$where$$k \ge 2$$ $k\ge 2$. According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour)$$x_1, x_2, \ldots , x_n$$ $x_1,x_2,\dots ,x_n$through thenpoints, such that$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} \le c_k$$ ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}\le c_k$, where$$|x-y|$$ $|x-y|$is the Euclidean distance betweenxandy, and$$c_k$$ $c_k$is an absolute constant that depends only onk, where$$x_{n+1} \equiv x_1$$ $x_{n+1}\equiv x_1$. From the other direction, for every$$k \ge 2$$ $k\ge 2$and$$n \ge 2$$ $n\ge 2$, there existnpoints in$$[0,1]^k$$ ${[0,1]}^k$, such that their shortest tour satisfies$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} = 2^{1/k} \cdot \sqrt{k}$$ ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}=2^{1/k}·\sqrt{k}$. For the plane, the best constant is$$c_2=2$$ $c_2=2$and this is the only exact value known. Bollobás and Meir showed that one can take$$c_k = 9 \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ $c_k=9{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$for every$$k \ge 3$$ $k\ge 3$and conjectured that the best constant is$$c_k = 2^{1/k} \cdot \sqrt{k}$$ $c_k=2^{1/k}·\sqrt{k}$, for every$$k \ge 2$$ $k\ge 2$. Here we significantly improve the upper bound and show that one can take$$c_k = 3 \sqrt{5} \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ $c_k=3\sqrt{5}{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$or$$c_k = 2.91 \sqrt{k} \ (1+o_k(1))$$ $c_k=2.91\sqrt{k}(1+o_k\left(1\right))$. Our bounds are constructive. We also show that$$c_3 \ge 2^{7/6}$$ $c_3\ge 2^{7/6}$, which disproves the conjecture for$$k=3$$ $k=3$. Connections to matching problems, power assignment problems, related problems, including algorithms, are discussed in this context. A slightly revised version of the Bollobás–Meir conjecture is proposed. 

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4. 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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5. A case study of SMEFT $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ effects in diboson processes: pp → W±(ℓ±ν)γ

   https://doi.org/10.1007/JHEP05(2024)223  

   Martin, Adam (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper we explorepp→W^±(ℓ^±ν)γto$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ $O\left(1/{\Lambda }^4\right)$in the SMEFT expansion. Calculations to this order are necessary to properly capture SMEFT contributions that grow with energy, as the interference between energy-enhanced SMEFT effects at$$ \mathcal{O}\left(1/{\Lambda}^2\right) $$ $O\left(1/{\Lambda }^2\right)$and the Standard Model is suppressed. We find that there are several dimension eight operators that interfere with the Standard Model and lead to the same energy growth, ~$$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$ $O\left(E^4/{\Lambda }^4\right)$, as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ $O\left(1/{\Lambda }^4\right)$SMEFT effects consistent with U(3)⁵flavor symmetry. Additionally, we include the decay of theW^±→ ℓ^±ν, making the calculation actually$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ $\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$. As such, we are able to study the impact of non-resonant SMEFT operators, such as$$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$ $\left(L^{†}{\overline{\sigma }}^{\mu }{\tau }^{I}L\right)\left(Q^{†}{\overline{\sigma }}^{\nu }{\tau }^{I}Q\right)$B_μν, which contribute to$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ $\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$directly and not to$$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$ $\overline{q}{q}^{\prime }\to W^{\pm }\gamma$. We show several distributions to illustrate the shape differences of the different contributions. 

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