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1. 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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2. Species scale in diverse dimensions

   https://doi.org/10.1007/JHEP05(2024)112  

   van_de_Heisteeg, Damian; Vafa, Cumrun; Wiesner, Max; Wu, David H (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In a quantum theory of gravity, the species scale Λ_scan be defined as the scale at which corrections to the Einstein action become important or alternatively as codifying the “number of light degrees of freedom”, due to the fact that$$ {\Lambda}_s^{-1} $$ ${\Lambda }_s^{-1}$is the smallest size black hole described by the EFT involving only the Einstein term. In this paper, we check the validity of this picture in diverse dimensions and with different amounts of supersymmetry and verify the expected behavior of the species scale at the boundary of moduli space. This also leads to the evaluation of the species scale in the interior of the moduli space as well as to the computation of the diameter of the moduli space. We also find evidence that the species scale satisfies the bound$$ {\frac{\left|\nabla {\Lambda}_s\right|}{\Lambda_s}}^2\le \frac{1}{d-2} $$ ${\frac{\left(\nabla {\Lambda }_s\right)}{{\Lambda }_s}}^2\le \frac{1}{d-2}$all over moduli space including the interior. 

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3. Counting imaginary quadratic fields with an ideal class group of 5-rank at least 2

   https://doi.org/10.1007/s11139-025-01184-6  

   Bartz, Kollin; Levin, Aaron; Thamminana, Aman_Dhruva (August 2025, The Ramanujan Journal)

   Abstract We prove that there are$$\gg \frac{X^{\frac{1}{3}}}{(\log X)^2}$$ $\gg \frac{X^{\frac{1}{3}}}{{(logX)}^2}$imaginary quadratic fieldskwith discriminant$$|d_k|\le X$$ $|d_k|\le X$and an ideal class group of 5-rank at least 2. This improves a result of Byeon, who proved the lower bound$$\gg X^{\frac{1}{4}}$$ $\gg X^{\frac{1}{4}}$in the same setting. We use a method of Howe, Leprévost, and Poonen to construct a genus 2 curveCover$$\mathbb {Q}$$ $Q$such thatChas a rational Weierstrass point and the Jacobian ofChas a rational torsion subgroup of 5-rank 2. We deduce the main result from the existence of the curveCand a quantitative result of Kulkarni and the second author. 

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4. A Refutation of the Pach-Tardos Conjecture for 0–1 Matrices

   https://doi.org/10.1007/s00493-025-00187-7  

   Pettie, Seth; Tardos, Gábor (December 2025, Combinatorica)

   Abstract The theory of forbidden 0–1 matrices generalizes Turán-style (bipartite) subgraph avoidance, Davenport-Schinzel theory, and Zarankiewicz-type problems, and has been influential in many areas, such as discrete and computational geometry, the analysis of self-adjusting data structures, and the development of the graph parametertwin width. The foremost open problem in this area is to resolve thePach-Tardos conjecturefrom 2005, which states that if a forbidden pattern$$P\in \{0,1\}^{k\times l}$$ $P\in {\{0,1\}}^{k\times l}$isacyclic, meaning it is the bipartite incidence matrix of a forest, then$$\operatorname {Ex}(P,n) = O(n\log ^{C_P} n)$$ $Ex(P,n)=O\left(n{log}^{C_P}n\right)$, where$$\operatorname {Ex}(P,n)$$ $Ex(P,n)$is the maximum number of 1s in aP-free$$n\times n$$ $n\times n$0–1 matrix and$$C_P$$ $C_P$is a constant depending only onP. This conjecture has been confirmed on many small patterns, specifically allPwith weight at most 5, and all but two with weight 6. The main result of this paper is a clean refutation of the Pach-Tardos conjecture. Specifically, we prove that$$\operatorname {Ex}(S_0,n),\operatorname {Ex}(S_1,n) \ge n2^{\Omega (\sqrt{\log n})}$$ $Ex(S_0,n),Ex(S_1,n)\ge n{2}^{\Omega \left(\sqrt{logn}\right)}$, where$$S_0,S_1$$ $S_0,S_1$are the outstanding weight-6 patterns. We also prove sharp bounds on the entire class ofalternatingpatterns$$(P_t)$$ $\left(P_t\right)$, specifically that for every$$t\ge 2$$ $t\ge 2$,$$\operatorname {Ex}(P_t,n)=\Theta (n(\log n/\log \log n)^t)$$ $Ex(P_t,n)=\Theta \left(n{(logn/loglogn)}^t\right)$. This is the first proof of an asymptotically sharp bound that is$$\omega (n\log n)$$ $\omega (nlogn)$. 

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5. Measurement of CP violation in B0 → D+D− and $$ {\textrm{B}}_{\textrm{s}}^0 $$ → $$ {\textrm{D}}_{\textrm{s}}^{+}{\textrm{D}}_{\textrm{s}}^{-} $$ decays

   https://doi.org/10.1007/JHEP01(2025)061  

   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 (January 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> A time-dependent, flavour-tagged measurement ofCPviolation is performed withB⁰→ D⁺D⁻and$$ {B}_s^0 $$ $B_s^0$→$$ {D}_s^{+}{D}_s^{-} $$ $D_s^{+}{D}_s^{-}$decays, using data collected by the LHCb detector in proton-proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 6 fb⁻¹. InB⁰→ D⁺D⁻decays theCP-violation parameters are measured to be$$ {\displaystyle \begin{array}{c}{S}_{D^{+}{D}^{-}}=-0.552\pm 0.100\left(\textrm{stat}\right)\pm 0.010\left(\textrm{syst}\right),\\ {}{C}_{D^{+}{D}^{-}}=0.128\pm 0.103\left(\textrm{stat}\right)\pm 0.010\left(\textrm{syst}\right).\end{array}} $$ $\begin{array}{c}{S}_{D^{+}{D}^{-}}=-0.552\pm 0.100\left(\text{stat}\right)\pm 0.010\left(\text{syst}\right),\\ C_{D^{+}{D}^{-}}=0.128\pm 0.103\left(\text{stat}\right)\pm 0.010\left(\text{syst}\right).\end{array}$ In$$ {B}_s^0 $$ $B_s^0$→$$ {D}_s^{+}{D}_s^{-} $$ $D_s^{+}{D}_s^{-}$decays theCP-violating parameter formulation in terms ofϕ_sand|λ|results in$$ {\displaystyle \begin{array}{c}{\phi}_s=-0.086\pm 0.106\left(\textrm{stat}\right)\pm 0.028\left(\textrm{syst}\right)\textrm{rad},\\ {}\mid {\lambda}_{D_s^{+}{D}_s^{-}}\mid =1.145\pm 0.126\left(\textrm{stat}\right)\pm 0.031\left(\textrm{syst}\right).\end{array}} $$ $\begin{array}{c}{\varphi }_s=-0.086\pm 0.106\left(\text{stat}\right)\pm 0.028\left(\text{syst}\right)\mathrm{rad},\\ \mid {\lambda }_{D_s^{+}{D}_s^{-}}\mid =1.145\pm 0.126\left(\text{stat}\right)\pm 0.031\left(\text{syst}\right).\end{array}$ These results represent the most precise single measurement of theCP-violation parameters in their respective channels. For the first time in a single measurement,CPsymmetry is observed to be violated inB⁰→ D⁺D⁻decays with a significance exceeding six standard deviations. 

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