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1. Search for dark matter produced in association with a single top quark and an energetic W boson in $$\sqrt{s}=$$ 13 TeV $$pp$$ collisions with the ATLAS detector

   https://doi.org/10.1140/epjc/s10052-023-11582-z  

   Aad, G.; Abbott, B.; Abbott, D. C.; Abeling, K.; Abidi, S. H.; Aboulhorma, A.; Abramowicz, H.; Abreu, H.; Abulaiti, Y.; Hoffman, A. C.; et al (July 2023, The European Physical Journal C)

   Abstract This paper presents a search for dark matter,$$\chi $$ $\chi$, using events with a single top quark and an energeticWboson. The analysis is based on proton–proton collision data collected with the ATLAS experiment at$$\sqrt{s}=$$ $\sqrt{s}=$13 TeV during LHC Run 2 (2015–2018), corresponding to an integrated luminosity of 139 fb$$^{-1}$$ ${}^{-1}$. The search considers final states with zero or one charged lepton (electron or muon), at least oneb-jet and large missing transverse momentum. In addition, a result from a previous search considering two-charged-lepton final states is included in the interpretation of the results. The data are found to be in good agreement with the Standard Model predictions and the results are interpreted in terms of 95% confidence-level exclusion limits in the context of a class of dark matter models involving an extended two-Higgs-doublet sector together with a pseudoscalar mediator particle. The search is particularly sensitive to on-shell production of the charged Higgs boson state,$$H^{\pm }$$ $H^{\pm }$, arising from the two-Higgs-doublet mixing, and its semi-invisible decays via the mediator particle,a:$$H^{\pm } \rightarrow W^\pm a (\rightarrow \chi \chi )$$ $H^{\pm }\to W^{\pm }a(\to \chi \chi )$. Signal models with$$H^{\pm }$$ $H^{\pm }$masses up to 1.5 TeV andamasses up to 350 GeV are excluded assuming a$$\tan \beta $$ $tan\beta$value of 1. For masses ofaof 150 (250) GeV,$$\tan \beta $$ $tan\beta$values up to 2 are excluded for$$H^{\pm }$$ $H^{\pm }$masses between 200 (400) GeV and 1.5 TeV. Signals with$$\tan \beta $$ $tan\beta$values between 20 and 30 are excluded for$$H^{\pm }$$ $H^{\pm }$masses between 500 and 800 GeV. 

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2. 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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3. Abelian varieties of prescribed order over finite fields

   https://doi.org/10.1007/s00208-024-03084-4  

   van_Bommel, Raymond; Costa, Edgar; Li, Wanlin; Poonen, Bjorn; Smith, Alexander (May 2025, Mathematische Annalen)

   Abstract Given a prime powerqand$$n \gg 1$$ $n\gg 1$, we prove that every integer in a large subinterval of the Hasse–Weil interval$$[(\sqrt{q}-1)^{2n},(\sqrt{q}+1)^{2n}]$$ $[{(\sqrt{q}-1)}^{2n},{(\sqrt{q}+1)}^{2n}]$is$$\#A({\mathbb {F}}_q)$$ $\#A\left(F_q\right)$for some ordinary geometrically simple principally polarized abelian varietyAof dimensionnover$${\mathbb {F}}_q$$ $F_q$. As a consequence, we generalize a result of Howe and Kedlaya for$${\mathbb {F}}_2$$ $F_2$to show that for each prime powerq, every sufficiently large positive integer is realizable, i.e.,$$\#A({\mathbb {F}}_q)$$ $\#A\left(F_q\right)$for some abelian varietyAover$${\mathbb {F}}_q$$ $F_q$. Our result also improves upon the best known constructions of sequences of simple abelian varieties with point counts towards the extremes of the Hasse–Weil interval. A separate argument determines, for fixedn, the largest subinterval of the Hasse–Weil interval consisting of realizable integers, asymptotically as$$q \rightarrow \infty $$ $q\to \infty$; this gives an asymptotically optimal improvement of a 1998 theorem of DiPippo and Howe. Our methods are effective: We prove that if$$q \le 5$$ $q\le 5$, then every positive integer is realizable, and for arbitraryq, every positive integer$$\ge q^{3 \sqrt{q} \log q}$$ $\ge q^{3\sqrt{q}logq}$is realizable. 

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4. Search for dark matter from the center of the Earth with 10 years of IceCube data

   https://doi.org/10.1140/epjc/s10052-025-14144-7  

   Abbasi, R; Ackermann, M; Adams, J; Agarwalla, S K; Aguilar, J A; Ahlers, M; Alameddine, J M; Amin, N M; Andeen, K; Argüelles, C; et al (May 2025, The European Physical Journal C)

   Abstract The nature of dark matter remains unresolved in fundamental physics. Weakly Interacting Massive Particles (WIMPs), which could explain the nature of dark matter, can be captured by celestial bodies like the Sun or Earth, leading to enhanced self-annihilation into Standard Model particles including neutrinos detectable by neutrino telescopes such as the IceCube Neutrino Observatory. This article presents a search for muon neutrinos from the center of the Earth performed with 10 years of IceCube data using a track-like event selection. We considered a number of WIMP annihilation channels ($$\chi \chi \rightarrow \tau ^+\tau ^-$$ $\chi \chi \to {\tau }^{+}{\tau }^{-}$/$$W^+W^-$$ $W^{+}{W}^{-}$/$$b\bar{b}$$ $b\overline{b}$) and masses ranging from 10 GeV to 10 TeV. No significant excess over background due to a dark matter signal was found while the most significant result corresponds to the annihilation channel$$\chi \chi \rightarrow b\bar{b}$$ $\chi \chi \to b\overline{b}$for the mass$$m_{\chi }=250$$ $m_{\chi }=250$ GeV with a post-trial significance of$$1.06\sigma $$ $1.06\sigma$. Our results are competitive with previous such searches and direct detection experiments. Our upper limits on the spin-independent WIMP scattering are world-leading among neutrino telescopes for WIMP masses$$m_{\chi }>100$$ $m_{\chi }>100$ GeV. 

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5. Measurement of beauty-quark production in pp collisions at $$ \sqrt{s} $$ = 13 TeV via non-prompt D mesons

   https://doi.org/10.1007/JHEP10(2024)110  

   Acharya, S; Adamová, D; Agarwal, A; Aglieri_Rinella, G; Aglietta, L; Agnello, M; Agrawal, N; Ahammed, Z; Ahmad, S; Ahn, S U; et al (October 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Thep_T-differential production cross sections of non-prompt D⁰, D⁺, and$$ {\textrm{D}}_{\textrm{s}}^{+} $$ $D_s^{+}$mesons originating from beauty-hadron decays are measured in proton–proton collisions at a centre-of-mass energy$$ \sqrt{s} $$ $\sqrt{s}$= 13 TeV. The measurements are performed at midrapidity, |y|<0.5, with the data sample collected by ALICE from 2016 to 2018. The results are in agreement with predictions from several perturbative QCD calculations. The fragmentation fraction of beauty quarks to strange mesons divided by the one to non-strange mesons,f_s/(f_u+f_d), is found to be 0.114 ± 0.016 (stat.) ± 0.006 (syst.) ± 0.003 (BR) ± 0.003 (extrap.). This value is compatible with previous measurements at lower centre-of-mass energies and in different collision systems in agreement with the assumption of universality of fragmentation functions. In addition, the dependence of the non-prompt D meson production on the centre-of-mass energy is investigated by comparing the results obtained at$$ \sqrt{s} $$ $\sqrt{s}$= 5.02 and 13 TeV, showing a hardening of the non-prompt D-mesonp_T-differential production cross section at higher$$ \sqrt{s} $$ $\sqrt{s}$. Finally, the$$ \textrm{b}\overline{\textrm{b}} $$ $b\overline{b}$production cross section per unit of rapidity at midrapidity is calculated from the non-prompt D⁰, D⁺,$$ {\textrm{D}}_{\textrm{s}}^{+} $$ $D_s^{+}$, and$$ {\Lambda}_{\textrm{c}}^{+} $$ ${\Lambda }_c^{+}$hadron measurements, obtaining$$ \textrm{d}\sigma /\textrm{d}y=75.2\pm 3.2\left(\textrm{stat}.\right)\pm 5.2{\left(\textrm{syst}.\right)}_{-3.2}^{+12.3}\left(\textrm{extrap}.\right) $$ $d\sigma /dy=75.2\pm 3.2\left(\text{stat}.\right)\pm 5.2{\left(\text{syst}.\right)}_{-3.2}^{+12.3}\left(\text{extrap}.\right)$μb. 

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