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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. Deep Einstein@Home All-sky Search for Continuous Gravitational Waves in LIGO O3 Public Data

   https://doi.org/10.3847/1538-4357/acdad4  

   Steltner, B; Papa, M A; Eggenstein, H-B; Prix, R; Bensch, M; Allen, B; Machenschalk, B (July 2023, The Astrophysical Journal)

   Abstract We present the results of an all-sky search for continuous gravitational waves in the public LIGO O3 data. The search covers signal frequencies 20.0 Hz ≤f≤ 800.0 Hz and a spin-down range down to −2.6 × 10⁻⁹Hz s⁻¹, motivated by detectability studies on synthetic populations of Galactic neutron stars. This search is the most sensitive all-sky search to date in this frequency/spin-down region. The initial search was performed using the first half of the public LIGO O3 data (O3a), utilizing graphical processing units provided in equal parts by the volunteers of the Einstein@Home computing project and by the ATLAS cluster. After a hierarchical follow-up in seven stages, 12 candidates remain. Six are discarded at the eighth stage, by using the remaining O3 LIGO data (O3b). The surviving six can be ascribed to continuous-wave fake signals present in the LIGO data for validation purposes. We recover these fake signals with very high accuracy with our last stage search, which coherently combines all O3 data. Based on our results, we set upper limits on the gravitational-wave amplitudeh₀and translate these into upper limits on the neutron star ellipticity and on ther-mode amplitude. The most stringent upper limits are at 203 Hz, withh₀= 8.1 × 10⁻²⁶at the 90% confidence level. Our results exclude isolated neutron stars rotating faster than 5 ms with ellipticities greater than $5\times {10}^{-8}\left(\frac{d}{100\mathrm{pc}}\right)$within a distancedfrom Earth andr-mode amplitudes $\alpha \ge {10}^{-5}\left(\frac{d}{100\mathrm{pc}}\right)$for neutron stars spinning faster than 150 Hz. 

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3. The NANOGrav 15 yr Data Set: Looking for Signs of Discreteness in the Gravitational-wave Background

   https://doi.org/10.3847/1538-4357/ad93d5  

   Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne M; Arzoumanian, Zaven; Baier, Jeremy George; Baker, Paul T; Bécsy, Bence; Blecha, Laura; Brazier, Adam; Brook, Paul R; et al (December 2024, The Astrophysical Journal)

   Abstract The cosmic merger history of supermassive black hole binaries (SMBHBs) is expected to produce a low-frequency gravitational wave background (GWB). Here we investigate how signs of the discrete nature of this GWB can manifest in pulsar timing arrays (PTAs) through excursions from, and breaks in, the expected $f_{\mathrm{GW}}^{-2/3}$power law of the GWB strain spectrum. To do this, we create a semianalytic SMBHB population model, fit to North American Nanohertz Observatory for Gravitational Waves (NANOGrav’s) 15 yr GWB amplitude, and with 1000 realizations, we study the populations’ characteristic strain and residual spectra. Comparing our models to the NANOGrav 15 yr spectrum, we find two interesting excursions from the power law. The first, at 2 nHz, is below our GWB realizations with ap-value significancep= 0.05–0.06 (≈1.8σ–1.9σ). The second, at 16 nHz, is above our GWB realizations withp= 0.04–0.15 (≈1.4σ–2.1σ). We explore the properties of a loud SMBHB that could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by 3 orders of magnitude, from ∼10⁶to ∼10³, between 2 and 20 nHz. This causes a break in the strain spectrum as the stochasticity of the background breaks down at ${26}_{-19}^{+28}\mathrm{nHz}$, consistent with predictions pre-dating GWB measurements. The diminished GWB signal from SMBHBs at frequencies above the 26 nHz break opens a window for PTAs to detect continuous GWs from individual SMBHBs or GWs from the early Universe. 

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4. 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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5. Advancements in the NRC-FCs2 primary frequency standard

   https://doi.org/10.1088/1681-7575/adcd7b  

   Beattie, Scott; Jian, Bin; Marceau, Claude; Gibble, Kurt; Gertsvolf, Marina (May 2025, Metrologia)

   Abstract We have made improvements in the stability, accuracy, and performance of the NRC-FCs2 fountain clock. The dominant systematic effects have been re-evaluated. Optically-stabilized microwaves are used to improve the short-term stability, now reaching ${\sigma }_y=3\times {10}^{-14}{\tau }^{-\frac{1}{2}}$. We have evaluated the distributed cavity phase shift using absorption imaging. This technique dramatically reduces the evaluation time and final uncertainty. We have re-evaluated biases due to microwave leakage and synchronous phase transients with higher accuracy. The total systematic uncertainty of NRC-FCs2 is now $1.1\times {10}^{-16}$in fractional frequency, a factor of 2 improvement over its most recent evaluation. 

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