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1. Search for CP violation in $$ {D}_{(s)}^{+}\to {h}^{+}{\pi}^0 $$ and $$ {D}_{(s)}^{+}\to {h}^{+}\eta $$ decays

   https://doi.org/10.1007/JHEP06(2021)019  

   Aaij, R.; Abellán Beteta, C.; Ackernley, T.; Adeva, B.; Adinolfi, M.; Afsharnia, H.; Aidala, C. A.; Aiola, S.; Ajaltouni, Z.; Akar, S.; et al (June 2021, Journal of High Energy Physics)

   A bstract Searches for CP violation in the two-body decays $$ {D}_{(s)}^{+}\to {h}^{+}{\pi}^0 $$ D s + → h + π 0 and $$ {D}_{(s)}^{+}\to {h}^{+}\eta $$ D s + → h + η (where h + denotes a π + or K + meson) are performed using pp collision data collected by the LHCb experiment corresponding to either 9 fb − 1 or 6 fb − 1 of integrated luminosity. The π 0 and η mesons are reconstructed using the e + e − γ final state, which can proceed as three-body decays π 0 → e + e − γ and η → e + e − γ , or via the two-body decays π 0 → γγ and η → γγ followed by a photon conversion. The measurements are made relative to the control modes $$ {D}_{(s)}^{+}\to {K}_{\mathrm{S}}^0{h}^{+} $$ D s + → K S 0 h + to cancel the production and detection asymmetries. The CP asymmetries are measured to be $$ {\displaystyle \begin{array}{c}{\mathcal{A}}_{CP}\left({D}^{+}\to {\pi}^{+}{\pi}^0\right)=\left(-1.3\pm 0.9\pm 0.6\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}^{+}\to {K}^{+}{\pi}^0\right)=\left(-3.2\pm 4.7\pm 2.1\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}^{+}\to {\pi}^{+}\eta \right)=\left(-0.2\pm 0.8\pm 0.4\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}^{+}\to {K}^{+}\eta \right)=\left(-6\pm 10\pm 4\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {K}^{+}{\pi}^0\right)=\left(-0.8\pm 3.9\pm 1.2\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {\pi}^{+}\eta \right)=\left(0.8\pm 0.7\pm 0.5\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {K}^{+}\eta \right)=\left(0.9\pm 3.7\pm 1.1\right)\%,\end{array}\end{array}\end{array}\end{array}} $$ A CP D + → π + π 0 = − 1.3 ± 0.9 ± 0.6 % , A CP D + → K + π 0 = − 3.2 ± 4.7 ± 2.1 % , A CP D + → π + η = − 0.2 ± 0.8 ± 0.4 % , A CP D + → K + η = − 6 ± 10 ± 4 % , A CP D s + → K + π 0 = − 0.8 ± 3.9 ± 1.2 % , A CP D s + → π + η = 0.8 ± 0.7 ± 0.5 % , A CP D s + → K + η = 0.9 ± 3.7 ± 1.1 % , where the first uncertainties are statistical and the second systematic. These results are consistent with no CP violation and mostly constitute the most precise measurements of $$ {\mathcal{A}}_{CP} $$ A CP in these decay modes to date. 

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2. Multiplicative Weights Update, Area Convexity and Random Coordinate Descent for Densest Subgraph Problems

   Nguyen, Ta Duy; Ene, Alina (July 2024, International Conference on Machine Learning)

   We study the densest subgraph problem and give algorithms via multiplicative weights update and area convexity that converge in $$O\left(\frac{\log m}{\epsilon^{2}}\right)$$ and $$O\left(\frac{\log m}{\epsilon}\right)$$ iterations, respectively, both with nearly-linear time per iteration. Compared with the work by Bahmani et al. (2014), our MWU algorithm uses a very different and much simpler procedure for recovering the dense subgraph from the fractional solution and does not employ a binary search. Compared with the work by Boob et al. (2019), our algorithm via area convexity improves the iteration complexity by a factor $$\Delta$$ — the maximum degree in the graph, and matches the fastest theoretical runtime currently known via flows (Chekuri et al., 2022) in total time. Next, we study the dense subgraph decomposition problem and give the first practical iterative algorithm with linear convergence rate $$O\left(mn\log\frac{1}{\epsilon}\right)$$ via accelerated random coordinate descent. This significantly improves over $$O\left(\frac{m\sqrt{mn\Delta}}{\epsilon}\right)$$ time of the FISTA-based algorithm by Harb et al. (2022). In the high precision regime $$\epsilon\ll\frac{1}{n}$$ where we can even recover the exact solution, our algorithm has a total runtime of $$O\left(mn\log n\right)$$, matching the state of the art exact algorithm via parametric flows (Gallo et al., 1989). Empirically, we show that this algorithm is very practical and scales to very large graphs, and its performance is competitive with widely used methods that have significantly weaker theoretical guarantees. 

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3. Search for Higgs boson decays to a Z boson and a photon in proton-proton collisions at $$ \sqrt{s} $$ = 13 TeV

   https://doi.org/10.1007/JHEP05(2023)233  

   Tumasyan, A.; Adam, W.; Andrejkovic, J. W.; Bergauer, T.; Chatterjee, S.; Damanakis, K.; Dragicevic, M.; Escalante Del Valle, A.; Frühwirth, R.; Jeitler, M.; et al (May 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> Results are presented from a search for the Higgs boson decay H→Zγ, where Z→ ℓ⁺ℓ⁻withℓ= e or μ. The search is performed using a sample of proton-proton (pp) collision data at a center-of-mass energy of 13 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb⁻¹. Events are assigned to mutually exclusive categories, which exploit differences in both event topology and kinematics of distinct Higgs production mechanisms to enhance signal sensitivity. The signal strengthμ, defined as the product of the cross section and the branching fraction$$ \left[\sigma \left(\textrm{pp}\to \textrm{H}\right)\mathcal{B}\left(\textrm{H}\to \textrm{Z}\upgamma \right)\right] $$ $\left(\sigma \left(\mathrm{pp}\to H\right)B\left(H\to \mathrm{Z\gamma }\right)\right)$relative to the standard model prediction, is extracted from a simultaneous fit to theℓ⁺ℓ⁻γ invariant mass distributions in all categories and is measured to beμ= 2.4 ± 0.9 for a Higgs boson mass of 125.38 GeV. The statistical significance of the observed excess of events is 2.7 standard deviations. This measurement corresponds to$$ \left[\sigma \left(\textrm{pp}\to \textrm{H}\right)\mathcal{B}\left(\textrm{H}\to \textrm{Z}\upgamma \right)\right]=0.21\pm 0.08 $$ $\left(\sigma \left(\mathrm{pp}\to H\right)B\left(H\to \mathrm{Z\gamma }\right)\right)=0.21\pm 0.08$pb. The observed (expected) upper limit at 95% confidence level onμis 4.1 (1.8), where the expected limit is calculated under the background-only hypothesis. The ratio of branching fractions$$ \mathcal{B}\left(\textrm{H}\to \textrm{Z}\upgamma \right)/\mathcal{B}\left(\textrm{H}\to \upgamma \upgamma \right) $$ $B\left(H\to \mathrm{Z\gamma }\right)/B\left(H\to \mathrm{\gamma \gamma }\right)$is measured to be$$ {1.5}_{-0.6}^{+0.7} $$ ${1.5}_{-0.6}^{+0.7}$, which agrees with the standard model prediction of 0.69 ± 0.04 at the 1.5 standard deviation level. 

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4. Measurements of Higgs boson production cross-sections in the H → τ+τ− decay channel in pp collisions at $$ \sqrt{s} $$ = 13 TeV with the ATLAS detector

   https://doi.org/10.1007/JHEP08(2022)175  

   Aad, G.; Abbott, B.; Abbott, D. C.; Abed Abud, A.; Abeling, K.; Abhayasinghe, D. K.; Abidi, S. H.; Aboulhorma, A.; Abramowicz, H.; Abreu, H.; et al (August 2022, Journal of High Energy Physics)

   A bstract Measurements of the production cross-sections of the Standard Model (SM) Higgs boson ( H ) decaying into a pair of τ -leptons are presented. The measurements use data collected with the ATLAS detector from pp collisions produced at the Large Hadron Collider at a centre-of-mass energy of $$ \sqrt{s} $$ s = 13 TeV, corresponding to an integrated luminosity of 139 fb − 1 . Leptonic ( τ → ℓν ℓ ν τ ) and hadronic ( τ → hadrons ν τ ) decays of the τ -lepton are considered. All measurements account for the branching ratio of H → ττ and are performed with a requirement |y H | < 2 . 5, where y H is the true Higgs boson rapidity. The cross-section of the pp → H → ττ process is measured to be 2 . 94 ± $$ 0.21{\left(\mathrm{stat}\right)}_{-0.32}^{+0.37} $$ 0.21 stat − 0.32 + 0.37 (syst) pb, in agreement with the SM prediction of 3 . 17 ± 0 . 09 pb. Inclusive cross-sections are determined separately for the four dominant production modes: 2 . 65 ± $$ 0.41{\left(\mathrm{stat}\right)}_{-0.67}^{+0.91} $$ 0.41 stat − 0.67 + 0.91 (syst) pb for gluon-gluon fusion, 0 . 197 ± $$ 0.028{\left(\mathrm{stat}\right)}_{-0.026}^{+0.032} $$ 0.028 stat − 0.026 + 0.032 (syst) pb for vector-boson fusion, 0 . 115 ± $$ 0.058{\left(\mathrm{stat}\right)}_{-0.040}^{+0.042} $$ 0.058 stat − 0.040 + 0.042 (syst) pb for vector-boson associated production, and 0 . 033 ± $$ 0.031{\left(\mathrm{stat}\right)}_{-0.017}^{+0.022} $$ 0.031 stat − 0.017 + 0.022 (syst) pb for top-quark pair associated production. Measurements in exclusive regions of the phase space, using the simplified template cross-section framework, are also performed. All results are in agreement with the SM predictions. 

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5. Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in $$\dot{H}^{s} \times \dot{H}^{s - 1}$$, $$s> \frac{1}{2}$$

   https://doi.org/10.1093/imrn/rnx323  

   Dodson, Benjamin (February 2018, International Mathematics Research Notices)

   Abstract In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is $$\dot{H}^{1/2} \times \dot{H}^{-1/2}$$. We show that if the initial data is radial and lies in $$\left (\dot{H}^{s} \times \dot{H}^{s - 1}\right ) \cap \left (\dot{H}^{1/2} \times \dot{H}^{-1/2}\right )$$ for some $$s> \frac{1}{2}$$, then the cubic initial value problem is globally well-posed. The proof utilizes the I-method, long time Strichartz estimates, and local energy decay. This method is quite similar to the method used in [11]. 

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