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1. Realizing trees of configurations in thin sets

   https://doi.org/10.2140/pjm.2025.335.355  

   Greenleaf, Allan; Iosevich, Alex; Taylor, Krystal (January 2025, Pacific Journal of Mathematics)

   Let $$\phi(x,y)$$ be a continuous function, smooth away from the diagonal, such that, for some $$\alpha>0$$, the associated generalized Radon transforms \begin{equation} \label{Radon} R_t^{\phi}f(x)=\int_{\phi(x,y)=t} f(y) \psi(y) d\sigma_{x,t}(y) \end{equation} map $$L^2({\mathbb R}^d) \to H^{\alpha}({\mathbb R}^d)$$ for all $t>0$. Let $$E$$ be a compact subset of $${\mathbb R}^d$$ for some $$d \ge 2$$, and suppose that the Hausdorff dimension of $$E$$ is $$>d-\alpha$$. We show that any tree graph $$T$$ on $k+1$ ($$k \ge 1$$) vertices is realizable in $$E$$, in the sense that there exist distinct $$x^1, x^2, \dots, x^{k+1} \in E$$ and $t>0$ such that the $$\phi$$-distance $$\phi(x^i, x^j)$$ is equal to $$t$$ for all pairs $(i,j)$ corresponding to the edges of the graph $$T$$. 

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2. Production of light-flavor hadrons in pp collisions at $$\sqrt{s}~=~7\text { and }\sqrt{s} = 13 \, \text { TeV} $$

   https://doi.org/10.1140/epjc/s10052-020-08690-5  

   Acharya, S.; Adamová, D.; Adler, A.; Adolfsson, J.; Aggarwal, M. M.; Rinella, G. Aglieri; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; et al (March 2021, The European Physical Journal C)

   null (Ed.)

   Abstract The production of $$\pi ^{\pm }$$ π ± , $$\mathrm{K}^{\pm }$$ K ± , $$\mathrm{K}^{0}_{S}$$ K S 0 , $$\mathrm{K}^{*}(892)^{0}$$ K ∗ ( 892 ) 0 , $$\mathrm{p}$$ p , $$\phi (1020)$$ ϕ ( 1020 ) , $$\Lambda $$ Λ , $$\Xi ^{-}$$ Ξ - , $$\Omega ^{-}$$ Ω - , and their antiparticles was measured in inelastic proton–proton (pp) collisions at a center-of-mass energy of $$\sqrt{s}$$ s = 13 TeV at midrapidity ( $$|y|<0.5$$ | y | < 0.5 ) as a function of transverse momentum ( $$p_{\mathrm{T}}$$ p T ) using the ALICE detector at the CERN LHC. Furthermore, the single-particle $$p_{\mathrm{T}}$$ p T distributions of $$\mathrm{K}^{0}_{S}$$ K S 0 , $$\Lambda $$ Λ , and $$\overline{\Lambda }$$ Λ ¯ in inelastic pp collisions at $$\sqrt{s} = 7$$ s = 7  TeV are reported here for the first time. The $$p_{\mathrm{T}}$$ p T distributions are studied at midrapidity within the transverse momentum range $$0\le p_{\mathrm{T}}\le 20$$ 0 ≤ p T ≤ 20 GeV/ c , depending on the particle species. The $$p_{\mathrm{T}}$$ p T spectra, integrated yields, and particle yield ratios are discussed as a function of collision energy and compared with measurements at lower $$\sqrt{s}$$ s and with results from various general-purpose QCD-inspired Monte Carlo models. A hardening of the spectra at high $$p_{\mathrm{T}}$$ p T with increasing collision energy is observed, which is similar for all particle species under study. The transverse mass and $$x_{\mathrm{T}}\equiv 2p_{\mathrm{T}}/\sqrt{s}$$ x T ≡ 2 p T / s scaling properties of hadron production are also studied. As the collision energy increases from $$\sqrt{s}$$ s = 7–13 TeV, the yields of non- and single-strange hadrons normalized to the pion yields remain approximately constant as a function of $$\sqrt{s}$$ s , while ratios for multi-strange hadrons indicate enhancements. The $$p_\mathrm{{T}}$$ p T -differential cross sections of $$\pi ^{\pm }$$ π ± , $$\mathrm {K}^{\pm }$$ K ± and $$\mathrm {p}$$ p ( $$\overline{\mathrm{p}}$$ p ¯ ) are compared with next-to-leading order perturbative QCD calculations, which are found to overestimate the cross sections for $$\pi ^{\pm }$$ π ± and $$\mathrm{p}$$ p ( $$\overline{\mathrm{p}}$$ p ¯ ) at high $$p_\mathrm{{T}}$$ p T . 

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3. Measurement of the CP-violating phase $$\phi _s$$ in $$ B_{s}^{0} \rightarrow J/\psi \phi $$ decays in ATLAS at 13 TeV

   https://doi.org/10.1140/epjc/s10052-021-09011-0  

   Aad, G.; Abbott, B.; Abbott, D. C.; Abdinov, O.; Abud, A. Abed; Abeling, K.; Abhayasinghe, D. K.; Abidi, S. H.; AbouZeid, O. S.; Abraham, N. L.; et al (April 2021, The European Physical Journal C)

   null (Ed.)

   Abstract A measurement of the $$ B_{s}^{0} \rightarrow J/\psi \phi $$ B s 0 → J / ψ ϕ decay parameters using $$ 80.5\, \mathrm {fb^{-1}} $$ 80.5 fb - 1 of integrated luminosity collected with the ATLAS detector from 13  $$\text {Te}\text {V}$$ Te proton–proton collisions at the LHC is presented. The measured parameters include the CP -violating phase $$\phi _{s} $$ ϕ s , the width difference $$ \Delta \Gamma _{s}$$ Δ Γ s between the $$B_{s}^{0}$$ B s 0 meson mass eigenstates and the average decay width $$ \Gamma _{s}$$ Γ s . The values measured for the physical parameters are combined with those from $$ 19.2\, \mathrm {fb^{-1}} $$ 19.2 fb - 1 of 7 and 8  $$\text {Te}\text {V}$$ Te data, leading to the following: $$\begin{aligned} \phi _{s}= & {} -0.087 \pm 0.036 ~\mathrm {(stat.)} \pm 0.021 ~\mathrm {(syst.)~rad} \\ \Delta \Gamma _{s}= & {} 0.0657 \pm 0.0043 ~\mathrm {(stat.)}\pm 0.0037 ~\mathrm {(syst.)~ps}^{-1} \\ \Gamma _{s}= & {} 0.6703 \pm 0.0014 ~\mathrm {(stat.)}\pm 0.0018 ~\mathrm {(syst.)~ps}^{-1} \end{aligned}$$ ϕ s = - 0.087 ± 0.036 ( stat . ) ± 0.021 ( syst . ) rad Δ Γ s = 0.0657 ± 0.0043 ( stat . ) ± 0.0037 ( syst . ) ps - 1 Γ s = 0.6703 ± 0.0014 ( stat . ) ± 0.0018 ( syst . ) ps - 1 Results for $$\phi _{s} $$ ϕ s and $$ \Delta \Gamma _{s}$$ Δ Γ s are also presented as 68% confidence level contours in the $$\phi _{s} $$ ϕ s – $$ \Delta \Gamma _{s}$$ Δ Γ s plane. Furthermore the transversity amplitudes and corresponding strong phases are measured. $$\phi _{s} $$ ϕ s and $$ \Delta \Gamma _{s}$$ Δ Γ s measurements are in agreement with the Standard Model predictions. 

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4. Multiplicity and rapidity dependence of $$\textrm{K}^{*}(\mathrm {{\textbf {892}}})^{0}$$ and $$\mathrm {\phi ({\textbf {1020}})}$$ production in p–Pb collisions at $$\sqrt{s_{\textrm{NN}}} =$$ 5.02 TeV

   https://doi.org/10.1140/epjc/s10052-023-11449-3  

   Acharya, S.; Adamová, D.; Adler, A.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; Ahuja, I.; et al (June 2023, The European Physical Journal C)

   Abstract The transverse-momentum $$(p_{\textrm{T}})$$ ( p T ) spectra of K $$^{*}(892)^{0}~$$ ∗ ( 892 ) 0 and $$\mathrm {\phi (1020)}~$$ ϕ ( 1020 ) measured with the ALICE detector up to $$p_{\textrm{T}} $$ p T  = 16 GeV/ c in the rapidity range $$-1.2< y < 0.3,$$ - 1.2 < y < 0.3 , in p–Pb collisions at the center-of-mass energy per nucleon–nucleon collision $$\sqrt{s_{\textrm{NN}}} = 5.02$$ s NN = 5.02  TeV are presented as a function of charged particle multiplicity and rapidity. The measured $$p_{\textrm{T}} $$ p T distributions show a dependence on both multiplicity and rapidity at low $$p_{\textrm{T}} $$ p T whereas no significant dependence is observed at high $$p_{\textrm{T}} $$ p T . A rapidity dependence is observed in the $$p_{\textrm{T}} $$ p T -integrated yield (d N /d y ), whereas the mean transverse momentum $$\left( \langle p_{\textrm{T}} \rangle \right) $$ ⟨ p T ⟩ shows a flat behavior as a function of rapidity. The rapidity asymmetry ( $$Y_{\textrm{asym}}$$ Y asym ) at low $$p_{\textrm{T}} $$ p T (< 5 GeV/ c ) is more significant for higher multiplicity classes. At high $$p_{\textrm{T}} $$ p T , no significant rapidity asymmetry is observed in any of the multiplicity classes. Both K $$^{*}(892)^{0}~$$ ∗ ( 892 ) 0 and $$\mathrm {\phi (1020)}~$$ ϕ ( 1020 ) show similar $$Y_{\textrm{asym}}$$ Y asym . The nuclear modification factor $$(Q_{\textrm{CP}})$$ ( Q CP ) as a function of $$p_{\textrm{T}} $$ p T shows a Cronin-like enhancement at intermediate $$p_{\textrm{T}} $$ p T , which is more prominent at higher rapidities (Pb-going direction) and in higher multiplicity classes. At high $$p_{\textrm{T}}$$ p T (> 5 GeV/ $$c$$ c ), the $$Q_{\textrm{CP}}$$ Q CP values are greater than unity and no significant rapidity dependence is observed. 

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5. Totally Nonnegative Critical Varieties

   https://doi.org/10.1093/imrn/rnad084  

   Galashin, Pavel (April 2023, International Mathematics Research Notices)

   Abstract We study totally nonnegative parts of critical varieties in the Grassmannian. We show that each totally nonnegative critical variety $$\operatorname{Crit}^{\geqslant 0}_f$$ is the image of an affine poset cyclohedron under a continuous map and use this map to define a boundary stratification of $$\operatorname{Crit}^{\geqslant 0}_f$$. For the case of the top-dimensional positroid cell, we show that the totally nonnegative critical variety $$\operatorname{Crit}^{\geqslant 0}_{k,n}$$ is homeomorphic to the second hypersimplex $$\Delta _{2,n}$$. 

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