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1. 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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2. Spin density matrix elements in exclusive $$\rho ^0$$ meson muoproduction

   https://doi.org/10.1140/epjc/s10052-023-11359-4  

   Alexeev, G D; Alexeev, M G; Alice, C; Amoroso, A; Andrieux, V; Anosov, V; Augsten, K; Augustyniak, W; Azevedo, C_D R; Badelek, B; et al (October 2023, The European Physical Journal C)

   Abstract We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive$$\rho ^0$$ ${\rho }^0$meson muoproduction at COMPASS using 160 GeV/cpolarised$$ \mu ^{+}$$ ${\mu }^{+}$and$$ \mu ^{-}$$ ${\mu }^{-}$beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0 GeV/$$c^2$$ $c^2$$$< W<$$ $<W<$17.0 GeV/$$c^2$$ $c^2$, 1.0 (GeV/c)$$^2$$ ${}^2$$$< Q^2<$$ $<Q^2<$10.0 (GeV/c)$$^2$$ ${}^2$and 0.01 (GeV/c)$$^2$$ ${}^2$$$< p_{\textrm{T}}^2<$$ $<p_{\text{T}}^2<$0.5 (GeV/c)$$^2$$ ${}^2$. Here,Wdenotes the mass of the final hadronic system,$$Q^2$$ $Q^2$the virtuality of the exchanged photon, and$$p_{\textrm{T}}$$ $p_{\text{T}}$the transverse momentum of the$$\rho ^0$$ ${\rho }^0$meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($$\gamma ^*_T \rightarrow V^{ }_L$$ ${\gamma }_T^{\ast }\to V_L^{}$) indicate a violation ofs-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive$$\rho ^0$$ ${\rho }^0$production. 

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3. Measurements of the associated production of a W boson and a charm quark in proton–proton collisions at $$\sqrt{s}=8\,\text {TeV} $$

   https://doi.org/10.1140/epjc/s10052-022-10897-7  

   Tumasyan, A.; Adam, W.; Bergauer, T.; Dragicevic, M.; Erö, J.; Valle, A. Escalante; Frühwirth, R.; Jeitler, M.; Krammer, N.; Lechner, L.; et al (December 2022, The European Physical Journal C)

   Abstract Measurements of the associated production of a W boson and a charm ($${\text {c}}$$ $\text{c}$) quark in proton–proton collisions at a centre-of-mass energy of 8$$\,\text {TeV}$$ $\text{TeV}$are reported. The analysis uses a data sample corresponding to a total integrated luminosity of 19.7$$\,\text {fb}^{-1}$$ ${\text{fb}}^{-1}$collected by the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm quark jets are selected using distinctive signatures of charm hadron decays. The product of the cross section and branching fraction$$\sigma (\text {p}\text {p}\rightarrow \text {W}+ {\text {c}}+ \text {X}) {\mathcal {B}}(\text {W}\rightarrow \ell \upnu )$$ $\sigma (\text{pp}\to \text{W}+\text{c}+\text{X})B(\text{W}\to \ell \nu )$, where$$\ell = \text {e}$$ $\ell =\text{e}$or$$\upmu $$ $\mu$, and the cross section ratio$$\sigma (\text {p}\text {p}\rightarrow {{\text {W}}^{+} + \bar{{\text {c}}} + \text {X}}) / \sigma (\text {p}\text {p}\rightarrow {{\text {W}}^{-} + {\text {c}}+ \text {X}})$$ $\sigma (\text{pp}\to {\text{W}}^{+}+\overline{\text{c}}+\text{X})/\sigma (\text{pp}\to {\text{W}}^{-}+\text{c}+\text{X})$are measured in a fiducial volume and differentially as functions of the pseudorapidity and of the transverse momentum of the lepton from the W boson decay. The results are compared with theoretical predictions. The impact of these measurements on the determination of the strange quark distribution is assessed. 

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4. Dimension-free discretizations of the uniform norm by small product sets

   https://doi.org/10.1007/s00222-024-01306-9  

   Becker, Lars; Klein, Ohad; Slote, Joseph; Volberg, Alexander; Zhang, Haonan (December 2024, Inventiones mathematicae)

   Abstract Let$$f$$ $f$be an analytic polynomial of degree at most$$K-1$$ $K-1$. A classical inequality of Bernstein compares the supremum norm of$$f$$ $f$over the unit circle to its supremum norm over the sampling set of the$$K$$ $K$-th roots of unity. Many extensions of this inequality exist, often understood under the umbrella of Marcinkiewicz–Zygmund-type inequalities for$$L^{p},1\le p\leq \infty $$ $L^p,1\le p\le \infty$norms. We study dimension-free extensions of these discretization inequalities in the high-dimension regime, where existing results construct sampling sets with cardinality growing with the total degree of the polynomial. In this work we show that dimension-free discretizations are possible with sampling sets whose cardinality is independent of$$\deg (f)$$ $deg\left(f\right)$and is instead governed by the maximumindividualdegree of$$f$$ $f$;i.e., the largest degree of$$f$$ $f$when viewed as a univariate polynomial in any coordinate. For example, we find that for$$n$$ $n$-variate analytic polynomials$$f$$ $f$of degree at most$$d$$ $d$and individual degree at most$$K-1$$ $K-1$,$$\|f\|_{L^{\infty }(\mathbf{D}^{n})}\leq C(X)^{d}\|f\|_{L^{\infty }(X^{n})}$$ ${\parallel f\parallel }_{L^{\infty }\left(D^n\right)}\le C{\left(X\right)}^d{\parallel f\parallel }_{L^{\infty }\left(X^n\right)}$for any fixed$$X$$ $X$in the unit disc$$\mathbf{D}$$ $D$with$$|X|=K$$ $\left|X\right|=K$. The dependence on$$d$$ $d$in the constant is tight for such small sampling sets, which arise naturally for example when studying polynomials of bounded degree coming from functions on products of cyclic groups. As an application we obtain a proof of the cyclic group Bohnenblust–Hille inequality with an explicit constant$$\mathcal{O}(\log K)^{2d}$$ $O{(logK)}^{2d}$. 

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5. Reduction of the electroweak correlation in the PDF updating by using the forward–backward asymmetry of Drell–Yan process

   https://doi.org/10.1140/epjc/s10052-022-10280-6  

   Yang, Siqi; Fu, Yao; Liu, Minghui; Zhang, Renyou; Hou, Tie-Jiun; Wang, Chen; Yin, Hang; Han, Liang; Yuan, C. -P. (April 2022, The European Physical Journal C)

   Abstract We propose a new observable for the measurement of the forward–backward asymmetry$$(A_{FB})$$ $\left(A_{\mathrm{FB}}\right)$in Drell–Yan lepton production. At hadron colliders, the$$A_{FB}$$ $A_{\mathrm{FB}}$distribution is sensitive to both the electroweak (EW) fundamental parameter$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$, the weak mixing angle, and the parton distribution functions (PDFs). Hence, the determination of$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$and the updating of PDFs by directly using the same$$A_{FB}$$ $A_{\mathrm{FB}}$spectrum are strongly correlated. This correlation would introduce large bias or uncertainty into both precise measurements of EW and PDF sectors. In this article, we show that the sensitivity of$$A_{FB}$$ $A_{\mathrm{FB}}$on$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$is dominated by its average value around theZpole region, while the shape (or gradient) of the$$A_{FB}$$ $A_{\mathrm{FB}}$spectrum is insensitive to$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$and contains important information on the PDF modeling. Accordingly, a new observable related to the gradient of the spectrum is introduced, and demonstrated to be able to significantly reduce the potential bias on the determination of$$\sin ^{2} \theta _{W}$$ ${sin}^2{\theta }_W$when updating the PDFs using the same$$A_{FB}$$ $A_{\mathrm{FB}}$data. 

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