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1. 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)

   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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2. Measurement of the mass dependence of the transverse momentum of lepton pairs in Drell–Yan production in proton–proton collisions at $$\sqrt{s} = 13\,\text {Te\hspace{-.08em}V} $$

   https://doi.org/10.1140/epjc/s10052-023-11631-7  

   Tumasyan, A. ; Adam, W. ; Andrejkovic, J. W. ; Bergauer, T. ; Chatterjee, S. ; Dragicevic, M. ; Valle, A. Escalante ; Frühwirth, R. ; Jeitler, M. ; Krammer, N. ; et al ( July 2023 , The European Physical Journal C)

   The double differential cross sections of the Drell–Yan lepton pair ($$\ell ^+\ell ^-$$${\ell }^{+}{\ell }^{-}$, dielectron or dimuon) production are measured as functions of the invariant mass$$m_{\ell \ell }$$$m_{\ell \ell }$, transverse momentum$$p_{\textrm{T}} (\ell \ell )$$$p_{\text{T}}\left(\ell \ell \right)$, and$$\varphi ^{*}_{\eta }$$${\phi }_{\eta }^{\ast }$. The$$\varphi ^{*}_{\eta }$$${\phi }_{\eta }^{\ast }$observable, derived from angular measurements of the leptons and highly correlated with$$p_{\textrm{T}} (\ell \ell )$$$p_{\text{T}}\left(\ell \ell \right)$, is used to probe the low-$$p_{\textrm{T}} (\ell \ell )$$$p_{\text{T}}\left(\ell \ell \right)$region in a complementary way. Dilepton masses up to 1$$\,\text {Te\hspace{-.08em}V}$$$\text{Te}\text{V}$are investigated. Additionally, a measurement is performed requiring at least one jet in the final state. To benefit from partial cancellation of the systematic uncertainty, the ratios of the differential cross sections for various$$m_{\ell \ell }$$$m_{\ell \ell }$ranges to those in the Z mass peak interval are presented. The collected data correspond to an integrated luminosity of 36.3$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$of proton–proton collisions recorded with the CMS detector at the LHC at a centre-of-mass energy of 13$$\,\text {Te\hspace{-.08em}V}$$$\text{Te}\text{V}$. Measurements are compared with predictions based on perturbative quantum chromodynamics, including soft-gluon resummation.

    

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3. Ghost Distributions on Supersymmetric Spaces I: Koszul Induced Superspaces, Branching, and the Full Ghost Centre

   https://doi.org/10.1007/s00031-024-09878-9  

   Sherman, Alexander ( October 2024 , Transformation Groups)

   Given a Lie superalgebra$$\mathfrak {g}$$$g$, Gorelik defined the anticentre$$\mathcal {A}$$$A$of its enveloping algebra, which consists of certain elements that square to the center. We seek to generalize and enrich the anticentre to the context of supersymmetric pairs$$(\mathfrak {g},\mathfrak {k})$$$(g,k)$, or more generally supersymmetric spacesG/K. We define certain invariant distributions onG/K, which we call ghost distributions, and which in some sense are induced from invariant distributions on$$G_0/K_0$$$G_0/K_0$. Ghost distributions, and in particular their Harish-Chandra polynomials, give information about branching fromGto a symmetric subgroup$$K'$$$K^{\prime }$which is related (and sometimes conjugate) toK. We discuss the case of$$G\times G/G$$$G\times G/G$for an arbitrary quasireductive supergroupG, where our results prove the existence of a polynomial which determines projectivity of irreducibleG-modules. Finally, a generalization of Gorelik’s ghost centre is defined which we call the full ghost centre,$$\mathcal {Z}_{full}$$$Z_{\mathrm{full}}$. For type I basic Lie superalgebras$$\mathfrak {g}$$$g$we fully describe$$\mathcal {Z}_{full}$$$Z_{\mathrm{full}}$, and prove that if$$\mathfrak {g}$$$g$contains an internal grading operator,$$\mathcal {Z}_{full}$$$Z_{\mathrm{full}}$consists exactly of those elements in$$\mathcal {U}\mathfrak {g}$$$Ug$acting by$$\mathbb {Z}$$$Z$-graded constants on every finite-dimensional irreducible representation.

    

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4. Undecidable Translational Tilings with Only Two Tiles, or One Nonabelian Tile

   https://doi.org/10.1007/s00454-022-00426-4  

   Greenfeld, Rachel ; Tao, Terence ( January 2023 , Discrete & Computational Geometry)

   We construct an example of a group$$G = \mathbb {Z}^2 \times G_0$$$G=Z^2\times G_0$for a finite abelian group $$G_0$$$G_0$, a subsetEof $$G_0$$$G_0$, and two finite subsets$$F_1,F_2$$$F_1,F_2$of G, such that it is undecidable in ZFC whether$$\mathbb {Z}^2\times E$$$Z^2\times E$can be tiled by translations of$$F_1,F_2$$$F_1,F_2$. In particular, this implies that this tiling problem isaperiodic, in the sense that (in the standard universe of ZFC) there exist translational tilings ofEby the tiles$$F_1,F_2$$$F_1,F_2$, but no periodic tilings. Previously, such aperiodic or undecidable translational tilings were only constructed for sets of eleven or more tiles (mostly in $$\mathbb {Z}^2$$$Z^2$). A similar construction also applies for$$G=\mathbb {Z}^d$$$G=Z^d$for sufficiently large d. If one allows the group$$G_0$$$G_0$to be non-abelian, a variant of the construction produces an undecidable translational tiling with only one tile F. The argument proceeds by first observing that a single tiling equation is able to encode an arbitrary system of tiling equations, which in turn can encode an arbitrary system of certain functional equations once one has two or more tiles. In particular, one can use two tiles to encode tiling problems for an arbitrary number of tiles.

    

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5. Measurement of non-prompt $${{\textrm{D}}^{0}}$$-meson elliptic flow in Pb–Pb collisions at $$\sqrt{s_{\textrm{NN}}} = 5.02$$ TeV

   https://doi.org/10.1140/epjc/s10052-023-12259-3  

   Acharya, S ; Adamová, D ; Aglieri_Rinella, G ; Agnello, M ; Agrawal, N ; Ahammed, Z ; Ahmad, S ; Ahn, S U ; Ahuja, I ; Akindinov, A ; et al ( December 2023 , The European Physical Journal C)

   The elliptic flow$$(v_2)$$$\left(v_2\right)$of$${\textrm{D}}^{0}$$${\text{D}}^0$mesons from beauty-hadron decays (non-prompt$${\textrm{D}}^{0})$$${\text{D}}^0)$was measured in midcentral (30–50%) Pb–Pb collisions at a centre-of-mass energy per nucleon pair$$\sqrt{s_{\textrm{NN}}} = 5.02$$$\sqrt{s_{\text{NN}}}=5.02$ TeV with the ALICE detector at the LHC. The$${\textrm{D}}^{0}$$${\text{D}}^0$mesons were reconstructed at midrapidity$$(|y|<0.8)$$$\left(\right|y|<0.8)$from their hadronic decay$$\mathrm {D^0 \rightarrow K^-\uppi ^+}$$$D^0\to K^{-}{\pi }^{+}$, in the transverse momentum interval$$2< p_{\textrm{T}} < 12$$$2<p_{\text{T}}<12$ GeV/c. The result indicates a positive$$v_2$$$v_2$for non-prompt$${{\textrm{D}}^{0}}$$${\text{D}}^0$mesons with a significance of 2.7$$\sigma $$$\sigma$. The non-prompt$${{\textrm{D}}^{0}}$$${\text{D}}^0$-meson$$v_2$$$v_2$is lower than that of prompt non-strange D mesons with 3.2$$\sigma $$$\sigma$significance in$$2< p_\textrm{T} < 8~\textrm{GeV}/c$$$2<p_{\text{T}}<8\text{GeV}/c$, and compatible with the$$v_2$$$v_2$of beauty-decay electrons. Theoretical calculations of beauty-quark transport in a hydrodynamically expanding medium describe the measurement within uncertainties.

    

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