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1. 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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2. Semileptonic form factors for $$B\rightarrow D^*\ell \nu $$ at nonzero recoil from $$2+1$$-flavor lattice QCD: Fermilab Lattice and MILC Collaborations

   https://doi.org/10.1140/epjc/s10052-022-10984-9  

   Bazavov, A. ; DeTar, C. E. ; Du, D. ; El-Khadra, A. X. ; Gámiz, E. ; Gelzer, Z. ; Gottlieb, S. ; Heller, U. M. ; Kronfeld, A. S. ; Laiho, J. ; et al ( December 2022 , The European Physical Journal C)

   We present the first unquenched lattice-QCD calculation of the form factors for the decay$$B\rightarrow D^*\ell \nu $$$B\to D^{\ast }\ell \nu$at nonzero recoil. Our analysis includes 15 MILC ensembles with$$N_f=2+1$$$N_f=2+1$flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from$$a\approx 0.15$$$a\approx 0.15$fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valencebandcquarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element$$|V_{cb}|$$$|V_{\mathrm{cb}}|$. We obtain$$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$$\left(V_{\mathrm{cb}}\right)=(38.40\pm 0.{68}_{\text{th}}\pm 0.{34}_{\text{exp}}\pm 0.{18}_{\text{EM}})\times {10}^{-3}$. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall$$\chi ^2\text {/dof} = 126/84$$${\chi }^2\text{/dof}=126/84$, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict$$R(D^*) = 0.265 \pm 0.013$$$R\left(D^{\ast }\right)=0.265\pm 0.013$, which confirms the current tension between theory and experiment.

    

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3. Search for light Higgs bosons from supersymmetric cascade decays in $$\text {pp}$$ collisions at $$\sqrt{s}=13\,\textrm{TeV}$$

   https://doi.org/10.1140/epjc/s10052-023-11581-0  

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

   A search is reported for pairs of light Higgs bosons ($${\textrm{H}} _1$$${\text{H}}_1$) produced in supersymmetric cascade decays in final states with small missing transverse momentum. A data set of LHC$$\hbox {pp}$$$\text{pp}$collisions collected with the CMS detector at$$\sqrt{s}=13\,\text {TeV} $$$\sqrt{s}=13\text{TeV}$and corresponding to an integrated luminosity of 138$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$is used. The search targets events where both$${\textrm{H}} _1$$${\text{H}}_1$bosons decay into Equation missing<#comment/>pairs that are reconstructed as large-radius jets using substructure techniques. No evidence is found for an excess of events beyond the background expectations of the standard model (SM). Results from the search are interpreted in the next-to-minimal supersymmetric extension of the SM, where a “singlino” of small mass leads to squark and gluino cascade decays that can predominantly end in a highly Lorentz-boosted singlet-like$${\textrm{H}} _1$$${\text{H}}_1$and a singlino-like neutralino of small transverse momentum. Upper limits are set on the product of the squark or gluino pair production cross section and the square of the Equation missing<#comment/>branching fraction of the$${\textrm{H}} _1$$${\text{H}}_1$in a benchmark model containing almost mass-degenerate gluinos and light-flavour squarks. Under the assumption of an SM-like Equation missing<#comment/>branching fraction,$${\textrm{H}} _1$$${\text{H}}_1$bosons with masses in the range 40–120$$\,\text {GeV}$$$\text{GeV}$arising from the decays of squarks or gluinos with a mass of 1200–2500$$\,\text {GeV}$$$\text{GeV}$are excluded at 95% confidence level.

    

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4. 3D Mirror Symmetry for Instanton Moduli Spaces

   https://doi.org/10.1007/s00220-023-04831-5  

   Koroteev, Peter ; Zeitlin, Anton M. ( September 2023 , Communications in Mathematical Physics)

   We prove that the Hilbert scheme ofkpoints on$${\mathbb {C}}^2$$$C^2$($$\hbox {Hilb}^k[{\mathbb {C}}^2]$$${\text{Hilb}}^k\left[C^2\right]$) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding quantum equivariant K-theory is invariant upon interchanging its Kähler and equivariant parameters as well as inverting the weight of the$${\mathbb {C}}^\times _\hbar $$$C_{ħ}^{\times }$-action. First, we find a two-parameter family$$X_{k,l}$$$X_{k,l}$of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of$$\hbox {Hilb}^k[{\mathbb {C}}^2]$$${\text{Hilb}}^k\left[C^2\right]$is obtained via direct limit$$l\longrightarrow \infty $$$l⟶\infty$and by imposing certain periodic boundary conditions on the quiver data. Throughout the proof, we employ the quantum/classical (q-Langlands) correspondence between XXZ Bethe Ansatz equations and spaces of twisted$$\hbar $$$ħ$-opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-Nsheaves on$${\mathbb {P}}^2$$$P^2$with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual.

    

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5. The $$L^p$$-Fisher–Rao metric and Amari–C̆encov $$\alpha $$-Connections

   https://doi.org/10.1007/s00526-024-02660-5  

   Bauer, Martin ; Le Brigant, Alice ; Lu, Yuxiu ; Maor, Cy ( February 2024 , Calculus of Variations and Partial Differential Equations)

   We introduce a family of Finsler metrics, called the$$L^p$$$L^p$-Fisher–Rao metrics$$F_p$$$F_p$, for$$p\in (1,\infty )$$$p\in (1,\infty )$, which generalizes the classical Fisher–Rao metric$$F_2$$$F_2$, both on the space of densities$${\text {Dens}}_+(M)$$${\text{Dens}}_{+}\left(M\right)$and probability densities$${\text {Prob}}(M)$$$\text{Prob}\left(M\right)$. We then study their relations to the Amari–C̆encov$$\alpha $$$\alpha$-connections$$\nabla ^{(\alpha )}$$${\nabla }^{\left(\alpha \right)}$from information geometry: on$${\text {Dens}}_+(M)$$${\text{Dens}}_{+}\left(M\right)$, the geodesic equations of$$F_p$$$F_p$and$$\nabla ^{(\alpha )}$$${\nabla }^{\left(\alpha \right)}$coincide, for$$p = 2/(1-\alpha )$$$p=2/(1-\alpha )$. Both are pullbacks of canonical constructions on$$L^p(M)$$$L^p\left(M\right)$, in which geodesics are simply straight lines. In particular, this gives a new variational interpretation of$$\alpha $$$\alpha$-geodesics as being energy minimizing curves. On$${\text {Prob}}(M)$$$\text{Prob}\left(M\right)$, the$$F_p$$$F_p$and$$\nabla ^{(\alpha )}$$${\nabla }^{\left(\alpha \right)}$geodesics can still be thought as pullbacks of natural operations on the unit sphere in$$L^p(M)$$$L^p\left(M\right)$, but in this case they no longer coincide unless$$p=2$$$p=2$. Using this transformation, we solve the geodesic equation of the$$\alpha $$$\alpha$-connection by showing that the geodesic are pullbacks of projections of straight lines onto the unit sphere, and they always cease to exists after finite time when they leave the positive part of the sphere. This unveils the geometric structure of solutions to the generalized Proudman–Johnson equations, and generalizes them to higher dimensions. In addition, we calculate the associate tensors of$$F_p$$$F_p$, and study their relation to$$\nabla ^{(\alpha )}$$${\nabla }^{\left(\alpha \right)}$.

    

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