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1. A modular construction of unramified 𝑝-extensions of ℚ(ℕ^{1/𝕡})

   https://doi.org/10.1090/bproc/141  

   Lang, Jaclyn ; Wake, Preston ( October 2022 , Proceedings of the American Mathematical Society, Series B)

   We show that for primes$N, p \geq 5$with$N \equiv -1 \bmod p$, the class number of$\mathbb {Q}(N^{1/p})$is divisible by$p$. Our methods are via congruences between Eisenstein series and cusp forms. In particular, we show that when$N \equiv -1 \bmod p$, there is always a cusp form of weight$2$and level$\Gamma _0(N^2)$whose$\ell$th Fourier coefficient is congruent to$\ell + 1$modulo a prime above$p$, for all primes$\ell$. We use the Galois representation of such a cusp form to explicitly construct an unramified degree-$p$extension of$\mathbb {Q}(N^{1/p})$.

    

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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. Lp quasi-norm minimization: algorithm and applications

   https://doi.org/10.1186/s13634-024-01114-6  

   Sleem, Omar M. ; Ashour, M. E. ; Aybat, N. S. ; Lagoa, Constantino M. ( February 2024 , EURASIP Journal on Advances in Signal Processing)

   Sparsity finds applications in diverse areas such as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts and need less storage. This paper proposes a heuristic method for retrieving sparse approximate solutions of optimization problems via minimizing the$$\ell _{p}$$${\ell }_p$quasi-norm, where$$0$0<p<1$. An iterative two-block algorithm for minimizing the$$\ell _{p}$$${\ell }_p$quasi-norm subject to convex constraints is proposed. The proposed algorithm requires solving for the roots of a scalar degree polynomial as opposed to applying a soft thresholding operator in the case of$$\ell _{1}$$${\ell }_1$norm minimization. The algorithm’s merit relies on its ability to solve the$$\ell _{p}$$${\ell }_p$quasi-norm minimization subject to any convex constraints set. For the specific case of constraints defined by differentiable functions with Lipschitz continuous gradient, a second, faster algorithm is proposed. Using a proximal gradient step, we mitigate the convex projection step and hence enhance the algorithm’s speed while proving its convergence. We present various applications where the proposed algorithm excels, namely, sparse signal reconstruction, system identification, and matrix completion. The results demonstrate the significant gains obtained by the proposed algorithm compared to other$$\ell _{p}$$${\ell }_p$quasi-norm based methods presented in previous literature.

    

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4. 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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5. Search for Higgs boson pair production in association with a vector boson in pp collisions at $$\sqrt{s}=13\,\text {TeV}$$ with the ATLAS detector

   https://doi.org/10.1140/epjc/s10052-023-11559-y  

   Aad, G. ; Abbott, B. ; Abbott, D. C. ; Abeling, K. ; Abidi, S. H. ; Aboulhorma, A. ; Abramowicz, H. ; Abreu, H. ; Abulaiti, Y. ; Hoffman, A. C. ; et al ( June 2023 , The European Physical Journal C)

   This paper reports a search for Higgs boson pair (hh) production in association with a vector boson ($$W\; {\text {o}r}\; Z$$$W\text{o}rZ$) using 139 fb$$^{-1}$$${}^{-1}$of proton–proton collision data at$$\sqrt{s}=13\,\text {TeV}$$$\sqrt{s}=13\text{TeV}$recorded with the ATLAS detector at the Large Hadron Collider. The search is performed in final states in which the vector boson decays leptonically ($$W\rightarrow \ell \nu ,\, Z\rightarrow \ell \ell ,\nu \nu $$$W\to \ell \nu ,Z\to \ell \ell ,\nu \nu$with$$\ell =e, \mu $$$\ell =e,\mu$) and the Higgs bosons each decay into a pair ofb-quarks. It targetsVhhsignals from both non-resonanthhproduction, present in the Standard Model (SM), and resonanthhproduction, as predicted in some SM extensions. A 95% confidence-level upper limit of 183 (87) times the SM cross-section is observed (expected) for non-resonantVhhproduction when assuming the kinematics are as expected in the SM. Constraints are also placed on Higgs boson coupling modifiers. For the resonant search, upper limits on the production cross-sections are derived for two specific models: one is the production of a vector boson along with a neutral heavy scalar resonanceH, in the mass range 260–1000 GeV, that decays intohh, and the other is the production of a heavier neutral pseudoscalar resonanceAthat decays into aZboson andHboson, where theAboson mass is 360–800 GeV and theHboson mass is 260–400 GeV. Constraints are also derived in the parameter space of two-Higgs-doublet models.

    

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