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1. Precision studies for string derived $$Z'$$ dynamics at the LHC

   https://doi.org/10.1140/epjc/s10052-023-11223-5  

   McEntaggart, Andrew ; Faraggi, Alon E. ; Guzzi, Marco ( January 2023 , The European Physical Journal C)

   We consider$$Z'$$$Z^{\prime }$s in heterotic string derived models and study$$Z'$$$Z^{\prime }$resonant production at the TeV scale at the Large Hadron Collider (LHC). We use various kinematic differential distributions for the Drell–Yan process at NNLO in QCD to explore the parameter space of such models and investigate$$Z'$$$Z^{\prime }$couplings. In particular, we study the impact ofZ-$$Z'$$$Z^{\prime }$kinetic-mixing interactions on forward-backward asymmetry ($$A_{FB}$$$A_{\mathrm{FB}}$) and other distributions at the LHC.

    

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2. Decay of Multi-point Correlation Functions in $$\mathbb {Z}^d$$

   https://doi.org/10.1007/s00220-023-04884-6  

   Han, Rui ; Yang, Fan ( February 2024 , Communications in Mathematical Physics)

   We prove multi-point correlation bounds in$$\mathbb {Z}^d$$$Z^d$for arbitrary$$d\ge 1$$$d\ge 1$with symmetrized distances, answering open questions proposed by Sims–Warzel (Commun Math Phys 347(3):903–931, 2016) and Aza–Bru–Siqueira Pedra (Commun Math Phys 360(2):715–726, 2018). As applications, we prove multi-point correlation bounds for the Ising model on$$\mathbb {Z}^d$$$Z^d$, and multi-point dynamical localization in expectation for uniformly localized disordered systems, which provides the first examples of this conjectured phenomenon by Bravyi–König (Commun Math Phys 316(3):641–692, 2012) .

    

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3. Photo-response of the $$N=Z$$ nucleus $$^{24}$$Mg

   https://doi.org/10.1140/epja/s10050-023-01111-7  

   Deary, J ; Scheck, M ; Schwengner, R ; O’Donnell, D ; Bemmerer, D ; Beyer, R ; Hensel, Th ; Junghans, A R ; Kögler, T ; Müller, S E ; et al ( September 2023 , The European Physical Journal A)

   The electricE1 and magneticM1 dipole responses of the$$N=Z$$$N=Z$nucleus$$^{24}$$${}^{24}$Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the$$^{24}$$${}^{24}$Mg($$\gamma ,\gamma ^{\prime }$$$\gamma ,{\gamma }^{\prime }$) reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one$$J^{\pi }=1^-$$$J^{\pi }=1^{-}$, four$$J^{\pi }=1^+$$$J^{\pi }=1^{+}$, and six$$J^{\pi }=2^+$$$J^{\pi }=2^{+}$states in$$^{24}$$${}^{24}$Mg. De-excitation$$\gamma $$$\gamma$rays were detected using the four high-purity germanium detectors of the$$\gamma $$$\gamma$ELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total$$B(M1)\uparrow = 2.7(3)~\mu _N^2$$$B\left(M1\right)\uparrow =2.7\left(3\right){\mu }_N^2$is observed, but this$$N=Z$$$N=Z$nucleus exhibits only marginalE1 strength of less than$$\sum B(E1)\uparrow \le 0.61 \times 10^{-3}$$$\sum B\left(E1\right)\uparrow \le 0.61\times {10}^{-3}$ e$$^2 \, $$${}^2$fm$$^2$$${}^2$. The$$B(\varPi 1, 1^{\pi }_i \rightarrow 2^+_1)/B(\varPi 1, 1^{\pi }_i \rightarrow 0^+_{gs})$$$B(\Pi 1,1_i^{\pi }\to 2_1^{+})/B(\Pi 1,1_i^{\pi }\to 0_{\mathrm{gs}}^{+})$branching ratios in combination with the expected results from the Alaga rules demonstrate thatKis a good approximative quantum number for$$^{24}$$${}^{24}$Mg. The use of the known$$\rho ^2(E0, 0^+_2 \rightarrow 0^+_{gs})$$${\rho }^2(E0,0_2^{+}\to 0_{\mathrm{gs}}^{+})$strength and the measured$$B(M1, 1^+ \rightarrow 0^+_2)/B(M1, 1^+ \rightarrow 0^+_{gs})$$$B(M1,1^{+}\to 0_2^{+})/B(M1,1^{+}\to 0_{\mathrm{gs}}^{+})$branching ratio of the 10.712 MeV$$1^+$$$1^{+}$level allows, in a two-state mixing model, an extraction of the difference$$\varDelta \beta _2^2$$$\Delta {\beta }_2^2$between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV$$0^+_2$$$0_2^{+}$level.

    

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4. Search for heavy resonances decaying into a Z or W boson and a Higgs boson in final states with leptons and b-jets in 139 fb−1 of pp collisions at $$ \sqrt{s} $$ = 13 TeV with the ATLAS detector

   https://doi.org/10.1007/JHEP06(2023)016  

   Aad, G. ; Abbott, B. ; Abbott, D. C. ; Abeling, K. ; Abidi, S. H. ; Aboulhorma, A. ; Abramowicz, H. ; Abreu, H. ; Abulaiti, Y. ; Abusleme Hoffman, A. C. ; et al ( June 2023 , Journal of High Energy Physics)

   This article presents a search for new resonances decaying into aZorWboson and a 125 GeV Higgs bosonh, and it targets the$$ \nu \overline{\nu}b\overline{b} $$$\nu \overline{\nu }b\overline{b}$,$$ {\ell}^{+}{\ell}^{-}b\overline{b} $$${\ell }^{+}{\ell }^{-}b\overline{b}$, or$$ {\ell}^{\pm}\nu b\overline{b} $$${\ell }^{\pm }\mathrm{\nu b}\overline{b}$final states, whereℓ=eorμ, in proton-proton collisions at$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV. The data used correspond to a total integrated luminosity of 139 fb⁻¹collected by the ATLAS detector during Run 2 of the LHC at CERN. The search is conducted by examining the reconstructed invariant or transverse mass distributions ofZhorWhcandidates for evidence of a localised excess in the mass range from 220 GeV to 5 TeV. No significant excess is observed and 95% confidence-level upper limits between 1.3 pb and 0.3 fb are placed on the production cross section times branching fraction of neutral and charged spin-1 resonances and CP-odd scalar bosons. These limits are converted into constraints on the parameter space of the Heavy Vector Triplet model and the two-Higgs-doublet model.

    

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5. From approximate to exact integer programming

   https://doi.org/10.1007/s10107-024-02084-1  

   Dadush, Daniel ; Eisenbrand, Friedrich ; Rothvoss, Thomas ( April 2024 , Mathematical Programming)

   Approximate integer programming is the following: For a given convex body$$K \subseteq {\mathbb {R}}^n$$$K\subseteq R^n$, either determine whether$$K \cap {\mathbb {Z}}^n$$$K\cap Z^n$is empty, or find an integer point in the convex body$$2\cdot (K - c) +c$$$2·(K-c)+c$which isK, scaled by 2 from its center of gravityc. Approximate integer programming can be solved in time$$2^{O(n)}$$$2^{O\left(n\right)}$while the fastest known methods for exact integer programming run in time$$2^{O(n)} \cdot n^n$$$2^{O\left(n\right)}·n^n$. So far, there are no efficient methods for integer programming known that are based on approximate integer programming. Our main contribution are two such methods, each yielding novel complexity results. First, we show that an integer point$$x^* \in (K \cap {\mathbb {Z}}^n)$$$x^{\ast }\in (K\cap Z^n)$can be found in time$$2^{O(n)}$$$2^{O\left(n\right)}$, provided that theremaindersof each component$$x_i^* \mod \ell $$$x_i^{\ast }mod\ell$for some arbitrarily fixed$$\ell \ge 5(n+1)$$$\ell \ge 5(n+1)$of$$x^*$$$x^{\ast }$are given. The algorithm is based on acutting-plane technique, iteratively halving the volume of the feasible set. The cutting planes are determined via approximate integer programming. Enumeration of the possible remainders gives a$$2^{O(n)}n^n$$$2^{O\left(n\right)}{n}^n$algorithm for general integer programming. This matches the current best bound of an algorithm by Dadush (Integer programming, lattice algorithms, and deterministic, vol. Estimation. Georgia Institute of Technology, Atlanta, 2012) that is considerably more involved. Our algorithm also relies on a newasymmetric approximate Carathéodory theoremthat might be of interest on its own. Our second method concerns integer programming problems in equation-standard form$$Ax = b, 0 \le x \le u, \, x \in {\mathbb {Z}}^n$$$Ax=b,0\le x\le u,x\in Z^n$. Such a problem can be reduced to the solution of$$\prod _i O(\log u_i +1)$$${\prod }_{i}O(log{u}_i+1)$approximate integer programming problems. This implies, for example thatknapsackorsubset-sumproblems withpolynomial variable range$$0 \le x_i \le p(n)$$$0\le x_i\le p\left(n\right)$can be solved in time$$(\log n)^{O(n)}$$${(logn)}^{O\left(n\right)}$. For these problems, the best running time so far was$$n^n \cdot 2^{O(n)}$$$n^n·2^{O\left(n\right)}$.

    

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