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1. The $$\pi f_0(500)$$ decay of the $$a_1(1260)$$

   https://doi.org/10.1140/epjc/s10052-021-09574-y  

   Molina, R.; Döring, M.; Liang, W_H; Oset, E. (September 2021, The European Physical Journal C)

   Abstract We evaluate the$$a_1(1260) \rightarrow \pi \sigma (f_0(500))$$ $a_1\left(1260\right)\to \pi \sigma \left(f_0\left(500\right)\right)$decay width from the perspective that the$$a_1(1260)$$ $a_1\left(1260\right)$resonance is dynamically generated from the pseudoscalar–vector interaction and the$$\sigma $$ $\sigma$arises from the pseudoscalar–pseudoscalar interaction. A triangle mechanism with$$a_1(1260) \rightarrow \rho \pi $$ $a_1\left(1260\right)\to \rho \pi$followed by$$\rho \rightarrow \pi \pi $$ $\rho \to \pi \pi$and a fusion of two pions within the loop to produce the$$\sigma $$ $\sigma$provides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of 13–22 MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decay width, which should provide valuable information on the nature of the axial vector and scalar meson resonances and help clarify the role of the$$\pi \sigma $$ $\pi \sigma$channel in recent lattice QCD calculations of the$$a_1$$ $a_1$. 

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2. Analytical sphere–thin rod interaction potential

   https://doi.org/10.1140/epje/s10189-025-00480-9  

   Wang, Junwen; Cheng, Shengfeng (April 2025, The European Physical Journal E)

   AbstractA compact analytical form is derived through an integration approach for the interaction between a sphere and a thin rod of finite and infinite lengths, with each object treated as a continuous medium of material points interacting by the Lennard-Jones 12-6 potential and the total interaction potential as a summation of the pairwise potential between material points on the two objects. Expressions for the resultant force and torque are obtained. Various asymptotic limits of the analytical sphere–rod potential are discussed. The integrated potential is applied to investigate the adhesion between a sphere and a thin rod. When the rod is sufficiently long and the sphere sufficiently large, the equilibrium separation between the two (defined as the distance from the center of the sphere to the axis of the rod) is found to be well approximated as$$a+0.787\sigma $$ $a+0.787\sigma$, whereais the radius of the sphere and$$\sigma $$ $\sigma$is the unit of length of the Lennard–Jones potential. Furthermore, the adhesion between the two is found to scale with$$\sqrt{a}$$ $\sqrt{a}$. Graphic abstract) 

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3. A new zero-free region for Rankin–Selberg 𝐿-functions

   https://doi.org/10.1515/crelle-2025-0009  

   Harcos, Gergely; Thorner, Jesse (March 2025, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract Let 𝜋 and ${\pi }^{\prime }$\pi^{\prime}be cuspidal automorphic representations of $\mathrm{GL}\left(n\right)$\mathrm{GL}(n)and $\mathrm{GL}\left(n^{\prime }\right)$\mathrm{GL}(n^{\prime})with unitary central characters.We establish a new zero-free region for all $\mathrm{GL}\left(1\right)$\mathrm{GL}(1)-twists of the Rankin–Selberg 𝐿-function $L(s,\pi \times {\pi }^{\prime })$L(s,\pi\times\pi^{\prime}), generalizing Siegel’s celebrated work on Dirichlet 𝐿-functions.As an application, we prove the first unconditional Siegel–Walfisz theorem for the Dirichlet coefficients of $-L^{\prime }(s,\pi \times {\pi }^{\prime })/L(s,\pi \times {\pi }^{\prime })$-L^{\prime}(s,\pi\times\pi^{\prime})/L(s,\pi\times\pi^{\prime}).Also, for $n\le 8$n\leq 8, we extend the region of holomorphy and nonvanishing for the twisted symmetric power 𝐿-functions $L(s,\pi ,{\mathrm{Sym}}^n\otimes \chi )$L(s,\pi,\mathrm{Sym}^{n}\otimes\chi)of any cuspidal automorphic representation of $\mathrm{GL}\left(2\right)$\mathrm{GL}(2). 

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4. 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)

   Abstract 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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5. Cyclic Shuffle-Compatibility Via Cyclic Shuffle Algebras

   https://doi.org/10.1007/s00026-023-00669-9  

   Liang, Jinting; Sagan, Bruce_E; Zhuang, Yan (October 2023, Annals of Combinatorics)

   Abstract A permutation statistic$${{\,\textrm{st}\,}}$$ $\text{st}$is said to be shuffle-compatible if the distribution of$${{\,\textrm{st}\,}}$$ $\text{st}$over the set of shuffles of two disjoint permutations$$\pi $$ $\pi$and$$\sigma $$ $\sigma$depends only on$${{\,\textrm{st}\,}}\pi $$ $\text{st}\pi$,$${{\,\textrm{st}\,}}\sigma $$ $\text{st}\sigma$, and the lengths of$$\pi $$ $\pi$and$$\sigma $$ $\sigma$. Shuffle-compatibility is implicit in Stanley’s early work onP-partitions, and was first explicitly studied by Gessel and Zhuang, who developed an algebraic framework for shuffle-compatibility centered around their notion of the shuffle algebra of a shuffle-compatible statistic. For a family of statistics called descent statistics, these shuffle algebras are isomorphic to quotients of the algebra of quasisymmetric functions. Recently, Domagalski, Liang, Minnich, Sagan, Schmidt, and Sietsema defined a version of shuffle-compatibility for statistics on cyclic permutations, and studied cyclic shuffle-compatibility through purely combinatorial means. In this paper, we define the cyclic shuffle algebra of a cyclic shuffle-compatible statistic, and develop an algebraic framework for cyclic shuffle-compatibility in which the role of quasisymmetric functions is replaced by the cyclic quasisymmetric functions recently introduced by Adin, Gessel, Reiner, and Roichman. We use our theory to provide explicit descriptions for the cyclic shuffle algebras of various cyclic permutation statistics, which in turn gives algebraic proofs for their cyclic shuffle-compatibility. 

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