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1. Restricted spaces of holomorphic sections vanishing along subvarieties

   https://doi.org/10.1007/s00209-025-03706-w  

   Coman, Dan; Marinescu, George; Nguyên, Viêt-Anh (May 2025, Mathematische Zeitschrift)

   Abstract LetXbe a compact normal complex space of dimensionnandLbe a holomorphic line bundle onX. Suppose that$$\Sigma =(\Sigma _1,\ldots ,\Sigma _\ell )$$ $\Sigma =({\Sigma }_1,\dots ,{\Sigma }_{\ell })$ is an$$\ell $$ $\ell$ -tuple of distinct irreducible proper analytic subsets ofX,$$\tau =(\tau _1,\ldots ,\tau _\ell )$$ $\tau =({\tau }_1,\dots ,{\tau }_{\ell })$ is an$$\ell $$ $\ell$ -tuple of positive real numbers, and let$$H^0_0(X,L^p)$$ $H_0^0(X,L^p)$ be the space of holomorphic sections of$$L^p:=L^{\otimes p}$$ $L^p:=L^{\otimes p}$ that vanish to order at least$$\tau _jp$$ ${\tau }_{j}p$ along$$\Sigma _j$$ ${\Sigma }_j$ ,$$1\le j\le \ell $$ $1\le j\le \ell$ . If$$Y\subset X$$ $Y\subset X$ is an irreducible analytic subset of dimensionm, we consider the space$$H^0_0 (X|Y, L^p)$$ $H_0^0\left(X\right|Y,L^p)$ of holomorphic sections of$$L^p|_Y$$ $L^p{|}_Y$ that extend to global holomorphic sections in$$H^0_0(X,L^p)$$ $H_0^0(X,L^p)$ . Assuming that the triplet$$(L,\Sigma ,\tau )$$ $(L,\Sigma ,\tau )$ is big in the sense that$$\dim H^0_0(X,L^p)\sim p^n$$ $dim{H}_0^0(X,L^p)\sim p^n$ , we give a general condition onYto ensure that$$\dim H^0_0(X|Y,L^p)\sim p^m$$ $dim{H}_0^0\left(X\right|Y,L^p)\sim p^m$ . WhenLis endowed with a continuous Hermitian metric, we show that the Fubini-Study currents of the spaces$$H^0_0(X|Y,L^p)$$ $H_0^0\left(X\right|Y,L^p)$ converge to a certain equilibrium current onY. We apply this to the study of the equidistribution of zeros inYof random holomorphic sections in$$H^0_0(X|Y,L^p)$$ $H_0^0\left(X\right|Y,L^p)$ as$$p\rightarrow \infty $$ $p\to \infty$ . 

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2. Sensitivity of the CUPID experiment to $$0\nu \beta \beta $$ decay of 100Mo

   https://doi.org/10.1140/epjc/s10052-026-15296-w  

   Alfonso, K; Armatol, A; Augier, C; Avignone, F T; Azzolini, O; Barabash, A S; Bari, G; Barresi, A; Baudin, D; Bellini, F; et al (June 2026, The European Physical Journal C)

   Abstract CUPID is a next-generation bolometric experiment to search for neutrinoless double-beta decay ($$0\nu \beta \beta $$ $0\nu \beta \beta$ ) of¹⁰⁰Mo using Li$$_2$$ $_2^{}$ MoO$$_4$$ $_4^{}$ scintillating crystals. It will operate 1596 crystals at$$\sim $$ $\sim$ 10 mK in the CUORE cryostat at the Laboratori Nazionali del Gran Sasso in Italy. Each crystal will be facing two Ge-based bolometric light detectors for$$\alpha $$ $\alpha$ rejection. We compute the discovery and the exclusion sensitivity of CUPID to$$0\nu \beta \beta $$ $0\nu \beta \beta$ in a Frequentist and a Bayesian framework. This computation is done numerically based on pseudo-experiments. For the CUPIDbaselinescenario, with a background and an energy resolution of$$1.0 \times 10^{-4}$$ $1.0\times {10}^{-4}$ counts/keV/kg/yr and 5 keV FWHM at the Q-value, respectively, this results in a Bayesian exclusion sensitivity (90% c.i.) of$$\hat{T}_{1/2} > 1.6 \times 10^{27} \ \textrm{yr}$$ ${\hat{T}}_{1/2}>1.6\times {10}^{27}\text{yr}$ , corresponding to the effective Majorana neutrino mass of$$\hat{m}_{\beta \beta } < \ 9.6$$ ${\hat{m}}_{\beta \beta }<9.6$ –$$28 \ \textrm{meV}$$ $28\text{meV}$ . The Frequentist discovery sensitivity (3$$\sigma $$ $\sigma$ ) is$$\hat{T}_{1/2}= 1.0 \times 10^{27} \ \textrm{yr}$$ ${\hat{T}}_{1/2}=1.0\times {10}^{27}\text{yr}$ , corresponding to$$\hat{m}_{\beta \beta }= \ 12$$ ${\hat{m}}_{\beta \beta }=12$ –$$36 \ \textrm{meV}$$ $36\text{meV}$ . 

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3. 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)

   Abstract 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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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. Local Descriptions of the Heterotic SU(3) Moduli Space

   https://doi.org/10.1007/s00220-025-05309-2  

   de_Lázari, Hannah; Lotay, Jason D; Sá_Earp, Henrique N; Svanes, Eirik Eik (August 2025, Communications in Mathematical Physics)

   Abstract The heterotic$$\textrm{SU}(3)$$ $\text{SU}\left(3\right)$ system, also known as the Hull–Strominger system, arises from compactifications of heterotic string theory to six dimensions. This paper investigates the local structure of the moduli space of solutions to this system on a compact 6-manifoldX, using a vector bundle$$Q=(T^{1,0}X)^* \oplus {{\textrm{End}}}(E) \oplus T^{1,0}X$$ $Q={\left(T^{1,0}X\right)}^{\ast }\oplus \text{End}\left(E\right)\oplus T^{1,0}X$ , where$$E\rightarrow X$$ $E\to X$ is the classical gauge bundle arising in the system. We establish that the moduli space has an expected dimension of zero. We achieve this by studying the deformation complex associated to a differential operator$$\bar{D}$$ $\overline{D}$ , which emulates a holomorphic structure onQ, and demonstrating an isomorphism between the two cohomology groups which govern the infinitesimal deformations and obstructions in the deformation theory for the system. We also provide a Dolbeault-type theorem linking these cohomology groups to Čech cohomology, a result which might be of independent interest, as well as potentially valuable for future research. 

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