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1. The $$^{12}$$C$$(\alpha ,\gamma )^{16}$$O reaction, in the laboratory and in the stars

   https://doi.org/10.1140/epja/s10050-025-01537-1  

   de_Boer, R J; Best, A; Brune, C R; Chieffi, A; Hebborn, C; Imbriani, G; Liu, W P; Shen, Y P; Timmes, F X; Wiescher, M (April 2025, The European Physical Journal A)

   Abstract The evolutionary path of massive stars begins at helium burning. Energy production for this phase of stellar evolution is dominated by the reaction path 3$$\alpha \rightarrow ^{12}$$ $\alpha {\to }^{12}$C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$O and also determines the ratio of$$^{12}$$ $_{}^{12}$C/$$^{16}$$ $_{}^{16}$O in the stellar core. This ratio then sets the evolutionary trajectory as the star evolves towards a white dwarf, neutron star or black hole. Although the reaction rate of the 3$$\alpha $$ $\alpha$process is relatively well known, since it proceeds mainly through a single narrow resonance in$$^{12}$$ $_{}^{12}$C, that of the$$^{12}$$ $_{}^{12}$C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$O reaction remains uncertain since it is the result of a more difficult to pin down, slowly-varying, portion of the cross section over a strong interference region between the high-energy tails of subthreshold resonances, the low-energy tails of higher-energy broad resonances and direct capture. Experimental measurements of this cross section require herculean efforts, since even at higher energies the cross section remains small and large background sources are often present that require the use of very sensitive experimental methods. Since the$$^{12}$$ $_{}^{12}$C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$O reaction has such a strong influence on many different stellar objects, it is also interesting to try to back calculate the required rate needed to match astrophysical observations. This has become increasingly tempting, as the accuracy and precision of observational data has been steadily improving. Yet, the pitfall to this approach lies in the intermediary steps of modeling, where other uncertainties needed to model a star’s internal behavior remain highly uncertain. 

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2. 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)

   Abstract 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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3. CUPID, the Cuore upgrade with particle identification

   https://doi.org/10.1140/epjc/s10052-025-14352-1  

   Alfonso, K; Armatol, A; Augier, C; Avignone_III, F T; Azzolini, O; Barabash, A S; Bari, G; Barresi, A; Baudin, D; Bellini, F; et al (July 2025, The European Physical Journal C)

   Abstract CUPID, the CUORE Upgrade with Particle Identification, is a next-generation experiment to search for neutrinoless double beta decay ($$0\mathrm {\nu \beta \beta }$$ $0\nu \beta \beta$) and other rare events using enriched Li$$_{2}$$ $_2^{}$$$^{100}$$ $_{}^{100}$MoO$$_{4}$$ $_4^{}$scintillating bolometers. It will be hosted by the CUORE cryostat located at the Laboratori Nazionali del Gran Sasso in Italy. The main physics goal of CUPID is to search for$$0\mathrm {\nu \beta \beta }$$ $0\nu \beta \beta$of$$^{100}$$ $_{}^{100}$Mo with a discovery sensitivity covering the full neutrino mass regime in the inverted ordering scenario, as well as the portion of the normal ordering regime with lightest neutrino mass larger than 10 meV. With a conservative background index of 10$$^{-4}$$ $_{}^{-4}$ cts$$/($$ $/($keV$$\cdot $$ $·$kg$$\cdot $$ $·$yr$$)$$ $)$, 240 kg isotope mass, 5 keV FWHM energy resolution at 3 MeV and 10 live-years of data taking, CUPID will have a 90% C.L. half-life exclusion sensitivity of$$1.8\cdot 10^{27}$$ $1.8·{10}^{27}$ yr, corresponding to an effective Majorana neutrino mass ($$m_{\beta \beta }$$ $m_{\beta \beta }$) sensitivity of 9–15 meV, and a$$3\sigma $$ $3\sigma$discovery sensitivity of$$1\cdot 10^{27}$$ $1·{10}^{27}$ yr, corresponding to an$$m_{\beta \beta }$$ $m_{\beta \beta }$range of 12–21 meV. 

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4. Search for $$B_{(s)}^{*0}\rightarrow \mu ^+\mu ^-$$ in $$B_c^+\rightarrow \pi ^+\mu ^+\mu ^-$$ decays

   https://doi.org/10.1140/epjc/s10052-024-13573-0  

   Aaij, R; Abdelmotteleb, A_S W; Beteta, C Abellan; Abudinén, F; Ackernley, T; Adefisoye, A A; Adeva, B; Adinolfi, M; Adlarson, P; Agapopoulou, C; et al (January 2025, The European Physical Journal C)

   Abstract A search for the very rare$$B^{*0}\rightarrow \mu ^+\mu ^-$$ $B_{}^{\ast 0}\to {\mu }^{+}{\mu }^{-}$and$$B_{s}^{*0}\rightarrow \mu ^+\mu ^-$$ $B_s^{\ast 0}\to {\mu }^{+}{\mu }^{-}$decays is conducted by analysing the$$B_c^+\rightarrow \pi ^+\mu ^+\mu ^-$$ $B_c^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$process. The analysis uses proton-proton collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9$$\text {\,fb}^{-1}$$ ${\text{,fb}}^{-1}$. The signal signatures correspond to simultaneous peaks in the$$\mu ^+\mu ^-$$ ${\mu }^{+}{\mu }^{-}$and$$\pi ^+\mu ^+\mu ^-$$ ${\pi }^{+}{\mu }^{+}{\mu }^{-}$invariant masses. No evidence for an excess of events over background is observed for either signal decay mode. Upper limits at the$$90\%$$ $90\%$confidence level are set on the branching fractions relative to that for$$B_c^+\rightarrow J\hspace{-1.66656pt}/\hspace{-1.111pt}\psi \pi ^+$$ $B_c^{+}\to J/\psi {\pi }^{+}$decays,$$\begin{aligned} \mathcal{R}_{B^{*0}(\mu ^+\mu ^-)\pi ^+/J\hspace{-1.66656pt}/\hspace{-1.111pt}\psi \pi ^+}&< 3.8\times 10^{-5}\ \text { and }\\ \mathcal{R}_{B_{s}^{*0}(\mu ^+\mu ^-)\pi ^+/J\hspace{-1.66656pt}/\hspace{-1.111pt}\psi \pi ^+}&< 5.0\times 10^{-5}. \end{aligned}$$ $\begin{array}{cc}R_{B_{}^{\ast 0}\left({\mu }^{+}{\mu }^{-}\right){\pi }^{+}/J/\psi {\pi }^{+}}^{}& <3.8\times {10}^{-5}\text{and}\\ R_{B_s^{\ast 0}\left({\mu }^{+}{\mu }^{-}\right){\pi }^{+}/J/\psi {\pi }^{+}}^{}& <5.0\times {10}^{-5}.\end{array}$ 

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5. Towards a Schinzel–Wójcik theorem for number fields

   https://doi.org/10.1007/s40879-025-00819-8  

   Pollack, Paul (April 2025, European Journal of Mathematics)

   Abstract Schinzel and Wójcik have shown that for every$$\alpha ,\beta \in \mathbb {Q}^{\times }\hspace{0.55542pt}{\setminus }\hspace{1.111pt}\{\pm 1\}$$ $\alpha ,\beta \in Q^{\times }\backslash \{\pm 1\}$, there are infinitely many primespwhere$$v_p(\alpha )=v_p(\beta )=0$$ $v_p\left(\alpha \right)=v_p\left(\beta \right)=0$and where$$\alpha $$ $\alpha$and$$\beta $$ $\beta$generate the same multiplicative group modp. We prove a weaker result in the same direction for algebraic numbers$$\alpha , \beta $$ $\alpha ,\beta$. Let$$\alpha , \beta \in \overline{\mathbb {Q}} ^{\times }$$ $\alpha ,\beta \in {\overline{Q}}^{\times }$, and suppose$$|N_{\mathbb {Q}(\alpha ,\beta )/\mathbb {Q}}(\alpha )|\ne 1$$ $|N_{Q(\alpha ,\beta )/Q}\left(\alpha \right)|\ne 1$and$$|N_{\mathbb {Q}(\alpha ,\beta )/\mathbb {Q}}(\beta )|\ne 1$$ $|N_{Q(\alpha ,\beta )/Q}\left(\beta \right)|\ne 1$. Then for some positive integer$$C = C(\alpha ,\beta )$$ $C=C(\alpha ,\beta )$, there are infinitely many prime idealsPof Equation missing<#comment/>where$$v_P(\alpha )=v_P(\beta )=0$$ $v_P\left(\alpha \right)=v_P\left(\beta \right)=0$and where the group$$\langle \beta \bmod {P}\rangle $$ $⟨\beta modP⟩$is a subgroup of$$\langle \alpha \bmod {P}\rangle $$ $⟨\alpha modP⟩$with$$[\langle \alpha \bmod {P}\rangle \,{:}\, \langle \beta \bmod {P}\rangle ]$$ $[⟨\alpha modP⟩:⟨\beta modP⟩]$dividingC. A key component of the proof is a theorem of Corvaja and Zannier bounding the greatest common divisor of shiftedS-units. 

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