Abstract We develop a method for solving two- and three-body bound state problems using unsupervised machine learning with deep neural networks (DNN). By taking coordinates as direct inputs, the DNN provides a functional-ansatz-free alternative to traditional methods, allowing for a vast exploration of the parametric space. We apply this technique to calculate the properties of the deuteron and triton using a realistic chiral effective field theory ( $$\chi $$ χ EFT) potential at N $$^3$$ 3 LO, explicitly including central, tensor, and spin-orbit forces. Our results demonstrate high precision in binding energies and wave function structures. This approach offers a promising framework for the study of nuclear and hadronic many-body problems.

Abstract Rare event searches demand extremely low background levels, necessitating ever-advancing screening techniques to enhance sensitivity. Liquid scintillators are highly attractive as detector media due to their inherent radiopurity and scalability in mass. In this work, we present a screening procedure to measure ultra-trace concentrations of natural contaminants – $$^{238}$$ 238 U and $$^{232}$$ 232 Th – with sensitivities at the $${10}^{-15}$$ 10 - 15 g/g level. Our method combines neutron activation analysis with radiochemical techniques, followed by $$\beta $$ β / $$\gamma $$ γ coincidence spectroscopy to minimize interference backgrounds. This approach achieves sensitivities of $$0.65 \cdot 10^{-15}$$ 0.65 · 10 - 15 g/g for $$^{238}$$ 238 U and $$1.9 \cdot 10^{-15}$$ 1.9 · 10 - 15 g/g for $$^{232}$$ 232 Th, among the best reported worldwide. Potential pathways for further sensitivity improvements are outlined in the conclusions.

Abstract We analyze the rare semileptonic decays $$B_{c}^+ \rightarrow D^{*+}(\rightarrow P_1 P_2)\ell ^{+}\ell ^{-}$$ B c + → D ∗ + ( → P 1 P 2 ) ℓ + ℓ - , with $$P_1 P_2 = D^+ \pi ^0$$ P 1 P 2 = D + π 0 or $$D^0 \pi ^+$$ D 0 π + , and $$\ell =\mu , \tau $$ ℓ = μ , τ . We focus on the impact of weak annihilation contributions alongside penguin, box, and long-distance effects. Using the effective Hamiltonian for $$b \rightarrow d \ell ^+ \ell ^-$$ b → d ℓ + ℓ - transitions and $$B_c \rightarrow D^{*}$$ B c → D ∗ form factors from covariant confined quark model inputs, we compute the differential branching ratios, forward–backward asymmetry, longitudinal helicity fraction of the $$D^{*}$$ D ∗ , and various normalized angular coefficients. The results of the observables show that weak annihilation effects are sizable, particularly at low $$q^2$$ q 2 , significantly modifying several observables and shifting zero-crossings. Resonance effects dominate at high $$q^2$$ q 2 , restricting reliable analysis windows. We conclude that the inclusion of weak annihilation is essential for precise Standard Model predictions and for isolating possible New Physics effects in $$B_c^+ \rightarrow D^{*+} \ell ^+ \ell ^-$$ B c + → D ∗ + ℓ + ℓ - decays.

Abstract Recently, references [1, 2] found that the repetitive Penrose process cannot extract all the extractable rotational energy of a Kerr black hole, and reference [3] found that the repetitive electric Penrose process cannot extract all the electrical energy of a Reissner-Nordström (RN) black hole. In this paper, we intend to study the repetitive Penrose process in the Kerr-de Sitter (Kerr-dS) black hole. We will explore influences of the cosmological parameter on the repetitive Penrose process. The results show that, apart from the comparable features documented earlier, the Kerr-dS black hole yields a higher energy return on investment (EROI) and single-extraction energy capability compared to the Kerr black hole. Specifically, the larger the cosmological parameter, the stronger the EROI and the single-extraction energy capability. Furthermore, we also find that at a lower decay radius, the Kerr black hole exhibits a higher energy utilization efficiency (EUE) and more extracted energy after the repetitive Penrose process is completed. However, at a higher decay radius, the situation is reversed, i.e., the Kerr-dS black hole exhibits a higher EUE and more extracted energy, which is due to the existence of stopping condition of the iteration.

Abstract The similarity between the dark matter and baryon energy densities suggests an existence of a dark sector analogous to QCD. In addition, small-scale structure anomalies can be addressed by dark matter self-interactions with cross sections comparable to those of QCD. Both observations point toward a GeV-scale dark QCD sector. Motivated by these two coincidences, we investigate the parameter space of a distinctive chiral dark QCD model featuring a MeV-scale dark photon with axial-vector couplings. We also discuss a possible third coincidence associated with the latest measurement of $$N_\textrm{eff}$$ N eff . Current constraints leave a finite and testable region of parameter space that can be probed by future experiments such as the Gamma Factory.

Abstract In this study, we analyze the first measurement of the electron-positron invariant mass spectrum in $$J/\psi \rightarrow \pi ^0 e^+e^-$$ J / ψ → π 0 e + e - by BESIII, using the framework of resonance chiral theory. Our results indicate that both strong interaction and electromagnetic transition are essential to accurately describe the data. We obtain the $$\pi ^0$$ π 0 transition form factor for $$J/\psi \rightarrow \pi ^0\gamma ^*$$ J / ψ → π 0 γ ∗ and the corresponding decay branching ratios for $$J/\psi \rightarrow \pi ^0 l^+l^-$$ J / ψ → π 0 l + l - . The decay process $$J/\psi \rightarrow \pi ^0 V$$ J / ψ → π 0 V is also examined. It is found that $$J/\psi \rightarrow \pi ^0 \rho ^0$$ J / ψ → π 0 ρ 0 is dominated by the strong interaction, while the other two channels, $$J/\psi \rightarrow \pi ^0 \omega $$ J / ψ → π 0 ω and $$\pi ^0 \phi $$ π 0 ϕ , arise primarily from electromagnetic transitions.

Abstract We generalize neutrino energy density content in the early Universe near BBN era $$T\simeq 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> MeV within Tsallis nonextensive statistics. By using Curado–Tsallis constraints we obtain generalized distribution functions $$f_q(E)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>E</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . We compute the generalized thermodynamic integral for the energy density $$\rho _q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:math> . We define a reescaling which is a ratio between the deformed energy density and the standard extensive case. The last was used to directly map and deform neutrino content via the effective number of neutrinos $$N_\textrm{eff}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msub> </mml:math> . The deformation prediction was confronted against CMB+BAO and BBN data for $$N_\textrm{eff}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msub> </mml:math> by a joint/combined $$\chi ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> type-fit. We obtained the constraints $$|q-1|\le 1.09\times 10^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>q</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mn>1.09</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> (95% CL) and $$|q-1|\le 1.32\times 10^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>q</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mn>1.32</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> (99% CL) from the combined analysis by numerically calculating the best value of the Tsallis parameter $$q_\textrm{best}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>q</mml:mi> <mml:mtext>best</mml:mtext> </mml:msub> </mml:math> .

Abstract We investigate the realization of a nonsingular cosmological bounce in metric f ( R ) gravity using a controlled exponential deformation of the Starobinsky $$R^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> model. Adopting a smooth Gaussian-type bouncing scale factor, we first demonstrate a no-go result showing that a positive-curvature vacuum bounce cannot be supported by the model $$f(R)=R+\alpha R^{2}(1-e^{-R/R_b})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>R</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> alone. We then show that a minimal extension obtained by introducing a constant term restores the bounce exactly, with the constant fixed algebraically by the bounce condition. A systematic parameter-space scan is performed to identify regions free of ghost and tachyonic instabilities. Working in the Einstein frame, we study the evolution of scalar and tensor perturbations across the bounce and show that both remain finite and well behaved. Our results establish a minimal, perturbatively stable realization of a vacuum bounce in f ( R ) gravity that goes beyond background-level constructions.

Abstract We investigate and update observational constraints on cosmological parameters within the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM and dynamical dark energy frameworks, using a new compilation of the transverse (or 2D) BAO data, measurements that provide a relatively model-independent estimate of the BAO angular scale at a given redshift. Firstly, we assess the consistency of this compilation with CMB-Planck data and recent BAO results from the DESI collaboration. After confirming minimal tension with CMB data, we perform a series of joint analyses combining CMB data with the 2D BAO compilation, as well as with several recent Type Ia supernova (SNIa) samples. In all cases, we compare the constraining power of the 2D BAO data with that of DESI DR2 data (3D BAO). Our results indicate that combining 2D BAO with CMB and SNIa data provides observational constraints that are in agreement with those obtained using DESI DR2 data. Although the precision of DESI DR2 results remains higher, as expected due to the more accurate 3D measurements, the 2D BAO compilation combined with other probes yields strong constraints. For example, in the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM context, we find (CMB + 2D BAO): $$H_0 = 68.16^{+0.41}_{-0.37} \,\,\, \text {km s}^{-1}\,\text {Mpc}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>68</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>16</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.37</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.41</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace/> <mml:mspace/> <mml:mspace/> <mml:mtext>km</mml:mtext> <mml:mspace/> <mml:msup> <mml:mtext>s</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:msup> <mml:mtext>Mpc</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> and $$\Sigma m_{\nu } &lt; 0.081~\textrm{eV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Σ</mml:mi> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>ν</mml:mi> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>0.081</mml:mn> <mml:mspace/> <mml:mtext>eV</mml:mtext> </mml:mrow> </mml:math> (95% CL). These results are consistent with analogous analyses using DESI DR2. Several other cases are investigated and discussed in the main text. Our results show that this new 2D BAO compilation is robust and delivers meaningful cosmological constraints. Parameters from 2D BAO alone agree with CMB-only results, with no significant tension. Overall, 2D and 3D BAO provide consistent and complementary information when combined with other probes.

Abstract The weak cosmic censorship conjecture plays a foundational role in classical gravity by asserting that spacetime singularities are generically hidden behind event horizons. In this work, we explore its robustness in the Einstein–Maxwell-scalar theory with fractional coupling by studying both static black hole solutions and their fully nonlinear dynamical evolution. We identify a class of scalarized black holes that develop negative energy density near the event horizon, indicating violations of the classical energy conditions. Numerical evolutions of perturbed configurations reveal that sufficiently strong fractional coupling drives rapid curvature growth and geometric degeneration in the near-horizon region, accompanied by persistent negative energy density. While the simulations do not resolve the ultimate end state, the observed dynamics consistently point toward a weakening of the horizon-supporting structure and are suggestive of incipient naked singularity formation. These results uncover a classical mechanism through which fractional coupling can challenge the validity of the weak cosmic censorship conjecture in asymptotically flat spacetimes.