We examine possible correlations between $b \to s \ell_1^- \ell_2^+$ transitions -- both in the lepton flavor conserving ($\ell_1=\ell_2$) and violating case ($\ell_1 \neq \ell_2$) -- and purely leptonic flavor violating decays within the ABCD model [1], a minimal abelian extension of the Standard Model (SM) introducing a new $\text{U}(1)'$ symmetry. The associated neutral $Z'$ boson has generation-dependent, flavor non-universal couplings to SM fermions, governed by three rational parameters $\epsilon_{1,2,3}$, which sum to zero to ensure gauge anomaly cancellation. Each $\epsilon_i$ is common to all fermions of a given generation, thus inducing correlations among quark and lepton observables. For lepton flavor conserving (LFC) processes, only small deviations from SM predictions were found [2], reflecting the mutual constraints between the quark and lepton sectors, which preclude large discrepancies. On the other hand, the model allows tree-level lepton flavor violating (LFV) decays, yielding correlations between LFV $b\to s$ transitions and charged lepton decays. The analysis of such correlations shows that the current experimental upper bounds for the rates of $\tau^- \to \mu^-\mu^+\mu^-$, \ $\mu^-\to e^- \gamma$, \ $\mu^- \to e^- e^+e^-$ and $\mu^- \to e^-$ conversion in nuclei constrain branching ratios of LFV $B_{(s)}$ decays in hierarchical order [2].

We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages. In the first stage one approximates the stochastic equation by a differential equation with smooth coefficients randomly sampled at each time step. In the second stage the resulting regular equation is solved with the conventional operator-splitting techniques. This separation renders the approach flexible, allowing one to freely combine the numerical techniques most suitable to the problem at hand. The approach applies to ordinary and partial stochastic differential equations. In the latter case, it naturally gives rise to pseudo-spectral algorithms. We numerically test the strong convergence of several schemes obtained with this method in mechanical examples. Application to partial differential equations is illustrated by real-time simulations of a scalar field with quartic self-interaction coupled to a heat bath. The simulations accurately reproduce the thermodynamic properties of the field and are used to explore dynamics of thermal false vacuum decay in the case of negative quartic coupling.

The internal structure of exotic hadrons remains one of the most compelling puzzles in strong interaction physics. In this work, we provide crucial insights into the nature of doubly-charmed pentaquarks by investigating their electromagnetic properties. Using QCD light-cone sum rules, we present the first comprehensive calculation of the magnetic dipole moments of $D\Lambda_c$, $D^*\Lambda_c$, and $D\Lambda_c^*$ molecular pentaquarks with $J^P = \frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{3}{2}^-$, respectively. Our analysis reveals a striking hierarchy of magnetic moments: $\mu_{D\Lambda_c^*} > \mu_{D^*\Lambda_c} > \mu_{D\Lambda_c}$, driven by distinct quark-level mechanisms. While light quarks dominate the overall response, we find that charm quark contributions become strategically important when light quark contributions partially cancel. Beyond dipole moments, we predict higher multipoles--electric quadrupole and magnetic octupole moments--for the spin-$3/2$ $D^*\Lambda_c$ and $D\Lambda_c^*$ states, which fingerprint the spatial deformation of these configurations, revealing prolate versus oblate charge distributions. These results provide the first systematic predictions for electromagnetic moments of molecular pentaquark configurations, establishing essential benchmarks for future theoretical and experimental studies. By systematically comparing our predictions with both compact doubly-charmed and hidden-charm pentaquark configurations, we establish robust benchmarks that discriminate between competing structural models, ultimately resolving the nature of doubly-charmed exotic hadrons.