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A symmetry-preserving regularisation of a vector $$\times $$ × vector contact interaction (SCI) is used to deliver a unified treatment of semileptonic transitions involving $$\pi $$ π , K, $$D_{(s)}$$ D ( s ) , $$B_{(s,c)}$$ B ( s , c ) initial states. The framework is characterised by algebraic simplicity, few parameters, and the ability to simultaneously treat systems from Nambu–Goldstone modes to heavy+heavy mesons. Although the SCI form factors are typically somewhat stiff, the results are comparable with experiment and rigorous theory results. Hence, predictions for the five unmeasured $$B_{s,c}$$ B s , c branching fractions should be a reasonable guide. The analysis provides insights into the effects of Higgs boson couplings via current-quark masses on the transition form factors; and results on $$B_{(s)}\rightarrow D_{(s)}$$ B ( s ) → D ( s ) transitions yield a prediction for the Isgur–Wise function in fair agreement with contemporary data.

Using a symmetry-preserving regularisation of a vector $$\times $$ × vector contact interaction (SCI), we complete a systematic treatment of twelve semileptonic transitions with vector meson final states: $$D\rightarrow \rho $$ D → ρ , $$D_{(s)}\rightarrow K^*$$ D ( s ) → K ∗ , $$D_s\rightarrow \phi $$ D s → ϕ , $$B\rightarrow \rho $$ B → ρ , $$B_s\rightarrow K^*$$ B s → K ∗ , $$B_{(s)}\rightarrow D_{(s)}^*$$ B ( s ) → D ( s ) ∗ , $$B_c \rightarrow B_{(s)}^*, J/\psi , D^*$$ B c → B ( s ) ∗ , J / ψ , D ∗ ; and thereby finalise a unified analysis of semileptonic decays of heavy + heavy and heavy + light pseudoscalar mesons to both pseudoscalar and vector meson final states. The analysis is marked by algebraic simplicity, few parameters, and the ability to consistently describe systems from Nambu-Goldstone modes to heavy + heavy mesons. Regarding the behaviour of the transition form factors, the SCI results compare well wherever sound experimental or independent theory analyses are available; hence, the SCI branching fraction predictions should be a reasonable guide. Considering the ratios $$R(D_{(s)}^{(*)})$$ R ( D ( s ) ( ∗ ) ) , $$R(J/\psi )$$ R ( J / ψ ) , $$R(\eta _c)$$ R ( η c ) , whose values are key tests of lepton universality in weak interactions, the SCI values agree with Standard Model predictions. The $$B_{(s)}\rightarrow D_{(s)}^*$$ B ( s ) → D ( s ) ∗ transitions are used to predict the precursor functions that evolve into the universal Isgur–Wise function in the heavy-quark limit, with results that conform with those from other sources where such are available. The study also exposes effects on the transition form factors that flow from interference between emergent hadron mass from the strong interaction and Higgs boson couplings via current-quark masses, including flavour symmetry violation.

The skyrmion stability at finite isospin chemical potential is studied using the Skyrme Lagrangian with a finite pion mass . A critical value , above which a stable soliton does not exist, is found. We also explore some properties of the skyrmion as function of , i.e., the isoscalar rms radius and the isoscalar magnetic rms radius. Finally, considering the finite temperature effect on the skyrmion mass, we obtain a critical temperature , using the profile function of the skyrmion, above which the skyrmion mass does not have a minimum, which can be interpreted as the occurrence of the deconfinement phase transition.

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