Shared Rule in Federal Political Systems: Conceptual Lessons from Subnational Switzerland

This article reconceptualizes shared rule and uses novel data to measure it, thus addressing two shortcomings of federal literature. First, while most studies focus on self-rule, one question that is largely neglected is how lower-level governments can influence politics at a higher level in the absence of “second” chambers. The answer is through shared rule. A second shortcoming is that even when addressing this question, scholars concentrate on constitutional-administrative aspects of vertical intergovernmentalism, neglecting more informal, “political” dynamics. Comparing the twenty-six Swiss cantons allows drawing two lessons for federal studies: That shared rule is multifaceted and complex, and that to study informal territorial actors as well as direct political processes is indispensable to understand how power is actually distributed in federal political systems.

Δ I = 1 / 2 rule for kaon decays derived from QCD infrared fixed point

This article gives details of our proposal to replace ordinary chiral SU(3)L×SU(3)R perturbation theory χPT3 by three-flavor chiral-scale perturbation theory χPTσ. In χPTσ, amplitudes are expanded at low energies and small u,d,s quark masses about an infrared fixed point αIR of three-flavor QCD. At αIR, the quark condensate ⟨q¯q⟩vac≠0 induces nine Nambu-Goldstone bosons: π,K,η, and a 0++ QCD dilaton σ. Physically, σ appears as the f0(500) resonance, a pole at a complex mass with real part ≲ mK. The ΔI=1/2 rule for nonleptonic K decays is then a consequence of χPTσ, with a KSσ coupling fixed by data for γγ→ππ and KS→γγ. We estimate RIR≈5 for the nonperturbative Drell-Yan ratio R=σ(e+e−→hadrons)/σ(e+e−→μ+μ−) at αIR and show that, in the many-color limit, σ/f0 becomes a narrow qq¯ state with planar-gluon corrections. Rules for the order of terms in χPTσ loop expansions are derived in Appendix A and extended in Appendix B to include inverse-power Li-Pagels singularities due to external operators. This relates to an observation that, for γγ channels, partial conservation of the dilatation current is not equivalent to σ-pole dominance.