Universal Relations in Composite Higgs Models

We initiate a phenomenological study of `universal relations' in composite Higgs models, which are dictated by nonlinear shift symmetries acting on the 125 GeV Higgs boson. These are relations among one Higgs couplings with two electroweak gauge bosons (HVV), two Higgses couplings with two electroweak gauge bosons (HHVV), one Higgs couplings with three electroweak gauge bosons (HVVV), as well as triple gauge boson couplings (TGC), which are all controlled by a single input parameter: the decay constant $f$ of the pseudo-Nambu-Goldstone Higgs boson. Assuming custodial invariance in strong sector, the relation is independent of the symmetry breaking pattern in the UV, for an arbitrary symmetric coset $G/H$. The complete list of corrections to HVV, HHVV, HVVV and TGC couplings in composite Higgs models is presented to all orders in $1/f$, and up to four-derivative level, without referring to a particular $G/H$. We then present several examples of universal relations in ratios of coefficients which could be extracted experimentally. Measuring the universal relation requires a precision sensitive to effects of dimension-8 operators in the effective Lagrangian and highlights the importance of verifying the tensor structure of HHVV interactions in the standard model, which remains untested to date.Comment: 31 pages, 6 figure

Universal scaling relations in molecular superconductors

Scaling relations between the superconducting transition temperature $T_{\rm c}$, the superfluid stiffness $\rho_{\rm s}$ and the normal state conductivity $\sigma_0(T_{\rm c})$ are identified within the class of molecular superconductors. These new scaling properties hold as $T_{\rm c}$ varies over two orders of magnitude for materials with differing dimensionality and contrasting molecular structure, and are dramatically different from the equivalent scaling properties observed within the family of cuprate superconductors. These scaling relations place strong constraints on theories for molecular superconductivity.Comment: 4 pages, 4 figure

Linear response theory in stochastic many-body systems revisited

The Green-Kubo relation, the Einstein relation, and the fluctuation-response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these universal relations for stochastic many-body systems. Through these simple proofs, we characterize the three relations as follows. The Green-Kubo relation is a direct result of the local detailed balance condition, the fluctuation-response relation represents the dynamic extension of both the Green-Kubo relation and the fluctuation relation in equilibrium statistical mechanics, and the Einstein relation can be understood by considering thermodynamics. We also clarify the interrelationships among the universal relations.Comment: 35 page