Abstract: Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators b(p)(dagger) – labeled by prime numbers p – acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.

Abstract: We present a study of the many-body interaction between a D* and multi-rho. We use an extrapolation to SU(4) of the hidden gauge formalism, which produced dynamically the resonances f(2)(1270) in the rho rho interaction and D-2* (2460) in the rho D* interaction. We then let a third particle, rho, D*, or a resonance, collide with them, evaluating the scattering amplitudes in terms of the fixed center approximation of the Faddeev equations. We find several clear resonant structures above 2800 MeV in the multibody scattering amplitudes. They would correspond to new charmed resonances, D-3*, D-4*, D-5*, and D-6*, which are not yet listed in the Particle Data Group, which would be analogous to the rho(3)(1690), f(4)(2050), rho(5)(2350), f(6)(2510) and K-3*(1780), K-4*(2045), K-5*(2380) described before as multi-rho and K*-multi-rho states, respectively.

Abstract: We consider cumulant moments (cumulants) of the thrust distribution using predictions of the full spectrum for thrust including O(alpha(3)(s)) fixed order results, resummation of singular (NLL)-L-3 logarithmic contributions, and a class of leading power corrections in a renormalon-free scheme. From a global fit to the first thrust moment we extract the strong coupling and the leading power correction matrix element Omega(1). We obtain alpha(s)(m(Z)) = 0.1140 +/- (0.0004)(exp) +/- (0.0013)(hadr) +/- (0.0007)(pert), where the 1-sigma uncertainties are experimental, from hadronization (related to Omega(1)) and perturbative, respectively, and Omega(1) = 0.377 +/- (0.044)(exp) +/- (0.039)(pert) GeV. The nth thrust cumulants for n >= 2 are completely insensitive to Omega(1), and therefore a good instrument for extracting information on higher order power corrections, Omega'(n)/Q(n), from moment data. We find ((Omega) over tilde '2)(1/2) = 0.74 +/- (0.11)(exp) +/- (0.09)(pert) GeV.