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: Dark matter remains one of the most puzzling mysteries in Fundamental Physics of our times. Experiments at high-energy physics colliders are expected to shed light to its nature and determine its properties. This review focuses on recent searches for dark matter signatures at the Large Hadron Collider, also discussing related prospects in future e(+)e(-) colliders.

Abstract: We study the interaction between two B = 1 states in the Chiral Dilaton Model where baryons are described as nontopological solitons arising from the interaction of chiral mesons and quarks. By using the hedgehog solution for B = 1 states we construct, via a product ansatz, three possible B = 2 configurations to analyse the role of the relative orientation of the hedgehog quills in the dynamics of the soliton-soliton interaction and investigate the behavior of these solutions in the range of long/intermediate distance. One of the solutions is quite binding due to the dynamics of the pi and sigma fields at intermediate distance and should be used for nuclear matter studies. Since the product ansatz break down as the two solitons get close, we explore the short range distance regime with a model that describes the interaction via a six-quark bag ansatz. We calculate the interaction energy as a function of the inter-soliton distance and show that for small separations the six quarks bag, assuming a hedgehog structure, provides a stable bound state that at large separations connects with a special configuration coming from the product ansatz.

Abstract: We study the collisional aspects of jet quenching in a high-energy nuclear collision, especially in the final state pion gas. The jet has a large energy, and acquires momentum transverse to its axis more effectively by multiple soft collisions than by few hard scatterings (as known from analogous systems such as J/psi production at Hera). Such regime of large E and small momentum transfer corresponds to Regge kinematics and is characteristically dominated by the pomeron. From this insight we estimate the jet quenching parameter in the hadron medium (largely a pion gas) at the end of the collision, which is naturally small and increases with temperature in line with the gas density and compare it to the jet quenching parameter obtained within the quark-gluon plasma (QGP) phase in widely known perturbative approximations. The physics in the quark-gluon plasma/liquid phase is less obvious, and here we revisit a couple of simple estimates that suggest indeed that the pomeron-mediated interactions are very relevant and should be included in analysis of the jet quenching parameter. Finally, since the occasional hard collisions produce features characteristic of a Levy flight in the q(perpendicular to)(2) plane perpendicular to the jet axis, we suggest one- and two-particle q perpendicular to correlations as interesting experimental probes sensitive to the nature (softness versus hardness) of the interactions of a jet inside the QGP.

Abstract: We analyze relevant signals expected at the LHC for a left sneutrino as the lightest supersymmetric particle (LSP). The discussion is carried out in the “mu from nu” supersymmetric standard model (mu nu SSM), where the presence of R-parity breaking couplings involving right-handed neutrinos solves the μproblem and reproduces neutrino data. The sneutrinos are pair produced via a virtual W, Z or gamma in the s channel. From the prompt decay of a pair of left sneutrinos LSPs of any family, a significant diphoton signal plus missing transverse energy (MET) from neutrinos can be present in the mass range 118-132 GeV, with 13 TeV center-of-mass energy and an integrated luminosity of 100 fb(-1). In addition, in the case of a pair of tau left sneutrinos LSPs, given the large value of the tau Yukawa coupling diphoton plus leptons and/or multileptons can appear. We find that the number of expected events for the multilepton signal, together with properly adopted search strategies, is sufficient to give a significant evidence for a sneutrino of mass in the range 130-310 GeV, even with the integrated luminosity of 20 fb(-1). In the case of the signal producing diphoton plus leptons, an integrated luminosity of 100 fb(-1) is needed to give a significant evidence in the mass range 95-145 GeV. Finally, we discuss briefly the presence of displaced vertices and the associated range of masses.