We study the very long-range bond-percolation problem on a linear chain with both sites and bonds dilution. Very long range means that the probability $p_{ij}$ for a connection between two occupied sites $i,j$ at a distance $r_{ij}$ decays as a power
law, i.e. $p_{ij} = rho/[r_{ij}^alpha N^{1-alpha}]$ when $ 0 le alpha < 1$, and $p_{ij} = rho/[r_{ij} ln(N)]$ when $alpha = 1$. Site dilution means that the occupancy probability of a site is $0 < p_s le 1$. The behavior of this model results from the competition between long-range connectivity, which enhances the percolation, and site dilution, which weakens percolation. The case $alpha=0$ with $p_s =1 $ is well-known, being the exactly solvable mean-field model. The percolation order parameter $P_infty$ is investigated numerically for different values of $alpha$, $p_s$ and $rho$. We show that in the ranges $ 0 le alpha le 1$ and $0 < p_s le 1$ the percolation order parameter $P_infty$ depends only on the average connectivity $gamma$ of sites, which can be explicitly computed in terms of the three parameters $alpha$, $p_s$ and $rho$.
One of the first channels to be experimentally analyzed at the LHC is $ p + p longrightarrow l^+ + l ^- + X $. A resonance in this channel would be a clear indication of a new gauge neutral boson, as proposed in many extended models. In this paper we
call attention to the possibility that the new resonance in this channel could have spin zero. A new high mass spin zero state could be a strong indication of the composite nature of the standard model particles. We have made a comparison between spin zero and spin one for the new hypothetical heavy gauge particle production and decays and we show some distributions that can easily identify their spins.
Torsion models constitute a well known class of extended quantum gravity models. In this paper we study some phenomenological consequences of a torsion field interacting with fermions at LHC. A torsion field could appear as a new heavy state characte
rized by its mass and couplings to fermions. These new states will form a resonance decaying into difermions, as occurs in many extensions of the Standard Model, such as models predicting the existence of additional neutral gauge bosons, usually named $Z^prime$. Using the dielectron channel we evaluate the integrated luminosity needed for a $5sigma$ discovery as a function of the torsion mass, for different coupling values. We also calculate the luminosity needed for discriminate, with 95% C.L., the two possible different torsion natures. Finally, we show that the observed signal coming from the torsion field could be distinguished from a signal coming from a new neutral gauge boson, provided there is enough luminosity.
In this paper we discuss the consequences of including a new heavy right-handed neutrino singlet $N_R$ in the littlest Higgs model. This new state is not connected with the light neutrinos {it via} the seesaw mechanism. A very interesting property of
this extended model is the full coupling of the new neutral gauge boson $A_H$ to $N_R$, giving large total cross sections and suggesting a wide range of experimental search for the $N_R$ at the p p collider CERN-LHC and future electron-positron collider ILC.
