Average formation lengths of baryons and antibaryons in string model

In this work it is continued the investigation of the space-time scales of the hadronization process in the framework of string model. The average formation lengths of several widely using species of baryons (antibaryons) such as $p$ ($\bar{p}$), $n$ ($\bar{n}$), $\Delta$ ($\bar{\Delta}$), $\Lambda$ ($\bar{\Lambda}$) and $\Sigma$ ($\bar{\Sigma}$) are studied. It is shown that they depend from electrical charges or, more precise, from quark contents of the hadrons. In particular, the average formation lengths of positively charged hadrons, for example protons, are considerably larger than of their negatively charged antiparticles, antiprotons. This statement is fulfilled for all nuclear targets and any value of the Bjorken scaling variable $x_{Bj}$. The main mechanism is direct production. Additional production mechanism in result of decay of resonances gives small contribution. It is shown that the average formation lengths of protons (antiprotons) are slowly rising (decreasing) functions of $x_{Bj}$, the ones of neutrons and antineutrons are slowly decreasing functions of $x_{Bj}$. The shape and behavior of average formation lengths for baryons qualitatively coincide with the ones for pseudoscalar mesons obtained earlier.Comment: 7 pages, 6 figure

Average formation length in string model

The space-time scales of the hadronization process in the framework of string model are investigated. It is shown that the average formation lengths of pseudoscalar mesons, produced in semi-inclusive deep inelastic scattering (DIS) of leptons on different targets, depend from their electrical charges. In particular the average formation lengths of positively charged hadrons are larger than of negatively charged ones. This statement is fulfiled for all using scaling functions, for $z$ (the fraction of the virtual photon energy transferred to the detected hadron) larger than 0.15, for all nuclear targets and any value of the Bjorken scaling variable $x_{Bj}$. In all cases, the main mechanism is direct production of pseudoscalar mesons. Including in consideration additional mechanism of production in result of decay of resonances, leads to decrease of average formation lengths. It is shown that the average formation lengths of positively (negatively) charged mesons are slowly rising (decreasing) functions of $x_{Bj}$. The obtained results can be important, in particular, for the understanding of the hadronization process in nuclear environment

Scalar field critical collapse in 2+1 dimensions

We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2+1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the $n=4$ Garfinkle solution, matched at the lightcone to a Vaidya-like solution, and corrected to leading order for the effect of $\Lambda<0$. This approximation is only $C^3$ at the lightcone and has three growing modes. We {\em conjecture} that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of $\gamma=8/7$ and a mass-scaling exponent of $\delta=16/23$, compatible with our numerical experiments.Comment: 27 page

Nonlinear perturbations of the Kaluza-Klein monopole

We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five dimensional vacuum Einstein equations. Using both numerical and analytical methods we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi IX ansatz recently introduced in \cite{bcs}. We also show that for sufficiently large perturbations the Kaluza-Klein monopole loses stability and collapses to a Kaluza-Klein black hole. The relevance of our results for the stability of BPS states in M/String theory is briefly discussed.Comment: 4 pages, 4 figure

Anomalously small wave tails in higher dimensions

We consider the late-time tails of spherical waves propagating on even-dimensional Minkowski spacetime under the influence of a long range radial potential. We show that in six and higher even dimensions there exist exceptional potentials for which the tail has an anomalously small amplitude and fast decay. Along the way we clarify and amend some confounding arguments and statements in the literature of the subject.Comment: 13 page