Narrow Results

The problem of the knee in primary cosmic ray at energy about 3–5 PeV is the most exciting problem in cosmic ray physics. Since 1958, physicists have been trying to solve this problem. In our opinion, the problem could be solved from the experimental point of view, whereas the primary spectrum would follow a pure power law. A key to the "knee" problem lies in the hadronic structure of EAS and its propagation in the Earth's atmosphere. Neither exotic processes nor new physics are used. An explanation of the approach and some results of Monte Carlo simulations are given below.

The famous formula for the emission angle of Cherenkov radiation should be modified when applied to hadronic reactions because of recoil effects and the color nature of the participants. They impose an upper limit on the energy of the gluon emitted at a given angle. Also, it leads to essential corrections to the nuclear refractive index value as determined from the angular position of Cherenkov rings.

It is widely believed that chiral symmetry is restored not only at high temperatures, but also at high nuclear densities. The drop of the order parameter of the chiral phase transition, the chiral condensate, with density has indeed been calculated in various models and is as such a rather robust result. In this talk I point out that the connection of this property with actual observables is far less clear. For this task a good hadronic description of the primary production of hadrons, their propagation inside the nuclear medium, their decay and the propagation of the decay products through the medium to the detector all have to be treated with equal accuracy and weight. In this talk I illustrate with the examples of ω production and π⁰π⁰ production how important in particular final state interactions are.

We discuss some problems concerning the application of perturbative QCD to high energy processes. In particular for hard processes, we analyze higher order and higher twist corrections. It is argued that these effects are of great importance for understanding the behaviour of pion electromagnetic form factor at moderately large momentum transfers. For soft processes, we show that summing the contributions of the lowest twist operators leads to a Regge-like amplitude.

The Hagedorn temperature, T_H is determined from the number of hadronic resonances including all mesons and baryons. This leads to a stable result T_H = 174 MeV consistent with the critical and the chemical freeze-out temperatures at zero chemical potential. We use this result to calculate the speed of sound and other thermodynamic quantities in the resonance hadron gas model for a wide range of baryon chemical potentials following the chemical freeze-out curve. We compare some of our results to those obtained previously in other papers.

The CMD-3 detector has been taking data since December 2010 at the VEPP-2000 electron–positron collider. The collected data sample corresponds to about 60 inverse picobarn of integrated luminosity in the c.m. energy range from 0.32 GeV to 2.0 GeV. Preliminary results of the analysis of various hadronic cross-sections, in particular, $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$, ${\pi }^{+}{\pi }^{-}{\pi }^0$, $K_L{K}_S$, $K^{+}{K}^{-}$, $\eta \gamma$, 3$({\pi }^{+}{\pi }^{-})$, $2({\pi }^{+}{\pi }^{-}{\pi }^0)$, $K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$, $K^{+}{K}^{-}\eta$, $K^{+}{K}^{-}{\pi }^0$, $\eta {\pi }^{+}{\pi }^{-}$, $\omega {\pi }^{+}{\pi }^{-}$ and $\omega \to {\pi }^0{e}^{+}{e}^{-}$ are presented. The processes with multi-hadron final states have several intermediate states which have to be taken into account to correctly describe the angular and invariant mass distributions, as well as cross-section energy dependence.

We present the unified description of the existing data on elastic small angle $pp$ and $p\bar{p}$ scattering at the energies 1.8, 1.96, 2.76, 7, 8 and 13 TeV in the framework of Additive Quark Model (AQM). The agreement with the data is quite reasonable.

Transverse momentum $(p_T)$ spectra of ${\pi }^{-}$ mesons calculated using ultra-relativistic quantum molecular dynamic (UrQMD) model (Latest version 3.3-p2) simulations have been compared with $p_T$ spectra of ${\pi }^{-}$ mesons, obtained experimentally in interactions of protons beam with carbon nuclei (propane as target) at momentum of 4.2 GeV/c. Spectral temperatures of negative pions obtained in experimental and UrQMD model simulated interactions of protons beam with carbon nuclei have been calculated by fitting both spectra with four different fitting functions, i.e. Hagedorn thermodynamic, Boltzmann distribution, Gaussian and exponential functions. These functions are used commonly for describing hadron spectra and their spectral temperatures. Hagedorn thermodynamic function has been recommended as the most suitable function to extract the temperature of negative pions at above momentum among these four functions.

We herein construct a Heisenberg-like algebra for the one-dimensional quantum free Klein–Gordon equation defined on the interval of the real line of length L. Using the realization of the ladder operators of this Heisenberg-type algebra in terms of physical operators we build a (3+1)-dimensional free quantum field theory based on this algebra. We introduce fields written in terms of the ladder operators of this Heisenberg-type algebra and a free quantum Hamiltonian in terms of these fields. The mass spectrum of the physical excitations of this quantum field theory is given by , where n=1,2,… and m_q is the mass of a particle in a relativistic infinite square-well potential of width L.

In this talk, I address some open problems in hadron physics and stress their importance for a better understanding of QCD in the confinement regime.

Diffractive production is considered in the ultrahigh energy region where pomeron exchange amplitudes are transformed into black disk ones due to rescattering corrections. The corresponding corrections in hadron reactions h₁ + h₃ → h₁ + h₂ + h₃ with small momenta transferred are calculated in terms of the K-matrix technique modified for ultrahigh energies. Small values of the momenta transferred are crucial for introducing equations for amplitudes. The three-body equation for hadron diffractive production reaction h₁ + h₃ → h₁ + h₂ + h₃ is written and solved precisely in the eikonal approach. In the black disk regime final state scattering processes do not change the shapes of amplitudes principally but dump amplitudes by a factor ~ ¼; initial state rescatterings result in additional factor ~ ½. In the resonant disk regime initial and final state scatterings damp strongly the production amplitude that corresponds to σ_inel/σ_tot → 0 at in this mode.

In this work, we use the approach recently introduced by Barros to study hadron spectra and some quark confinement properties in a Schwarzchild-like space–time generated by a nongravitational field. As a starting point, for the nongravitational field, we make the choice of a strong Yukawa-like field whose associated potential is a generalized Yukawa-like potential, typical of strong interactions. Then, from the latter field, the energy momentum tensor is constructed, the Einstein field equations are solved and the curvature function of the Schwarzchild metric is obtained. The correspondence principle applied to the Schwarzchild metric has enable us to construct the Dirac equation in the latter space. The resolution of the coupled differential equations of Dirac made it possible to obtain the energy spectrum of the strong interaction. The latter is obtained in a more general form than in the previous investigations. Then, the energy spectrum, masses and confinement radius of few hadrons are estimated and compared with experimental data and other theoretical studies. In most considered cases, our predictions are found to be in good agreement with experimental data. The good agreement observed between our outcomes and the experiment can be attributed to the choice of our potential, which has more free parameters than in past studies with the same approach.

Shortly after his escape, in 1968, from the DDR to the Western world, Harald Fritzsch made a fast career in physics while investigating the strong force in elementary particles. Inspired by Gell-Mann, Yang and Mills and many others, he contributed to the rise of the Standard Model, and in particular the developments of theories for the color confinement mechanism.

A written account of my talk delivered at the Harald Fritzsch Memorial Symposium in Munich is given. The emphasis is on Harald’s achievements specifically in quark physics and in quantum chromodynamics. Beyond that exemplary results for low-energy baryons are discussed, as obtained over the past years in the framework of the relativistic constituent-quark model based on Goldstone-boson-exchange dynamics.

In this paper we study the transition from hadron matter to quark matter in the presence of a gas of trapped electron neutrinos assuming color and flavor conservation during the transition. For the hadronic phase we use a parametrization of a nonlinear Walecka model which includes the whole baryon octet. For the quark matter phase we use MIT model including color superconductivity. Deconfinement is considered to be a first-order phase transition that conserves color and flavor. Our results show that neutrino trapping increases the deconfinement density but color superconductivity decreases it. As a consequence, the transition density in the protoneutron star phase is determined by a competition between between temperature, neutrino trapping and quark pairing.

Temperature is an important and commonly used parameter among others to study properties of matter created during high energy collisions of nuclei. Experimental data from JINR and UrQMD (version 3.3p2) model simulations have been used to estimate temperature and other properties of positive pions in collisions of deuteron with carbon nuclei at incident momentum of 4.2GeV/$c$ in this paper. Transverse mass and transverse momentum spectra have been used to get inverse slope parameter/temperature of said particles, with the help of some fitting equations. These equations are referred as Hagedorn Thermodynamic and Boltzmann Distribution functions. Such functions or equations are used to describe particles spectra. Temperature of positive pions has been found to be equal to $104\pm 2$ and $112\pm 2$MeV in experimental and model, respectively, using Hagedorn function. Results from both experimental and model calculations have also been compared with each other and thus most reliable fitting function has been suggested. It is found that Hagedorn Thermodynamic function is the most reliable function to get pions’ temperature in said collision system at given momentum. Similarly, results obtained in this paper have been compared with results from other experiments in the world and worthy conclusions have been reached and reported.

The VEPP-2000 electron-positron collider was commissioned in 2010. About 60 pb^-1 were collected so far by CMD-3 detector in the whole available c.m. energy range from 0.32 GeV to 2.0 GeV. The preliminary results of data analysis for various modes of e⁺e⁻ → hadrons are discussed.

The preliminary results on multihadron processes obtained with the SND detector at the e⁺e⁻ collider VEPP-2000 in the energy range from 1 to 2 GeV are presented. The results are interesting in connection with their contribution to the total hadronic cross section, the muon g-2 and a possibility to study excited vector mesons properties. The nucleon anti-nucleon production was also studied.

A number of production cross sections for electron-positron annihilation to a hadronic final state have been measured using the Belle dataset, which is possible given the general purpose design of the Belle detector and its large solid-angle coverage. The cross section measurements predominantly fall above 3 GeV, which still leaves the opportunity for using the dataset to systematically measure cross sections below 3 GeV. These low-energy cross sections are important for improving the precision of the Standard Model prediction for the muon anomalous magnetic moment.

We report preliminary results on the measurement of the cross section of the process e⁺e^- → K⁺K^-π⁺π^- in the c.m. energy range from 1.5 GeV to 2 GeV. It is shown that the cross section is dominated by the contributions of several intermediate states K⁺K^-ρ, K*Kπ, ϕπ⁺π^- and K*K*.