Sea Level Muon Spectrum Derived from the All Particle Primary Spectrum of GRIGOROV et al.

The all particle primary spectrum of GRIGOROV et al. surveyed by HILLAS has been fitted by a power law fit of the form I_{all particle}(>E) = 1.3 E^?1.65 (cm² s sr)^?1 where E is the energy in GeV/nucleus. Using our recently determined conversion factor for protonnuclei flux ratio of equal energies the primary proton spectrum has been calculated and the result agrees with the Goddard Space Flight Centre primary proton spectrum data satisfactorily. The primary nucleon spectrum has also been calculated and follows the form N_nucleons(E) dE = 2.664 E^?2.75 dE (cm² s sr GeV/nucleon)^?1. Using this primary nucleon spectrum as the source of hadrons and accelerator data for various inclusive reactions viz. used for the estimation of hadronic energy moments in the frame work of FEYNMAN- Scaling, the differential meson spectra have been estimated. The meson atmospheric diffusion equation after Bugaev et al. has been considered for the derivation of sea level muon spectrum. The magnetic spectrograph data of Allkofer et al., Ayre et al., Green et al., and MUTRON group are in accord with the calculated muon spectrum.     

Secondary Neutral Pion-nucleon Flux Ratio at the Top of the Atmosphere

The CERN Intersecting Storage Ring data on the inclusive reaction p + p → π° + X has been fitted with a phenomenological form where W_c(a,b,z) is the generalized confluent function defined by . M(a, b, z) being the well known Kummer's function. Using this form and primary proton spectrum of Goddard Space Flight Center Group the secondary neutral pion-nucleon flux ratio at the top of the atmosphere has been estimated. The derived result has been compared with those expected from p + p → π^± + X data, via different models.     

Subthreshold antiproton andK − production in heavy ion collisions

Subthreshold ¯p andK ^– and energetic ^– production was studied in Ne + NaF, Cu, Sn and Bi, and in Ni + Ni collisions with incident energies between 1.6 and 2 GeV/u. The measured cross sections indicate a dominant contribution of baryonic resonances. This is also consistent with a generalized scaling behaviour of the cross sections with the energy available in the collision and the energy necessary to produce particles as observed with Ne induced reactions. Deviations from scaling especially pronounced in the Ni-Ni system will be discussed in terms of absorption effects. The flat slope of the excitation function for ¯p production can be related to a reduced production threshold caused by a reduction of the antiproton mass in the dense and heated medium by about 100—150 MeV/c². A similar in-medium mass reduction is also indicated forK ^– mesons. An increased ¯p reabsorption probability for the heavier systems is concluded from the comparison of the ¯p yields in Ne + NaF, Ne + Sn and Ni + Ni collisions.Dedicated to Professor Klaus Dietrich on the occasion of his 60th birthday.     

The Spectra of Cosmic Pions and Nucleons at Low and High Geomagnetic Latitudes at the Top of the Atmosphere

The spectra of cosmic pions and nucleons at an atmospheric depth of 100 g cm^?2 have been derived from sea level muon spectra at low and high latitudes. The derived spectra of pions and nucleons at low and high latitudes follow the relations N(Eπ) dEπ = 0.23 E_π^?2.68dEπ and N(E_p) dE_p = 2.98 E dE_p per cm² sec str GeV in the energy range 15–1200 GeV. Below 15 GeV it is found that the exponent of the energy spectrum is very much dependent upon the incident energy and latitude of the location. The major difference between low and high latitude pion spectra can be explained in terms of geomagnetic effects.     

Neutral kaon production in p+p and p+Nb collisions

The kaon nucleus (KN) interaction in dense nuclear matter is predicted to be repulsive and increasing with density. However, determined values for this potential are not yet consistent with each other (Benabderrahmane et al., Phys Rev Lett 102:182501, 2009; Agakishiev et?al., Phys Rev C 82:044907, 2010; Büscher et?al., Eur Phys J A 22:301–317, 2004). We analyze $K^0_S$ mesons identified with the HADES detector in p+p and p+?⁹³Nb reactions at 3.5?GeV kinetic beam energy. To determine the KN potential at normal nuclear density we propose to compare the $K^0_S$ differential distributions in p+?⁹³Nb and p+p collisions. High statistics of low p _t -kaons (p _t ?<?100?MeV/c) ensure the sensitivity of our measurements to the nuclear matter effects. We present the data analysis method and first results.     

Open charm measurements at STAR

We report on the measurements of D⁰ meson production via direct reconstruction through the hadronic decay channel D⁰→Kπ in minimum bias d+Au and Au+Au collisions at with p_T up to ∼3 GeV/c. We derive the charm production total cross-section per nucleon–nucleon collision from a combination of three measurements: the D⁰ meson spectra, the non-photonic electron spectra from charm semi-leptonic decays obtained in p+p, d+Au, and Au+Au collisions, and the charm-decayed single muon (prompt muon) spectra at low p_T in Au+Au collisions. The cross-section is found to follow binary scaling, which is a signature of charm production exclusively at the initial impact. The implications of charm quark energy-loss and thermalization in the strongly interacting matter are discussed. PACS 25.75.Dw; 13.20.Fc; 13.25.Ft; 24.85.+p     

Measurement of the LT-asymmetry in πelectroproduction at the energy of the Δ(1232)-resonance

The reaction p(e, e'p)π⁰ has been studied at Q² = 0.2 (GeV/c)² in the region of W = 1232MeV. From measurements left and right of , cross-section asymmetries ρ_LT have been obtained in forward kinematics ρ_LT( = 20^°) = (- 11.68±2.36_stat±2.36_sys) and backward kinematics ρ_LT( = 160^°) = (12.18±0.27_stat±0.82_sys) π⁰. Multipole ratios {S₁₊ ^* M₁₊}/| M₁₊|² and {S₀₊ ^* M₁₊}/| M₁₊|² were determined in the framework of the MAID2003 model. The results are in agreement with older data. The unusally strong negative {S₀₊ ^* M₁₊}/| M₁₊|² required to bring also the result of Kalleicher et al. in accordance with the rest of the data is almost excluded.     

Energy spectra of cosmic pions and nucleons at the top of the atmosphere

The production spectra of cosmic pions and their primaries have been derived from the experimental muon spectrum by using the theories of Barrettet al. and Feynman. The calculated pion production spectrum takes the formI(E _π)d E _π = 0.206E _π ^{? 2.65} d E _πper cm² sec str GeV in the energy range 3<E _π<1500 GeV and the nucleon spectrum follows the relationN(E _p)d E _p = 2.7 × 10⁴ (E _p/GeV)^2.65 d E _pper m² sec str GeV in the range 5 <E _p <3000 Gev.     

Derivation of Absolute Depth-Intensity Spectrum under Standard Rock from the Recently Estimated Primary Cosmic Ray Spectrum

Using the recently derived primary cosmic ray nucleon spectrum from JACEE and GSFC balloon flight data and Fermilab results for pp → π^± + X anything inclusive reaction data in the light of Feynman scaling the depth-intensity spectrum under standard rock has been estimated. A precisely constructed range-energy relation has been applied in this analysis. The derived spectrum when corrected for range fluctuation agrees approximately with the experimental data under standard rocks measured by MIYAZAKI , BARTON , CASTAGNOLI et al., MEYER et al., BERGAMASCO et al., SHELDON et al. and BASCHIERA et al.     

Inclusive production of φ-mesons in neutron-proton interaction at 30–70 GeV/c

A signal of the-K⁺K^– decays has been observed in neutron-hydrogen interactions at energies of 30–70 GeV in an experiment using the BIS-2 spectrometer. The longitudinal momentum spectrum in the forward region,x _F<0·1 atp _T<1 GeV/c, can be well described by a power law dependence (1–x _F)^N withN=4·28±0·42. Thep _T ² -spectrum has been parametrized by the exp(–Bp _T ² ) law with the exponentB=(3·02±0·55) (GeV/c)^–2. The extrapolation of the measured cross section to the full kinematic region yields a value of (220±85) b in agreement with measurements from the proton beams.     

Dao Scaling Model and Sea Level Cosmic Ray Muon Spectrum from Goddard Space Flight Group Measured Primary Proton Spectrum

A new type of scaling model for p + p → π^? + X inclusive reactions, proposed by DAO et al., is applied to derive the sea level muon spectrum. The nucleon spectrum data of Goddard Space Flight Group were taken as input. It is found that the sea level muon spectrum depends explicitly on the average value of the FEYNMAN variable x whose most probable value is estimated to be 0.18.     

Elastic pp scattering in the cern sps energy region

The pronounced dip-bump structure with a sharp minimum at |t| = 1.5 (GeV/c)², recently observed in elastic $\text{p}$p scattering at P_L = 50 GeV/c at the CERN SPS, is explained by the quark multiple scattering model with a realistic wavefunction for the proton and the antiproton. It is predicted that a second dip will appear around |t| = 7 (GeV/c)² at P_L = 50 GeV/ c and at higher energies.     

Scaling in the mean of the p+p→π0+X inclusive reaction data and the energy dependence of Feynman variable

We have studied the p+p⁰+X inclusive reaction data of Carey et al. in the framework of the scaling in the mean hypothesis first proposed by Dao et al. These data have been used to obtain the gamma ray spectrum in terms of the average value of the Feynman variablex, written as x.A comparison with the observed gamma ray spectrum at Mt. Chacaltaya by the Japanese and Brazilian Group gives the energy dependence of x at very high energy.     

Inclusive K+-meson production in proton-nucleus interactions

The production of K⁺-mesons in pA (A = D, C, Cu, Ag, Au) collisions has been investigated at the COoler SYnchrotron COSY-Jülich for beam energies T_p = 1.0-2.3 GeV. Double differential inclusive pC cross-sections at forward angles _{K^+} < 12^° as well as the target mass dependence of the K⁺ momentum spectra have been measured with the ANKE spectrometer. Far below the free NN threshold at T_NN = 1.58 GeV the spectra reveal a high degree of collectivity in the target nucleus. From the target mass dependence of the cross-sections at higher energies, the repulsive in-medium potential of the K⁺-mesons can be deduced. Using pN cross-section parameterisations from the literature and our measured pD data we derive a cross-section ratio (pnK⁺X)/(ppK⁺X) (3-4).     

Collapse transition and asymptotic scaling behavior of lattice animals: Low-temperature expansion

A low-temperature expansion for the free energy density of lattice animals is derived. Analysis of the series yields a collapse transition temperature ofT _c - 0.54, in close agreement with previous estimates. It is demonstrated that _p,k, the number ofp-particle,p-bond animals, obeys the asymptotic scaling law log _p,k pg(k/p) + o(p). The low-temperature series and numerical data are used to estimate the scaling function.     

Besov spaces and the multifractal hypothesis

Parisi and Frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis, i.e., they conjecture that the velocity field has local Hölder exponents in a range [h _min,h _max], with exponents <h occurring on a setS(h) with a fractal dimensionD(h). Heuristic reasoning led them to an expression for the scaling exponentz _p ofpth order as the Legendre transform of the codimensiond-D(h). We show here that a part of the multifractal hypothesis is correct under even weaker assumptions: namely, if the velocity field hasL ^p -mean Hölder indexs, i.e., if it lies in the Besov spaceB _p ^s, , then local Hölder regularity is satisfied. Ifs<d/p, then the hypothesis is true in a generalized sense of Hölder space with negative exponents and we discuss the proper definition of local Hölder classes of negative index. Finally, if a certain box-counting dimension exists, then the Legendre transform of its codimension gives the scaling exponentz _p , and, more generally, the maximal Besov index of order,p, ass _p =z _p /p. Our method of proof is derived from a recent paper of S. Jaffard using compactly-supported, orthonormal wavelet bases and gives an extension of his results. We discuss implications of the theorems for ensemble-average scaling and fluid turbulence.     

Neutral-meson production in <Emphasis Type="Italic">pp</Emphasis> collisions at RHIC and QCD test of <Emphasis Type="Italic">z</Emphasis> scaling

New experimental data on inclusive cross section of neutral-vector-meson (ω ⁰, ϕ, K _S ⁰) production in proton-proton collisions at = 200 GeV obtained at RHIC are analyzed in the framework of z scaling. Properties of z-presentation are used to predict hadron yields over a wide range of transverse momentum p _T and collisions energy . The next-to-leading-order perturbative QCD calculations of inclusive cross sections of π ⁰ mesons produced in pp and collisions over a wide range of and p _T are compared with ISR, S pS, RHIC data and predictions of z scaling. The dependence of the spectra in p _T and z presentations for different parton distribution and fragmentation functions is studied. The sensitivity of the obtained results to the choice of the renormalization (μ _R ), initial-state factorization (μ _F ), and final-state factorization (fragmentation) (μ _H ) scales is verified. It is shown that self-similar features of particle production dictated by the z scaling give strong restriction on the asymptotic behavior of the inclusive spectra in high-p _T region. The text was submitted by the author in English.     

Direct photons in nuclear collisions at fair energies

Using the extrapolation of existing data, estimations of prompt-photon production at FAIR energies have been made. At y = y _c.m. the rapidity density of prompt photons with p _t > 1.5 GeV/c per central Au + Au event at 25 A GeV is estimated as ∼10⁻⁴. With the planned beam intensity 10⁹ per second and 1% interaction probability, for 10% of most central events one can expect the prompt-photon rate ∼10² photons per second. Direct photons from the hadron scenario of ion collisions generated by the Hadron-String-Dynamics (HSD) transport approach with implemented meson scatterings πρ → πγ, ππ → ργ have been analyzed. Photons from short-living resonances (e.g., ω → π ⁰ γ) decaying during the dense phase of the collision should be considered as direct photons. They contribute significantly in the directphoton spectrum at p _t = 0.5–1 GeV/c. At the FAIR energy 25 A GeV in Au + Au central collisions the HSD generator predicts, as a lower estimate, γ _direct/ ≃ 0.5% in the region p _t = 0.5–1 GeV/c. At p _t = 1.5–2 GeV/c γ _prompt/ ≃ 2%. Thermal direct photons have been evaluated with the Bjorken Hydro-Dynamics (BHD) model. The BHD spectra differ strongly from the HSD predictions. The direct-photon spectrumis very sensitive to the initial temperature parameter T ₀ of the model. The 10-MeV increase in the T ₀ value leads to ∼2 times higher photon yield. The text was submitted by the authors in English.     

Particle masses,force constants,and Spin(8)

From a number of qualitative conjectures, the constantsm _e ,c, , and a spin(8) gauge field theory, I derive the following particle masses (quark masses are constituent masses) and force constants: up quark mass=312.7542 MeV; down quark mass=312.7542 MeV; proton mass=938.2626 MeV; neutrino masses (all types)=0; muon mass=104.76 MeV; strange quark mass=523 MeV; charmed quark mass=1989 MeV; tauon mass=1877 MeV; bottom quark mass=5631 MeV; top quark mass=129.5 GeV;W ⁺ mass=80.87 GeV;W ^– mass=80.87 GeV;W ₀ mass=99.04 GeV; fine structure constant= 1/137.036082; weak constant times the proton mass squared M _p ² =0.97×10^–5; color constant=0.6286. From the pion mass in addition, I derive the Planck mass (1–1.6)×10¹⁹ GeV, so that the gravitational constant times the proton mass squared GM _p ² (3.6–8.8)×10^–39.     

Estimation of the Sea Level Muon Spectra at Different Zenith Angles below 10 TeV Energy

The moderate energy primary cosmic ray nucleon spectrum has been calculated from the direct measurements of Webber et al., Seo et al., and Menn et al. along with the other results surveyed by Swordy. Using these directly measured primary mass composition results all particle primary nucleon energy spectrum has been constructed using superposition model to estimate the energy spectra of muons from the decay of the cosmic ray non-prompt and prompt mesons in the atmosphere. The Z-factors have been estimated from the CERN LEBC-EHS on the Lorentz invariant cross section results on pp ^±X and pp K^±X inclusive reactions and FNAL data on ^±p ^±X reactions, and duly corrected for A--A collisions. Using these Z-factors the meson energy spectra in the atmosphere have been calculated. The sea level muon energy spectra at zenith angles 0°, 45°, 72°, and 75° have been derived from the decay of non-prompt mesons by adopting standard diffusion equation of hadronic cascades. The contribution of charmed mesons to muon spectrum has also been accounted by adapting the conventional procedure. The derived differential sea level muon energy spectra for energies 10 TeV have been found to follow the power law fits of the form N (E) const. E ^-. Our estimated muon energy spectra at zenith angles 75° have been found comparable with the global spectrograph muon flux results of MARS, DEIS, and MSU groups.