Feynman Scaling Hypothesis Research Articles

Production spectra of zero-degree neutral particles measured by the LHCf experiment

The LHC-forward (LHCf) experiment, situated at the LHC accelerator, has measured neutral particles production in a very forward region (pseudo-rapidity ƞ > 8.4) in proton-proton and proton-lead collisions. The main purpose of the LHCf experiment is to test hadronic interaction models used in ground based cosmic rays experiments to simulate cosmic rays induced air-showers in the Earth's atmosphere.The experiment is composed of two independent detectors located at 140m from the ATLAS interaction point (IP1) on opposite sides; each detector is composed of two sampling and position sensitive calorimeters.In this paper, latest published physics results from p-p and p-Pb collisions (at √s = 7, 2.76 TeV and sNN = 5.02 TeV, respectively) compared with Monte Carlo predictions of DPMJET, EPOS, PYTHIA, QGSJET and SIBYLL event generators will be presented. In particular, the inclusive energy spectra of neutrons in p-p collisions and the transverse and longitudinal momentum spectra of neutral pions for different pseudo-rapidity ranges in p-p and p-Pb collisions will be shown; then, test of Feynman scaling hypothesis using neutral pion spectra will be discussed. Preliminary results of photon inclusive energy spectra in p-p collisions at √s = 13 TeV will be also presented.

Measurement of Feynman-xspectra of photons and neutrons in the very forward direction in deep-inelastic scattering at HERA

Measurements of normalised cross sections for the production of photons and neutrons at very small angles with respect to the proton beam direction in deep-inelastic ep scattering at HERA are presented as a function of the Feynman variable xF and of the centre-of-mass energy of the virtual photon-proton system W. The data are taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 131 pb−1. The measurement is restricted to photons and neutrons in the pseudorapidity range η > 7.9 and covers the range of negative four momentum transfer squared at the positron vertex 6 < Q2 < 100 GeV2, of inelasticity 0.05 < y < 0.6 and of 70 < W < 245 GeV. To test the Feynman scaling hypothesis the W dependence of the xF dependent cross sections is investigated. Predictions of deep-inelastic scattering models and of models for hadronic interactions of high energy cosmic rays are compared to the measured cross sections.

Measurement of Feynman- $$x$$ x spectra of photons and neutrons in the very forward direction in deep-inelastic scattering at HERA

Measurements of normalised cross sections for the production of photons and neutrons at very small angles with respect to the proton beam direction in deep-inelastic $$ep$$ scattering at HERA are presented as a function of the Feynman variable $$x_F$$ and of the centre-of-mass energy of the virtual photon-proton system $$W$$ . The data are taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of $$131~\text {pb}^{-1}$$ . The measurement is restricted to photons and neutrons in the pseudorapidity range $$\eta >7.9$$ and covers the range of negative four momentum transfer squared at the positron vertex $$6<Q^2<100$$ GeV $$^2$$ , of inelasticity $$0.05<y<0.6$$ and of $$70<W<245~$$ GeV. To test the Feynman scaling hypothesis the $$W$$ dependence of the $$x_F$$ dependent cross sections is investigated. Predictions of deep-inelastic scattering models and of models for hadronic interactions of high energy cosmic rays are compared to the measured cross sections.

Diffractive Interaction and Scaling Violation inpp →π 0Interaction and GeV Excess in Galactic Diffuse Gamma‐Ray Spectrum of EGRET

The authors present here a new calculation of the gamma-ray spectrum from pp {yields} {pi}{sup 0} in the Galactic ridge environment. The calculation includes the diffractive p-p interaction and incorporates the Feynman scaling violation for the first time. Galactic diffuse gamma-rays come, predominantly, from {pi}{sup 0} {yields} {gamma}{gamma} in the sub-GeV to multi-GeV range. Hunter et al. found, however, an excess in the GeV range (GeV Excess) in the EGRET Galactic diffuse spectrum above the prediction based on experimental pp {yields} {pi}{sup 0} cross-sections and the Feynman scaling hypothesis. They show, in this work, that the diffractive process makes the gamma-ray spectrum harder than the incident proton spectrum by {approx} 0.05 in power-law index, and, that the scaling violation produces 30-80% more {pi}{sup 0} than the scaling model for incident proton energies above 100 GeV. Combination of the two can explain about a half of the GeV Excess with the local cosmic proton (power-law index {approx} 2.7). The excess can be fully explained if the proton spectral index in the Galactic ridge is a little harder ({approx} 0.2 in power-law index) than the local spectrum. Given also in the paper is that the diffractive process enhances e{sup +} over e{supmore » -} and the scaling violation gives 50-100% higher {bar p} yield than without the violation, both in the multi-GeV range.« less

Violation of the feynman scaling hypothesis and the cosmic-muon charge ratio: a model-dependent analysis

We have attempted here to study the nature of the sea-level cosmicmuon charge ratio at very high energies on the basis of one particular model of multiple production of hadrons in which the violation of the Feynman scaling is one of the very gross features. It is found that extreme emphasis on this feature alone would cause drastic departures from the experimental values of the charge ratio; but when this is combined with some other recently observed and/or proposed characteristics of high-energy interactions the model-based calculations agree quite well up to several TeV energy regime with the data. The model, in the final analysis, supports a very feebly rising nature of the muon charge ratio at ultrahigh energy.

Remote sensing, eigenanalysis, and information content of cosmic variations

Remote sensing of the primary component of cosmic 11‐year and diurnal variations over a wide rigidity range is carried out by nonlinear inversion of the Fredholm integral equation relating secondary variations to the primary spectra. Data from three and four stations are simultaneously analyzed, using recently developed coupling functions based on Feynman scaling hypothesis. The range of rigidity over which the retrieval of the primary spectra is possible is investigated. Information content of measured intensities is studied by eigenanalysis of the covariance matrix of kernels of the integral equation. It is concluded that a redundancy of existing stations in the low rigidity range and a lack of stations in the high rigidity range already exist. Implications, suggestions, errors, and possible extensions are discussed.

Energy spectrum of cosmic ray primaries at super high energies estimated from the recent balloon-borne calorimeter measurements

The energy spectrum of primary cosmic ray particles has been estimated from the analysis of the chemical composition data of high energy cosmic rays, data obtained by the Japanese American cooperative emulsion experiments for proton and helium intensities and the Goddard Space Flight Centre measurements for cosmic ray nuclei. The results indicate no drastic change in abundance ratios at high energies. The elemental fluxes have been calculated by assuming that the primary cosmic ray nuclei break up into their constituent nucleons near the top of the atmosphere. The calculated total primary spectrum in the range 2–300 TeV follows the form N(E) dE = 2.24 × 104 E−2.7 dE where E is the energy expressed in GeV/nucleon and N(E) is the intensity expressed in (m2∙s∙sr∙GeV/nucleon) −1.Using this primary spectrum as the source of nucleons near the top of the atmosphere, the sea level proton and neutron spectra have been estimated by using the Feynman scaling hypothesis and the conventional nucleon-atmospheric diffusion equation. The derived spectra are in accord with the measured proton and neutron spectra of Brooke and Wolfendale, Ashton and Coates, and Ashton et al.

Derivation of vertical muon spectra at superhigh energies from our predicted primary cosmic-ray spectrum using machine interaction parameters and Feynman scaling hypothesis

The vertical differential and integral, muon spectra at super-high energies,viz. up to 10 TeV have been estimated from our predicted primary spectrum of the formN(E)dE=2.4E −2.7dE (cm2s sr GeV)−1. The accelerator data of Johnsonet al., Elbertet al. have been used for the evaluation of fractional hadronic energy moments. By using the conventional Feynman scaling hypothesis and the meson atmospheric diffusion equation after Bugaevet al., the differential and integral muon spectra have been estimated and the results are well in accord with the experimental data of Bakeret al., Allkoferet al., Ayreet al., Aminevaet al., Menon and Ramana Murthy, and Sheldonet al. in the spectral range (0.1÷10) TeV.

Altitude variation of cosmic ray nucleons derived from feynman scaling hypothesis

The differential proton spectra at different atmospheric depths and the differential neutron spectrum at sea level have been calculated using the scaling hypothesis of Feynman for hadronic inclusive reaction at high energies. In evaluating such values we used the primary nucleon spectrum of Grigorov et al. It is found that the derived spectra fit well the experimental data given by different authors. The estimated neutron-proton flux ratio against atmospheric depths is in accord with the measured data surveyed by Aguirre.

Energy distribution of parent nucleons for muons observed at sea level and underground

The energy distributions of primary cosmic-ray nucleons responsible for muons detected at sea level and underground have been calculated using a phenomenological model. The Feynman scaling hypothesis of nucleon-nucleon interactions has been employed using cross sections determined from high-energy scattering experiments.

The absorption length of EAS at sea level

A simulation of integral size spectra with various assumptions about the primary energy spectrum has been performed at different depths and in several zenith angle bins (0 degrees -40 degrees ). The absorption length Lambda has been derived directly from the data with accurate consideration of the experimental procedures, the angular and barometric methods. A systematic consequence of the steepening of the primary spectrum ('knee effect') is seen to emerge in the behaviour of Lambda as a function of size between 104 and 108 particles. A consecutive interpretation of the present data in terms of dynamical ultra-high-energy interactions reveals a strong disagreement with the Feynman scaling hypothesis.

Effects of inelastic p-air cross section, the Feynman scaling hypothesis and the primary composition on the maximum depth in EAS (1015-1017eV)

Simulations of extensive air showers (EAS) for several models of ultra-high energy interactions, involving isobar production and Psi production, are carried out with energy dependent cross sections. The sensitivity of the maximum depth to power or logarithmic multiplicity laws for secondaries and to scaling models is discussed together with the effect of the cross section and the chemical composition of the primary cosmic component. Agreement with experimental data on the maximum depth is obtained without requiring such an important multiple production as E12/.

Calculation of Muon yields, response functions, and sea level integral energy spectrum using recent accelerator data and Feynman scaling

We calculate the number of muons of energy greater than Eµ due to a primary nucleon of energy E0 for Eµ ≳ 10 GeV. The yields have been calculated (assuming normal parentage for the muons) by solving the atmospheric diffusion equation governing the pion flux in the atmosphere and determining the corresponding muon production spectrum and hence the muon yields. This method assures that muons from pions many generations removed from the primary are included and, in addition, takes account of the effect of pion decay on the multiplication of the pion flux in the atmosphere. The basic input to the equation is the inclusive cross sections for the processes pp → π± + (anything) and πp → π + (anything) as determined from recent accelerator data (including intersecting storage ring (ISR) data for proton-proton (pp) interactions). These production spectra are extrapolated as necessary by use of the Feynman scaling hypothesis. We find a median primary energy ranging from about 15Eµ at Eµ ∼ 10 GeV to about 11Eµ at Eµ ∼ 1000 GeV. The derived sea level integral muon energy spectrum is in good agreement with the observed spectrum.