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In this letter we show that the results of degree growth (algebraic entropy) calculations for lattice equations strongly depend on the initial value problem that one chooses. We consider two problematic types of initial value configurations, one with problems in the past light-cone, the other one causing interference in the future light-cone, and apply them to Hirota's discrete KdV equation and to the discrete Liouville equation. Both of these initial value problems lead to exponential degree growth for Hirota's dKdV, the quintessential integrable lattice equation. For the discrete Liouville equation, though it is linearizable, one of the initial value problems yields exponential degree growth whereas the other is shown to yield non-polynomial (though still sub-exponential) growth. These results are in contrast to the common belief that discrete integrable equations must have polynomial growth and that linearizable equations necessarily have linear degree growth, regardless of the initial value problem one imposes. Finally, as a possible remedy for one of the observed anomalies, we also propose basing integrability tests that use growth criteria on the degree growth of a single initial value instead of all the initial values., Comment: 13 pages, 13 figures

The inclusive photon energy spectra measured by the Large Hadron Collider forward (LHCf) experiment in the very forward region of LHC proton-proton collisions at $\sqrt{s}=$ 900 GeV are reported. The results from the analysis of 0.30 $\mathrm{nb^{-1}}$ of data collected in May 2010 in the two pseudorapidity regions of $\eta > 10.15$ and $8.77 < \eta < 9.46$ are compared with the predictions of the hadronic interaction models DPMJET 3.04, EPOS 1.99, PYTHIA 8.145, QGSJET I -.1em I-03 and SIBYLL 2.1, which are widely used in ultra-high-energy cosmic-ray experiments. EPOS 1.99 and SYBILL 2.1 show a reasonable agreement with the spectral shape of the experimental data, whereas they predict lower cross-sections than the data. The other models, DPMJET 3.04, QGSJET I -.1em I-03 and PYTHIA 8.145, are in good agreement with the data below 300 GeV but predict harder energy spectra than the data above 300 GeV. The results of these comparisons exhibited features similar to those for the previously reported data for $\sqrt{s}=$ 7 TeV collisions.

The inclusive production rate of neutral pions in the rapidity range greater than $y=8.9$ has been measured by the Large Hadron Collider forward (LHCf) experiment during LHC $\sqrt{s}=7$\,TeV proton-proton collision operation in early 2010. This paper presents the transverse momentum spectra of the neutral pions. The spectra from two independent LHCf detectors are consistent with each other and serve as a cross check of the data. The transverse momentum spectra are also compared with the predictions of several hadronic interaction models that are often used for high energy particle physics and for modeling ultra-high-energy cosmic-ray showers., Comment: 18 Pages, 10 figures, submitted to Phys. Rev. D

In early 2010, the Large Hadron Collider forward (LHCf) experiment measured very forward neutral particle spectra in LHC proton-proton collisions. From a limited data set taken under the best beam conditions (low beam-gas background and low occurance of pile-up events), the single photon spectra at sqrt(s)=7TeV and pseudo-rapidity (eta) ranges from 8.81 to 8.99 and from 10.94 to infinity were obtained for the first time and are reported in this paper. The spectra from two independent LHCf detectors are consistent with one another and serve as a cross check of the data. The photon spectra are also compared with the predictions of several hadron interaction models that are used extensively for modeling ultra high energy cosmic ray showers. Despite conservative estimates for the systematic errors, none of the models agree perfectly with the measurements. A notable difference is found between the data and the DPMJET 3.04 and PYTHIA 8.145 hadron interaction models above 2TeV where the models predict higher photon yield than the data. The QGSJET II-03 model predicts overall lower photon yield than the data, especially above 2TeV in the rapidity range 8.81

LHCf is an experiment dedicated to the measurement of neutral particles emitted in the very forward region of LHC collisions. The physics goal is to provide data for calibrating hadron interaction models that are used in the study of Extremely High-Energy Cosmic-Rays. The LHCf experiment acquired data from April to July 2010 during commissioning time of LHC operations at low luminosity. Production spectra of photons and neutrons emitted in the very forward region ($\eta>$ 8.4) have been obtained. In this paper preliminary results of the photon spectra taken at $\sqrt{s}$ = 7TeV are reported., Comment: This paper has been presented in the international conference CRIS 2010 for 100 years of cosmic ray physics: from pioneering experiments to physics in space. The paper will be published in Nuclear Physics B (conference proceedings)