12,665 research outputs found

    Evidence for the saturation of the Froissart bound

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    It is well known that fits to high energy data cannot discriminate between asymptotic ln(s) and ln^2(s) behavior of total cross section. We show that this is no longer the case when we impose the condition that the amplitudes also describe, on average, low energy data dominated by resonances. We demonstrate this by fitting real analytic amplitudes to high energy measurements of the gamma p total cross section, for sqrt(s) > 4 GeV. We subsequently require that the asymptotic fit smoothly join the sqrt(s) = 2.01 GeV cross section described by Dameshek and Gilman as a sum of Breit-Wigner resonances. The results strongly favor the high energy ln^2(s) fit of the form sigma_{gamma p} = c_0 + c_1 ln(nu/m) + c_2 ln^2(nu/m) + beta_{P'}/sqrt(nu/m), basically excluding a ln(s) fit of the form sigma_{\gamma p} = c_0 + c_1 ln(nu/m) + beta_P'/sqrt(\nu/m), where nu is the laboratory photon energy. This evidence for saturation of the Froissart bound for gamma p interactions is confirmed by applying the same analysis to pi p data using vector meson dominance.Comment: 7 pages, Latex2e, 4 postscript figures, uses epsf.st

    The Elusive p-air Cross Section

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    For the \pbar p and pppp systems, we have used all of the extensive data of the Particle Data Group[K. Hagiwara {\em et al.} (Particle Data Group), Phys. Rev. D 66, 010001 (2002).]. We then subject these data to a screening process, the ``Sieve'' algorithm[M. M. Block, physics/0506010.], in order to eliminate ``outliers'' that can skew a χ2\chi^2 fit. With the ``Sieve'' algorithm, a robust fit using a Lorentzian distribution is first made to all of the data to sieve out abnormally high \delchi, the individual ith^{\rm th} point's contribution to the total χ2\chi^2. The χ2\chi^2 fits are then made to the sieved data. We demonstrate that we cleanly discriminate between asymptotic lns\ln s and ln2s\ln^2s behavior of total hadronic cross sections when we require that these amplitudes {\em also} describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to the ``sieved'' high energy measurements of pˉp\bar p p and pppp total cross sections and ρ\rho-values for s6\sqrt s\ge 6 GeV, while requiring that their asymptotic fits smoothly join the the σpˉp\sigma_{\bar p p} and σpp\sigma_{pp} total cross sections at s=\sqrt s=4.0 GeV--again {\em both} in magnitude and slope. Our results strongly favor a high energy ln2s\ln^2s fit, basically excluding a lns\ln s fit. Finally, we make a screened Glauber fit for the p-air cross section, using as input our precisely-determined pppp cross sections at cosmic ray energies.Comment: 15 pages, 6 figures, 2 table,Paper delivered at c2cr2005 Conference, Prague, September 7-13, 2005. Fig. 2 was missing from V1. V3 fixes all figure

    Predicting Proton-Air Cross Sections at sqrt s ~30 TeV, using Accelerator and Cosmic Ray Data

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    We use the high energy predictions of a QCD-inspired parameterization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, along with Glauber theory, to predict proton-air cross sections at energies near \sqrt s \approx 30 TeV. The parameterization of the proton-proton cross section incorporates analyticity and unitarity, and demands that the asymptotic proton is a black disk of soft partons. By comparing with the p-air cosmic ray measurements, our analysis results in a constraint on the inclusive particle production cross section.Comment: 9 pages, Revtex, uses epsfig.sty, 5 postscript figures. Minor text revisions. Systematic errors in k included, procedure for extracting k clarified. Previously undefined symbols now define

    Adaptive Ising Model and Bacterial Chemotactic Receptor Network

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    We present a so-called adaptive Ising model (AIM) to provide a unifying explanation for sensitivity and perfect adaptation in bacterial chemotactic signalling, based on coupling among receptor dimers. In an AIM, an external field, representing ligand binding, is randomly applied to a fraction of spins, representing the states of the receptor dimers, and there is a delayed negative feedback from the spin value on the local field. This model is solved in an adiabatic approach. If the feedback is slow and weak enough, as indeed in chemotactic signalling, the system evolves through quasi-equilibrium states and the ``magnetization'', representing the signal, always attenuates towards zero and is always sensitive to a subsequent stimulus.Comment: revtex, final version to appear in Europhysics Letter

    New physics, the cosmic ray spectrum knee, and pppp cross section measurements

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    We explore the possibility that a new physics interaction can provide an explanation for the knee just above 10610^6 GeV in the cosmic ray spectrum. We model the new physics modifications to the total proton-proton cross section with an incoherent term that allows for missing energy above the scale of new physics. We add the constraint that the new physics must also be consistent with published pppp cross section measurements, using cosmic ray observations, an order of magnitude and more above the knee. We find that the rise in cross section required at energies above the knee is radical. The increase in cross section suggests that it may be more appropriate to treat the scattering process in the black disc limit at such high energies. In this case there may be no clean separation between the standard model and new physics contributions to the total cross section. We model the missing energy in this limit and find a good fit to the Tibet III cosmic ray flux data. We comment on testing the new physics proposal for the cosmic ray knee at the Large Hadron Collider.Comment: 17 pages, 4 figure

    A new numerical method for obtaining gluon distribution functions G(x,Q2)=xg(x,Q2)G(x,Q^2)=xg(x,Q^2), from the proton structure function F2γp(x,Q2)F_2^{\gamma p}(x,Q^2)

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    An exact expression for the leading-order (LO) gluon distribution function G(x,Q2)=xg(x,Q2)G(x,Q^2)=xg(x,Q^2) from the DGLAP evolution equation for the proton structure function F2γp(x,Q2)F_2^{\gamma p}(x,Q^2) for deep inelastic γp\gamma^* p scattering has recently been obtained [M. M. Block, L. Durand and D. W. McKay, Phys. Rev. D{\bf 79}, 014031, (2009)] for massless quarks, using Laplace transformation techniques. Here, we develop a fast and accurate numerical inverse Laplace transformation algorithm, required to invert the Laplace transforms needed to evaluate G(x,Q2)G(x,Q^2), and compare it to the exact solution. We obtain accuracies of less than 1 part in 1000 over the entire xx and Q2Q^2 spectrum. Since no analytic Laplace inversion is possible for next-to-leading order (NLO) and higher orders, this numerical algorithm will enable one to obtain accurate NLO (and NNLO) gluon distributions, using only experimental measurements of F2γp(x,Q2)F_2^{\gamma p}(x,Q^2).Comment: 9 pages, 2 figure

    Analytic models and forward scattering from accelerator to cosmic-ray energies

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    Analytic models for hadron-hadron scattering are characterized by analytical parametrizations for the forward amplitudes and the use of dispersion relation techniques to study the total cross section σtot\sigma_{tot} and the ρ\rho parameter. In this paper we investigate four aspects related to the application of the model to pppp and pˉp\bar{p}p scattering, from accelerator to cosmic-ray energies: 1) the effect of different estimations for σtot\sigma_{tot} from cosmic-ray experiments; 2) the differences between individual and global (simultaneous) fits to σtot\sigma_{tot} and ρ\rho; 3) the role of the subtraction constant in the dispersion relations; 4) the effect of distinct asymptotic inputs from different analytic models. This is done by using as a framework the single Pomeron and the maximal Odderon parametrizations for the total cross section. Our main conclusions are the following: 1) Despite the small influence from different cosmic-ray estimations, the results allow us to extract an upper bound for the soft pomeron intercept: 1+ϵ=1.0941 + \epsilon = 1.094; 2) although global fits present good statistical results, in general, this procedure constrains the rise of σtot\sigma_{tot}; 3) the subtraction constant as a free parameter affects the fit results at both low and high energies; 4) independently of the cosmic-ray information used and the subtraction constant, global fits with the odderon parametrization predict that, above s70\sqrt s \approx 70 GeV, ρpp(s)\rho_{pp}(s) becomes greater than ρpˉp(s)\rho_{\bar{p}p}(s), and this result is in complete agreement with all the data presently available. In particular, we infer ρpp=0.134±0.005\rho_{pp} = 0.134 \pm 0.005 at s=200\sqrt s = 200 GeV and 0.151±0.0070.151 \pm 0.007 at 500 GeV (BNL RHIC energies).Comment: 16 pages, 7 figures, aps-revtex, wording changes, corrected typos, to appear in Physical Review

    Survival Probability of Large Rapidity Gaps in pbar p, pp, gamma p and gamma gamma Collisions

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    Using an eikonal analysis, we simultaneously fit a QCD-inspired parameterization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, together with cosmic ray data (using Glauber theory), to predict proton-air and proton-proton cross sections at energies near \sqrt s \approx 30 TeV. The p-air cosmic ray measurements greatly reduce the errors in the high energy proton-proton and proton-air cross section predictions--in turn, greatly reducing the errors in the fit parameters. From this analysis, we can then compute the survival probability of rapidity gaps in high energy pbar p and pp collisions, with high accuracy in a quasi model-free environment. Using an additive quark model and vector meson dominance, we note that that the survival probabilities are identical, at the same energy, for gamma p and gamma gamma collisions, as well as for nucleon-nucleon collisions. Significantly, our analysis finds large values for gap survival probabilities, \approx 30% at \sqrt s = 200 GeV, \approx 21% at \sqrt s = 1.8 TeV and \approx %%13% at \sqrt s = 14 TeV.Comment: 9 pages, Latex2e, uses epsfig.sty, 4 postscript figure
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