18,798 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

    Consequences of the Factorization Hypothesis in pbar p, pp, gamma p and gamma gamma Collisions

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    Using an eikonal analysis, we examine the validity of the factorization theorem for nucleon-nucleon, gamma p and gamma gamma collisions. As an example, using the additive quark model and meson vector dominance, we directly show that for all energies and values of the eikonal, that the factorization theorem sigma_{nn}/sigma_{gamma p} = sigma_{gamma p}/sigma_{gamma gamma} holds. We can also compute the survival probability of large rapidity gaps in high energy pbar p and pp collisions. We show that the survival probabilities are identical (at the same energy) for gamma p and gamma gamma collisions, as well as for nucleon-nucleon collisions. We further show that neither the factorization theorem nor the reaction-independence of the survival probabilities depends on the assumption of an additive quark model, but, more generally, depends on the opacity of the eikonal being independent of whether the reaction is n-n, gamma p or gamma gamma.Comment: 8 pages, Revtex, no figures. Expanded discussion, minor correction

    Forward Elastic Scattering of Light on Light, \gamma+\gamma\to\gamma+\gamma

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    The forward elastic scattering of light on light, {\em i.e.,} the reaction γ+γγ+γ\gamma+\gamma \to \gamma+\gamma in the forward direction, is analyzed utilizing real analytic amplitudes. We calculate ργγ\rho_{\gamma \gamma}, the ratio of the real to the imaginary portion of the forward scattering amplitude, by fitting the total γγ\gamma \gamma cross section data in the high energy region 5GeVs1305 GeV \le \sqrt s \le 130 GeV, assuming a cross section that rises asymptotically as ln2s\ln^2 s. We then compare ργγ\rho_{\gamma\gamma} to ρnn\rho_{nn}, the ratio of the even portions of the pppp and \pbar p forward scattering amplitudes, as well as to ργp\rho_{\gamma p}, the ρ\rho value for Compton scattering. Within errors, we find that the three ρ\rho-values in the c.m.s. energy region 5GeVs1305 GeV \le \sqrt s \le 130 GeV are the same, as predicted by a factorization theorem of Block and Kadailov.Comment: 5 pages, Latex2e, 2 postscript figures, uses epsfig.st