18,817 research outputs found

### Evidence for the saturation of the Froissart bound

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

For the \pbar p and $pp$ 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 $\chi^2$ 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 i$^{\rm th}$ point's
contribution to the total $\chi^2$. The $\chi^2$ fits are then made to the
sieved data. We demonstrate that we cleanly discriminate between asymptotic
$\ln s$ and $\ln^2s$ 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 $\bar p p$ and $pp$ total cross sections
and $\rho$-values for $\sqrt s\ge 6$ GeV, while requiring that their asymptotic
fits smoothly join the the $\sigma_{\bar p p}$ and $\sigma_{pp}$ total cross
sections at $\sqrt s=$4.0 GeV--again {\em both} in magnitude and slope. Our
results strongly favor a high energy $\ln^2s$ fit, basically excluding a $\ln
s$ fit. Finally, we make a screened Glauber fit for the p-air cross section,
using as input our precisely-determined $pp$ 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

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

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

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