Test of the Universal Rise of Hadronic Total Cross Sections at Super-high Energies

Saturation of the Froissart-Martin unitarity bound that the total cross sections increase like log2(s/s_0) appears to be confirmed. Due to this statement, the B log2(s/s_0) was assumed to extend the universal rise of all the total hadronic cross sections to reduce the number of adjustable parameters by the COMPETE Collaboration in the Particle Data Group (2006). Based on this assumption of parametrization, we test if the assumption on the universality of $B$ is justified through investigations of the value of B for pi p(K p)$ and pbar p, pp scatterings. We search for the simultaneous best fit to sigma(tot) and rho ratios, using a constraint from the FESR of the P' type for pi p scatterings and constraints which are free from unphysical regions for pbar p,pp and K p scatterings. By including rich informations of the low-energy scattering data owing to the use of FESR, the errors of B parameters decreases especially for pi p. The resulting value of B(pp) is consistent with B(pi p) within two standard deviation, which appears to support the universality hypothesis.Comment: 5 pages, 1 figur

New analyticity constraints on the high energy behavior of hadron-hadron cross sections

We here comment on a series of recent papers by Igi and Ishida[K. Igi and M. Ishida, Phys. Lett B 622, 286 (2005)] and Block and Halzen[M. M. Block and F. Halzen, Phys. Rev D 72, 036006 (2005)] that fit high energy $pp$ and $\bar pp$ cross section and $\rho$-value data, where $\rho$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. These authors used Finite Energy Sum Rules and analyticity consistency conditions, respectively, to constrain the asymptotic behavior of hadron cross sections by anchoring their high energy asymptotic amplitudes--even under crossing--to low energy experimental data. Using analyticity, we here show that i) the two apparently very different approaches are in fact equivalent, ii) that these analyticity constraints can be extended to give new constraints, and iii) that these constraints can be extended to crossing odd amplitudes. We also apply these extensions to photoproduction. A new interpretation of duality is given.Comment: 9 pages, 1 postscript figure; redone for clarity, removal of typos, changing reference; figure replace

Analyticity as a Robust Constraint on the LHC Cross Section

It is well known that high energy data alone do not discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of $pp$ and $\bar pp$ cross sections. By exploiting high quality low energy data, analyticity resolves this ambiguity in favor of cross sections that grow asymptotically as $\ln^2s$. We here show that two methods for incorporating the low energy data into the high energy fits give numerically identical results and yield essentially identical tightly constrained values for the LHC cross section. The agreement can be understood as a new analyticity constraint derived as an extension of a Finite Energy Sum Rule.Comment: 8 pages, Latex2e, 2 postscript figures; major changes made; accepted for publication in Phys Rev

Hadron pair photoproduction within the Veneziano model

We first suppose that low-energy hadron pair photoproduction reactions gamma(*) gamma(*) -> h h-bar are dominated by s-channel resonance contributions. Their normalization is then calculated by their correspondence with the Reggeon term in the Regge parametrization of the gamma h total cross sections. For the case of p p-bar, we make use of the measured gamma p total cross section, and for the case of K+K-, we make use of the corresponding total cross section that is estimated using Regge factorization. For hadrons that have no such data, we can only provide rough estimation based on the additive quark rule. As an effective approach that is convenient and parameter-free, we adopt the Veneziano model in the simplest form. The model is only applicable to the region of low centre-of-mass energy. When the transverse momentum is large, perturbative QCD takes over, whereas in the Regge region, it is known that the Regge pole picture fails in photoproduction. Despite the shortcomings of the model, we find that the parameter-free amplitudes offer a sound description of the data at hand.Comment: 24 pages, 11 figure

Investigations of the pi N total cross sections at high energies using new FESR: log nu or (log nu)^2

We propose to use rich informations on pi p total cross sections below N= 10 GeV in addition to high-energy data in order to discriminate whether these cross sections increase like log nu or (log nu)^2 at high energies, since it is difficult to discriminate between asymptotic log nu and (log nu)^2 fits from high-energy data alone. A finite-energy sum rule (FESR) which is derived in the spirit of the P' sum rule as well as the n=1 moment FESR have been required to constrain the high-energy parameters. We then searched for the best fit of pi p total cross sections above 70 GeV in terms of high-energy parameters constrained by these two FESR. We can show from this analysis that the (log nu)^2 behaviours is preferred to the log nu behaviours.Comment: to be published in Phys. Rev. D 5 pages, 2 eps figure