New limits on "odderon" amplitudes from analyticity constraints

In studies of high energy $pp$ and $\bar pp$ scattering, the odd (under crossing) forward scattering amplitude accounts for the difference between the $pp$ and $\bar pp$ cross sections. Typically, it is taken as $f_-=-\frac{p}{4\pi}Ds^{\alpha-1}e^{i\pi(1-\alpha)/2}$ ($\alpha\sim 0.5$), which has $\Delta\sigma, \Delta\rho\to0$ as $s\to\infty$, where $\rho$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. However, the odd-signatured amplitude can have in principle a strikingly different behavior, ranging from having $\Delta\sigma\to$non-zero constant to having $\Delta\sigma \to \ln s/s_0$ as $s\to\infty$, the maximal behavior allowed by analyticity and the Froissart bound. We reanalyze high energy $pp$ and $\bar pp$ scattering data, using new analyticity constraints, in order to put new and precise limits on the magnitude of ``odderon'' amplitudes.Comment: 13 pages LaTex, 6 figure

Elastic pppp and pˉp\bar pp scattering in the models of unitarized pomeron

Elastic scattering amplitudes dominated by the Pomeron singularity which obey the principal unitarity bounds at high energies are constructed and analyzed. Confronting the models of double and triple (at $t=0$) Pomeron pole (supplemented by some terms responsible for the low energy behaviour) with existing experimental data on $pp$ and $\bar pp$ total and differential cross sections at $\sqrt{s}\geq 5$ GeV and $|t|\leq 6$ GeV$^{2}$ we are able to tune the form of the Pomeron singularity. Actually the good agreement with those data is received for both models though the behaviour given by the dipole model is more preferable in some aspects. The predictions made for the LHC energy values display, however, the quite noticeable difference between the predictions of models at $t\approx -0.4$ GeV$^{2}$. Apparently the future results of TOTEM will be more conclusive to make a true choice.Comment: Revtex4, 8 pages, 5 figures. Text is improved, no changes in figures and conclusions. Version to be published in Phys. Rev.

Heisenberg's Universal (lns)**2 Increase of Total Cross Sections

The (lns)**2 behaviour of total cross-sections, first obtained by Heisenberg 50 years ago, receives now increased interest both on phenomenological and theoretical levels. In this paper we present a modification of the Heisenberg's model in connection with the presence of glueballs and we show that it leads to a realistic description of all existing hadron total cross-section data.Comment: 6 pages, 3 figure

Non-equivalence of anti-Müllerian hormone automated assays—clinical implications for use as a companion diagnostic for individualised gonadotrophin dosing

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Universality of low-energy scattering in (2+1) dimensions

We prove that, in (2+1) dimensions, the S-wave phase shift, $\delta_0(k)$, k being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or \delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$. This result is established first in the framework of the Schr\"odinger equation for a large class of potentials, second for a massive field theory from proved analyticity and unitarity, and, finally, we look at perturbation theory in $\phi_3^4$ and study its relation to our non-perturbative result. The remarkable fact here is that in n-th order the perturbative amplitude diverges like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln k)^{-1}$. We show how these two facts can be reconciled.Comment: 23 pages, Late

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

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 $\sigma_{tot}$ and the $\rho$ parameter. In this paper we investigate four aspects related to the application of the model to $pp$ and $\bar{p}p$ scattering, from accelerator to cosmic-ray energies: 1) the effect of different estimations for $\sigma_{tot}$ from cosmic-ray experiments; 2) the differences between individual and global (simultaneous) fits to $\sigma_{tot}$ and $\rho$; 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: $1 + \epsilon = 1.094$; 2) although global fits present good statistical results, in general, this procedure constrains the rise of $\sigma_{tot}$; 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 $\sqrt s \approx 70$ GeV, $\rho_{pp}(s)$ becomes greater than $\rho_{\bar{p}p}(s)$, and this result is in complete agreement with all the data presently available. In particular, we infer $\rho_{pp} = 0.134 \pm 0.005$ at $\sqrt s = 200$ GeV and $0.151 \pm 0.007$ at 500 GeV (BNL RHIC energies).Comment: 16 pages, 7 figures, aps-revtex, wording changes, corrected typos, to appear in Physical Review

Effective Regge QCD

A new framework for a high energy limit of quantum gauge field theories is introduced. Its potency is illustrated on a new derivation of the reggeization of the gluon.Comment: Latex, 9 pages + 2 figures as PS-file, extended version, to appear in Phys. Rev. Let