At the CERN intersecting storage ring the inclusive differential cross section ${[\frac{d\ensuremath{\sigma}}{d\ensuremath{\sigma}}]}_{y=1}$ has been measured for ${f}^{0}$, ${g}^{0}$, ${{K}^{*}}^{0}(1420)$, and ${{\overline{K}}^{*}}^{0}(1420)$ production: We obtain 0.58\ifmmode\pm\else\textpm\fi{}0.05 mb, 0.09\ifmmode\pm\else\textpm\fi{}0.05 mb, 38\ifmmode\pm\else\textpm\fi{}15 \ensuremath{\mu}b, and 26\ifmmode\pm\else\textpm\fi{}13 \ensuremath{\mu}b, respectively. The corresponding total inclusive cross sections are estimated to be 2.62\ifmmode\pm\else\textpm\fi{}0.26 mb, 0.40\ifmmode\pm\else\textpm\fi{}0.22 mb, 154\ifmmode\pm\else\textpm\fi{}60 \ensuremath{\mu}b, and 107\ifmmode\pm\else\textpm\fi{}52 \ensuremath{\mu}b, respectively. The magnitude of the ${K}^{*}$ cross section implies a cross section of approximately 5 \ensuremath{\mu}b for production of a charmed $D\overline{D}$ pair.
Landshoff and Donnachie [A. Donnachie and P. V. Landshoff, Phys. Lett. B 296, 227 (1992).; P. V. Landshoff, hep-ph/0509240] parametrize the energy behavior of $pp$ and $p\overline{p}$ scattering cross sections with five parameters, using: ${\ensuremath{\sigma}}^{+}=56.08{s}^{\ensuremath{-}0.4525}+21.70{s}^{0.0808}$ for $pp$, ${\ensuremath{\sigma}}^{\ensuremath{-}}=98.39{s}^{\ensuremath{-}0.4525}+21.70{s}^{0.0808}$ for $p\overline{p}$. Using the four analyticity constraints of Block and Halzen [M. M. Block and F. Halzen, Phys. Rev. D 72, 036006 (2005).], we simultaneously fit the Landshoff-Donnachie form to the same sieved set of $pp$ and $p\overline{p}$ cross section and $\ensuremath{\rho}$ data that Block and Halzen used for a very good fit to a ${ln}^{2}s$ parametrization. We show that the satisfaction of the analyticity constraints will require modification of the Landshoff-Donnachie parametrization for lower energies, thus altering its inherent appeal of simplicity and universality.
In studies of high energy $pp$ and $\overline{p}p$ scattering, the odd (under crossing) forward scattering amplitude accounts for the difference between the $pp$ and $\overline{p}p$ cross sections. Typically, it is taken as ${f}_{\ensuremath{-}}=\ensuremath{-}\frac{p}{4\ensuremath{\pi}}D{s}^{\ensuremath{\alpha}\ensuremath{-}1}{e}^{i\ensuremath{\pi}(1\ensuremath{-}\ensuremath{\alpha})/2}$ ($\ensuremath{\alpha}\ensuremath{\sim}0.5$), which has $\ensuremath{\Delta}\ensuremath{\sigma}$, $\ensuremath{\Delta}\ensuremath{\rho}\ensuremath{\rightarrow}0$ as $s\ensuremath{\rightarrow}\ensuremath{\infty}$, where $\ensuremath{\rho}$ 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 $\ensuremath{\Delta}\ensuremath{\sigma}\ensuremath{\rightarrow}\mathrm{\text{nonzero constant}}$ to having $\ensuremath{\Delta}\ensuremath{\sigma}\ensuremath{\rightarrow}\mathrm{ln}s/{s}_{0}$ as $s\ensuremath{\rightarrow}\ensuremath{\infty}$, the maximal behavior allowed by analyticity and the Froissart bound. We reanalyze high energy $pp$ and $\overline{p}p$ scattering data, using new analyticity constraints, in order to put new and precise limits on the magnitude of ``odderon'' amplitudes.
The elastic differential scattering cross sections, as well as inelastic cross sections, have been obtained for both ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ on ${\mathrm{He}}^{4}$ at 129, 140, and 150 $\frac{\mathrm{MeV}}{c}$, using a 50-cm helium bubble chamber. Following the suggestion of Sternheim and Hofstadter, we have analyzed these data in order to obtain the Coulomb-nuclear interference term. From this, the Coulomb amplitude is deduced, which gives information on the pion charge distribution. The data are analyzed in terms of (a) Born Coulomb amplitude containing a combined Gaussian form factor for the pion and the $\ensuremath{\alpha}$ particle, (b) pure nuclear phases, and (c) the distortion of the nuclear phases due to the long-range nature of the Coulomb field. These qualities, along with the corresponding nuclear potentials, suitably fitted to our data, are presented. We measure the rms combined radius of the pion-${\mathrm{He}}^{4}$ system as $R=1.1\ifmmode\pm\else\textpm\fi{}0.79$ F. This yields ${r}_{\ensuremath{\pi}}$, the rms radius for the pion, to be ${r}_{\ensuremath{\pi}}<0.9$ F.
Using Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we decouple the solutions for the singlet structure function $F_s(x,Q^2)$ and $G(x,Q^2)$ of the two leading-order coupled singlet DGLAP equations, allowing us to write fully decoupled solutions: F_s(x,Q^2)={\cal F}_s(F_{s0}(x), G_0(x)), G(x,Q^2)={\cal G}(F_{s0}(x), G_0(x)). Here ${\cal F}_s$ and $\cal G$ are known functions---found using the DGLAP splitting functions---of the functions $F_{s0}(x) \equiv F_s(x,Q_0^2)$ and $G_{0}(x) \equiv G(x,Q_0^2)$, the chosen starting functions at the virtuality $Q_0^2$. As a proof of method, we compare our numerical results from the above equations with the published MSTW LO gluon and singlet $F_s$ distributions, starting from their initial values at $Q_0^2=1 GeV^2$. Our method completely decouples the two LO distributions, at the same time guaranteeing that both distributions satisfy the singlet coupled DGLAP equations. It furnishes us with a new tool for readily obtaining the effects of the starting functions (independently) on the gluon and singlet structure functions, as functions of both $Q^2$ and $Q_0^2$. In addition, it can also be used for non-singlet distributions, thus allowing one to solve analytically for individual quark and gluon distributions values at a given $x$ and $Q^2$, with typical numerical accuracies of about 1 part in $10^5$, rather than having to evolve numerically coupled integral-differential equations on a two-dimensional grid in $x, Q^2$, as is currently done.
Operant keypress tasks, where each action has a consequence, have been analogized to the construct of "wanting" and produce lawful relationships in humans that quantify preferences for approach and avoidance behavior. It is unknown if rating tasks without an operant framework, which can be analogized to "liking", show similar lawful relationships. We studied three independent cohorts of participants (N = 501, 506, and 4,019 participants) collected by two distinct organizations, using the same 7-point Likert scale to rate negative to positive preferences for pictures from the International Affective Picture Set. Picture ratings without an operant framework produced similar value functions, limit functions, and trade-off functions to those reported in the literature for operant keypress tasks, all with goodness of fits above 0.75. These value, limit, and trade-off functions were discrete in their mathematical formulation, recurrent across all three independent cohorts, and demonstrated scaling between individual and group curves. In all three experiments, the computation of loss aversion showed 95% confidence intervals below the value of 2, arguing against a strong overweighting of losses relative to gains, as has previously been reported for keypress tasks or games of chance with calibrated uncertainty. Graphed features from the three cohorts were similar and argue that preference assessments meet three of four criteria for lawfulness, providing a simple, short, and low-cost method for the quantitative assessment of preference without forced choice decisions, games of chance, or operant keypressing. This approach can easily be implemented on any digital device with a screen (e.g., cellphones).
