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We discuss energy dependence of the slope parameter in elastic proton scattering. It is shown that unitarity generates energy dependence of the slope parameter in geometrical models consistent with the experimental results including recent LHC data.
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The impact parameter dependence of color charge correlators in the proton is obtained from the light front formalism in light cone gauge. We include NLO corrections due to the $|qqqgrangle$ Fock state via light-cone perturbation theory. Near the center of the proton, the $b$-dependence of the correlations is very different from a transverse profile function. The resulting $t$-dependence of exclusive $J/Psi$ photoproduction transitions from exponential to power law at $|t| approx 1$ GeV$^2$. This prediction could be tested at upcoming DIS facilities or in nucleus-proton ultraperipheral collisions (UPCs).
In this Comment we discuss a recent analysis by Yu et al. [RAA 11, 125 (2011)] about constraints on the smoothness $alpha$ parameter and dark energy models using observational $H(z)$ data. It is argued here that their procedure is conceptually inconsistent with the basic assumptions underlying the adopted Dyer-Roeder approach. In order to properly quantify the influence of the $H(z)$ data on the smoothness $alpha$ parameter, a $chi^2$-test involving a sample of SNe Ia and $H(z)$ data in the context of a flat $Lambda$CDM model is reanalyzed. This result is confronted with an earlier approach discussed by Santos et al. (2008) without $H(z)$ data. In the ($Omega_m, alpha$) plane, it is found that such parameters are now restricted on the intervals $0.66 leq alpha leq 1.0$ and $0.27 leq Omega_m leq 0.37$ within 95.4% confidence level (2$sigma$), and, therefore, fully compatible with the homogeneous case. The basic conclusion is that a joint analysis involving $H(z)$ data can indirectly improve our knowledge about the influence of the inhomogeneities. However, this happens only because the $H(z)$ data provide tighter constraints on the matter density parameter $Omega_m$.
We present a measurement of the slope parameter $alpha$ for the $etato 3pi^{0}$ decay, with the KLOE experiment at the DA$Phi$NE $phi$-factory, based on a background free sample of $sim$ 17 millions $eta$ mesons produced in $phi$ radiative decays. By fitting the event density in the Dalitz plot we determine $alpha = -0.0301 pm 0.0035,stat;_{-0.0035}^{+0.0022},syst,$. The result is in agreement with recent measurements from hadro- and photo-production experiments.
We report a preliminary measurement of the slope parameter $alpha$ for the $etato 3piz$ decay carried out with KLOE at DA$Phi$NE; where $alpha$ is the parameter describing the energy dependence of the square of the matrix element for this decay. By fitting the event density in the Dalitz plot with a collected statistic of 420 pb$^{-1}$ we determine $alpha = -0.027 pm 0.004 (stat) ^{+0.004}_{-0.006} (syst)$. This result is consistent with current chiral perturbation theory calculations within the unitary approach.
We study the impact parameter dependence of inelasticity in the framework of an updated geometrical model for multiplicity distribution. A formula in which the inelasticity is related to the eikonal is obtained. This framework permits a calculation of the multiplicity distributions as well as the inelasticity once the eikonal function is given. Adopting a QCD inspired parametrization for the eikonal, in which the gluon-gluon contribution dominates at high energy and determines the asymptotic behavior of the cross sections, we find that the inelasticity decreases as collision energy is increased. Our results predict the KNO scaling violation observed at LHC energies by CMS Collaboration.
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