123094940
Analyticity constraints on the Landshoff-Donnachie fit to total cross sections
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 pp scattering cross sections with five parameters, using: {sigma}{sup +}=56.08s{sup -0.4525}+21.70s{sup 0.0808} for pp, {sigma}{sup -}=98.39s{sup -0.4525}+21.70s{sup 0.0808} for pp. 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 pp cross section and {rho} data that Block and Halzen used for a very good fit to a ln{sup 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.
121023736
PHASE-SPACE INTEGRALS FOR MULTIPARTICLE SYSTEMS
The total phase-space integrals, occurring in the Fermi statistical theory of meson production, for 2-, 3-, 4-, and 5-body final states are reduced to forms suitable for numerical evaluation by hand computation. In addition, the momentum spectrum of any one particle, as derived from the statistical factor, is evaluated. For the 3- and 4-body systems, the $Q$ distribution for any two of the particles (effective mass minus the rest masses of the 2-particle subsystem) is derived. Numerical results are presented for nucleon-nucleon collisions at 0.8-, 1.5-, and 2.7-Bev bombarding kinetic energies.
120614937
Elastic scattering in nucleon-nucleon collisions
Recently, E811 has measured[1] the total cross section for pp scattering at √s = 1800 GeV. In this paper, we refit the experimental data for σtot, ϱ and B for both pp and pp to a QCD-inspired eikonal model, including the new σtot measurement.
122464578
Measurements of the proton--proton total cross section by means of Coulomb scattering at the CERN Intersecting Storage Rings.
Abstract Proton-proton elastic scattering has been measured at the CERN Intersecting Storage Rings in the four-momentum transfer range 0.001 ⩽… t …⩽ 0.015 GeV 2 at centre-of-mass energies of 23 and 31 GeV. The detection of Coulomb scattering and of its interference with nuclear scattering leads to the determination of the real part of the nuclear amplitude and of the total proton-proton cross section by the optical theorem.
13499391
New evidence for the saturation of the Froissart bound
Fits to high energy data alone cannot cleanly discriminate between asymptotic lns and ln{sup 2}s behavior of total hadronic cross sections. We demonstrate that this is no longer true when we require that these amplitudes also describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to high energy measurements of: (i) the {pi}{sup +}p and {pi}{sup -}p total cross sections and {rho}-values (ratio of the real to the imaginary portion of the forward scattering amplitude), for {radical}(s){>=}6 GeV, while requiring that the asymptotic fits smoothly join the {sigma}{sub {pi}{sup +}}{sub p} and {sigma}{sub {pi}{sup -}}{sub p} total cross sections at {radical}(s)=2.6 GeV--both in magnitude and slope, and (ii) separately simultaneously fit the pp and pp total cross sections and {rho}-values for {radical}(s){>=}6 GeV, while requiring that their asymptotic fits smoothly join the the {sigma}{sub pp} and {sigma}{sub pp} total cross sections at {radical}(s)=4.0 GeV--again both in magnitude and slope. In both cases, we have used all of the extensive data of the Particle Data Group [K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66, 010001 (2002).]. However, we then subject these data to a screening process, the Sieve algorithm [M. M. Block,more » physics/0506010.], in order to eliminate outliers that can skew a {chi}{sup 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 {delta}{chi}{sub i}{sup 2}, the individual ith point's contribution to the total {chi}{sup 2}. The {chi}{sup 2} fits are then made to the sieved data. Both the {pi}p and nucleon-nucleon systems strongly favor a high energy ln{sup 2}s fit of the form: {sigma}{sup {+-}}=c{sub 0}+c{sub 1}ln(({nu}/m))+c{sub 2}ln{sup 2}(({nu}/m))+{beta}{sub P{sup '}}(({nu}/m)){sup {mu}}{sup =} -{sup 1}{+-}{delta}(({nu}/m)){sup {alpha}}{sup -1}, basically excluding a lns fit of the form: {sigma}{sup {+-}}=c{sub 0}+c{sub 1}ln(({nu}/m))+{beta}{sub P{sup '}}(({nu}/m)){sup {mu}}{sup -1}{+-}{delta}(({nu}/m)){sup {alpha}}{sup -1}. The upper sign is for {pi}{sup +}p (pp) and the lower sign is for {pi}{sup -}p (pp) scattering, where {nu} is the laboratory pion (proton) energy, and m is the pion (proton) mass.« less
119733346
A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function
We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace transforms needed to obtain gluon distributions from the proton structure function $F_{2}^{\gamma p}(x,Q^{2})$. We numerically inverted the function g(s), s being the variable in Laplace space, to G(v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g(s)→0 less rapidly than 1/s as s→∞, e.g., as 1/sβ for 0<β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G(v) is given by the product of a power vβ−1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10−6 obtaining numerical results that imitate the Dirac delta function δ(v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q2=5 GeV2 down to the lower virtuality Q2=1.69 GeV2. For devolution, β is negative, giving rise to inverse Laplace transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.
10030510
DUST PRODUCTION AND MASS LOSS IN THE GALACTIC GLOBULAR CLUSTER NGC 362
We investigate dust production and stellar mass loss in the Galactic globular cluster NGC 362. Due to its close proximity to the Small Magellanic Cloud (SMC), NGC 362 was imaged with the Infrared Array Camera and Multiband Imaging Photometer cameras onboard the Spitzer Space Telescope as part of the Surveying the Agents of Galaxy Evolution (SAGE-SMC) Spitzer Legacy program. We detect several cluster members near the tip of the red giant branch (RGB) that exhibit infrared excesses indicative of circumstellar dust and find that dust is not present in measurable quantities in stars below the tip of the RGB. We modeled the spectral energy distribution (SED) of the stars with the strongest IR excess and find a total cluster dust mass-loss rate of 3.0{sup +2.0}{sub -1.2} x 10{sup -9} M{sub sun} yr{sup -1}, corresponding to a gas mass-loss rate of 8.6{sup +5.6}{sub -3.4} x 10{sup -6} M{sub sun} yr{sup -1}, assuming [Fe/H] =-1.16. This mass loss is in addition to any dustless mass loss that is certainly occurring within the cluster. The two most extreme stars, variables V2 and V16, contribute up to 45% of the total cluster dust-traced mass loss. The SEDs of the more moderate stars indicate themore » presence of silicate dust, as expected for low-mass, low-metallicity stars. Surprisingly, the SED shapes of the stars with the strongest mass-loss rates appear to require the presence of amorphous carbon dust, possibly in combination with silicate dust, despite their oxygen-rich nature. These results corroborate our previous findings in omega Centauri.« less