18081479
Duality 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 s behavior of pp and p̄p cross sections. By exploiting high quality low energy data, duality resolves this ambiguity in favor of cross sections that grow asymptotically as ln s. We here show that two methods for incorporating the low energy data into the high energy fits give numerically identical results, thus reinforcing the validity of duality. They yield essentially identical and tightly constrained values for the LHC cross section. High precision low energy data represent a powerful constraint on the high energy behavior of hadronic cross sections via duality[1, 2]. The low energy data can be separated into two energy regimes, the resonance region and a region with energies in excess of a laboratory energy ν0 (ν0 is ≈ 6 GeV for the p̄p and pp system) above where the resonances average into a featureless cross section, in the sense of duality. Data in both of these low energy regimes are routinely ignored when performing asymptotic fits to high energy data. Two methods have been used to impose duality on pp and p̄p cross sections. Igi and Ishida[1] constrain the high energy fit to the low energy data by a Finite Energy Sum Rule (FESR) which numerically averages the resonances. Block and Halzen[2] require that the high energy amplitudes also describe, on average, the low energy resonance-dominated data near ν0 and above. Both methods agree in discriminating between a ln s and ln s asymptotic behavior of the asymptotic cross section, conclusively favoring the latter. In this letter we will confront the two methods with a common “sieved” data set[3] and show that they yield identical fits to the high energy data. Duality thus can be used to achieve a robust and precise value for the total cross section at the LHC energy of 14 TeV, as well as at cosmic ray energies. Following Block and Cahn[4] we describe the data in terms of real analytic amplitudes
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
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.
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.
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.
29749856
SPATIAL VARIATIONS OF DUST ABUNDANCES ACROSS THE LARGE MAGELLANIC CLOUD
Using the data obtained with the Spitzer Space Telescope as part of the Surveying the Agents of a Galaxy's Evolution (SAGE) legacy survey, we have studied the variations of the dust composition and abundance across the Large Magellanic Cloud (LMC). Such variations are expected, as the explosive events which have lead to the formation of the many H I shells observed should have affected the dust properties. Using a model and comparing with a reference spectral energy distribution from our Galaxy, we deduce the relative abundance variations of small dust grains across the LMC. We examined the infrared color ratios as well as the relative abundances of very small grains (VSGs) and polycyclic aromatic hydrocarbons (PAHs) relative to the big grain abundance. Results show that each dust component could have different origins or evolution in the interstellar medium (ISM). The VSG abundance traces the star formation activity and could result from shattering of larger grains, whereas the PAH abundance increases around molecular clouds as well as in the stellar bar, where they could have been injected into the ISM during mass loss from old stars.