119386557
Hadronic forward scattering : Predictions for the Large Hadron Collider and cosmic rays
Abstract The status of hadron–hadron interactions is reviewed, with emphasis on the forward and near-forward scattering regions. Using unitarity, the optical theorem is derived. Analyticity and crossing symmetry, along with integral dispersion relations, are used to connect particle–particle and antiparticle–particle total cross sections and ρ -values, e.g., σ pp , σ p ¯ p , ρ pp and ρ p ¯ p , where ρ is the ratio of the real to the imaginary portion of the forward scattering amplitude. Real analytic amplitudes are then introduced to exploit analyticity and crossing symmetry. Again, from analyticity, finite energy sum rules (FESRs) are introduced from which new analyticity constraints are derived. These new analyticity conditions exploit the many very accurate low-energy experimental cross sections, i.e., they constrain the values of the asymptotic cross sections and their derivatives at low energies just above the resonance regions, allowing us new insights into duality. A robust fitting technique—using a minimization of the Lorentzian squared followed by the “Sieve” algorithm—is introduced in order to ‘clean up’ large data samples that are contaminated by outliers, allowing us to make much better fits to hadron–hadron scattering data over very large regions of energy. Experimental evidence for factorization theorems for γ γ , γ p and nucleon–nucleon collisions is presented. The Froissart bound is discussed—what do we mean here by the saturation of the Froissart bound? Using our analyticity constraints, new methods of fitting high-energy hadronic data are introduced which result in much more precise estimates of the fit parameters, allowing accurate extrapolations to much higher energies. It's shown that the γ p , π ± p and nucleon–nucleon cross sections all go asymptotically as ln 2 s , saturating the bound, while conclusively ruling out ln s and s α ( α ∼ 0.08 ) behavior. Implications of this saturation for predictions of σ pp and ρ pp at the Large Hadron Collider (LHC) and for cosmic rays are given. We discuss present day cosmic ray measurements, what they measure and how they deduce p–air cross sections. Connections are made between very high-energy measurements of σ p – air prod —which have rather poor energy determination—and predictions of σ p – air prod obtained, using a Glauber model, from values of σ pp that are extrapolated from fits of accelerator data at very precisely known, albeit lower, energies.
95016103
A Liquid Helium Bubble Chamber
1) To provide an efficient dewar with large windows on two sides which allow for illuminating and photo­ graphing the bubble chamber tracks without the difficulty of any intervening liquid nitrogen or helium baths in the light path between the bubble chamber and the room temperature photographic system. At the same time heat losses due to room temperature radiation must be reduced several hundred times below that expected from two such room temperature windows.
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.
9426399
Implications from analyticity constraints used in a Landshoff-Donnachie fit
Landshoff and Donnachie[hep/ph 0509240, (2005)] parametrize the energy behavior of pp and pp̄ scattering cross sections with five parameters, using: σ = 56.08s + 21.70s for pp, (1) σ = 98.39s + 21.70s for pp̄. (2) Using the 4 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 pp̄ cross section and ρ data that Block and Halzen used for a very good fit to a ln s parametrization. We show that the satisfaction of the analyticity constraints will require complicated modifications of the LandshoffDonnachie parametrization for lower energies, greatly altering its inherent appeal of simplicity and universality. Landshoff and Donnachie[1, 2, 3] parameterize the scattering cross section with five parameters, using: σ = 56.08s + 21.70s for pp, (3) σ = 98.39s + 21.70s for pp̄, (4) where s is in GeV. Using the high energy limit s → 2mν, where ν is the laboratory energy and m is the proton mass, we rewrite these equations, as well as ρ, the ratio of the real part to the imaginary part of the forward scattering amplitude, more generally as σ = A ( ν m )α−1 + B ( ν m )β−1 ± D ( ν m )α−1 , (5) dσ d(ν/m) = A(α − 1) ( ν m )α−2 + B(β − 1) ( ν m )β−2 ± D(α − 1) ( ν m )α−2 , (6)
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
119268816
Surveying the Agents of Galaxy Evolution in the Tidally Stripped, Low Metallicity Small Magellanic Cloud (SAGE-SMC). II. Cool Evolved Stars
We investigate the infrared (IR) properties of cool, evolved stars in the Small Magellanic Cloud (SMC), including the red giant branch (RGB) stars and the dust-producing red supergiant (RSG) and asymptotic giant branch (AGB) stars using observations from the Spitzer Space Telescope Legacy program entitled Surveying the Agents of Galaxy Evolution in the Tidally Stripped, Low Metallicity SMC, or SAGE-SMC. The survey includes, for the first time, full spatial coverage of the SMC bar, wing, and tail regions at IR wavelengths (3.6-160 μm). We identify evolved stars using a combination of near-IR and mid-IR photometry and point out a new feature in the mid-IR color-magnitude diagram that may be due to particularly dusty O-rich AGB stars. We find that the RSG and AGB stars each contribute 20% of the global SMC flux (extended + point-source) at 3.6 μm, which emphasizes the importance of both stellar types to the integrated flux of distant metal-poor galaxies. The equivalent SAGE survey of the higher-metallicity Large Magellanic Cloud (SAGE-LMC) allows us to explore the influence of metallicity on dust production. We find that the SMC RSG stars are less likely to produce a large amount of dust (as indicated by the [3.6] – [8] color). There is a higher fraction of carbon-rich stars in the SMC, and these stars appear to reach colors as red as their LMC counterparts, indicating that C-rich dust forms efficiently in both galaxies. A preliminary estimate of the dust production in AGB and RSG stars reveals that the extreme C-rich AGB stars dominate the dust input in both galaxies, and that the O-rich stars may play a larger role in the LMC than in the SMC.