118529955
Analytic treatment of leading-order parton evolution equations: Theory and tests
We recently derived an explicit expression for the gluon distribution function G(x,Q{sup 2})=xg(x,Q{sup 2}) in terms of the proton structure function F{sub 2}{sup {gamma}}{sup p}(x,Q{sup 2}) in leading-order (LO) QCD by solving the LO Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation for the Q{sup 2} evolution of F{sub 2}{sup {gamma}}{sup p}(x,Q{sup 2}) analytically, using a differential-equation method. We showed that accurate experimental knowledge of F{sub 2}{sup {gamma}}{sup p}(x,Q{sup 2}) in a region of Bjorken x and virtuality Q{sup 2} is all that is needed to determine the gluon distribution in that region. We rederive and extend the results here using a Laplace-transform technique, and show that the singlet quark structure function F{sub S}(x,Q{sup 2}) can be determined directly in terms of G from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi gluon evolution equation. To illustrate the method and check the consistency of existing LO quark and gluon distributions, we used the published values of the LO quark distributions from the CTEQ5L and MRST2001 LO analyses to form F{sub 2}{sup {gamma}}{sup p}(x,Q{sup 2}), and then solved analytically for G(x,Q{sup 2}). We find that the analytic and fitted gluon distributions from MRST2001LO agree well with each other for all x and Q{sup 2}, while those from CTEQ5L differ significantly from each othermore » for large x values, x > or approx. 0.03-0.05, at all Q{sup 2}. We conclude that the published CTEQ5L distributions are incompatible in this region. Using a nonsinglet evolution equation, we obtain a sensitive test of quark distributions which holds in both LO and next-to-leading order perturbative QCD. We find in either case that the CTEQ5 quark distributions satisfy the tests numerically for small x, but fail the tests for x > or approx. 0.03-0.05--their use could potentially lead to significant shifts in predictions of quantities sensitive to large x. We encountered no problems with the MRST2001LO distributions or later CTEQ distributions. We suggest caution in the use of the CTEQ5 distributions.« less
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.
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.
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.
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.
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.