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Valence Quark Spin Distribution Functions  [PDF]
Nathan Isgur
Physics , 1998, DOI: 10.1103/PhysRevD.59.034013
Abstract: The hyperfine interactions of the constituent quark model provide a natural explanation for many nucleon properties, including the Delta-N splitting, the charge radius of the neutron, and the observation that the proton's quark distribution function ratio d(x)/u(x)->0 as x->1. The hyperfine-perturbed quark model also makes predictions for the nucleon spin-dependent distribution functions. Precision measurements of the resulting asymmetries A_1^p(x) and A_1^n(x) in the valence region can test this model and thereby the hypothesis that the valence quark spin distributions are "normal".
Valence Quark Distribution in A=3 Nuclei  [PDF]
C. J. Benesh,T. Goldman,G. J. Stephenson, Jr.
Physics , 2003, DOI: 10.1103/PhysRevC.68.045208
Abstract: We calculate the quark distribution function for 3He/3H in a relativistic quark model of nuclear structure which adequately reproduces the nucleon approximation, nuclear binding energies, and nuclear sizes for small nuclei. The results show a clear distortion from the quark distribution function for individual nucleons (EMC effect) arising dominantly from a combination of recoil and quark tunneling effects. Antisymmetrization (Pauli) effects are found to be small due to limited spatial overlaps. We compare our predictions with a published parameterization of the nuclear valence quark distributions and find significant agreement.
Baryon Stopping and the Valence Quark Distribution at Small x  [PDF]
Kazunori Itakura,Yuri V. Kovchegov,Larry McLerran,Derek Teaney
Physics , 2003, DOI: 10.1016/j.nuclphysa.2003.10.016
Abstract: We argue that the amount of baryon stopping observed in the central rapidity region of heavy ion collisions at RHIC is proportional to the nuclear valence quark distributions at small x. By generalizing Mueller's dipole model to describe Reggeons we construct a non-linear evolution equation for the valence quark distributions at small x in the leading double-logarithmic approximation. The equation includes the effects of gluon saturation in it. The solution of the evolution equation gives a valence quark distribution function $dn_{val}/dy \sim e^{-(0.4\div0.5) y}$. We show that this y-dependence as well as the predictions of Regge theory are consistent with the net-proton rapidity distribution reported by BRAHMS.
Pion Valence-quark Parton Distribution Function  [PDF]
Lei Chang,Anthony W. Thomas
Physics , 2014, DOI: 10.1016/j.physletb.2015.08.036
Abstract: Within the Dyson-Schwinger equation formulation of QCD, a rainbow ladder truncation is used to calculate the pion valence-quark distribution function(PDF). The gap equation is renormalized at a typical hadronic scale, of order 0.5GeV, which is also set as the default initial scale for the pion PDF. We implement a corrected leading-order expression for the PDF which ensures that the valence-quarks carry all of the pion's light-front momentum at the initial scale. The scaling behavior of the pion PDF at a typical partonic scale of order 5.2GeV is found to be $(1-x)^{\nu}$, with $\nu\simeq 1.6$, as $x$ approaches one.
Pion and kaon valence-quark parton distribution functions  [PDF]
Trang Nguyen,Adnan Bashir,Craig D. Roberts,Peter C. Tandy
Physics , 2011, DOI: 10.1103/PhysRevC.83.062201
Abstract: A rainbow-ladder truncation of QCD's Dyson-Schwinger equations, constrained by existing applications to hadron physics, is employed to compute the valence-quark parton distribution functions of the pion and kaon. Comparison is made to pi-N Drell-Yan data for the pion's u-quark distribution and to Drell-Yan data for the ratio u_K(x)/u_\pi(x): the environmental influence of this quantity is a parameter-free prediction, which agrees well with existing data. Our analysis unifies the computation of distribution functions with that of numerous other properties of pseudoscalar mesons.
Basic features of the pion valence-quark distribution function  [PDF]
Lei Chang,Cédric Mezrag,Hervé Moutarde,Craig D. Roberts,Jose Rodríguez-Quintero,Peter C. Tandy
Physics , 2014, DOI: 10.1016/j.physletb.2014.08.009
Abstract: The impulse-approximation expression used hitherto to define the pion's valence-quark distribution function is flawed because it omits contributions from the gluons which bind quarks into the pion. A corrected leading-order expression produces the model-independent result that quarks dressed via the rainbow-ladder truncation, or any practical analogue, carry all the pion's light-front momentum at a characteristic hadronic scale. Corrections to the leading contribution may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea-quarks. Working with available empirical information, we use an algebraic model to express the principal impact of both classes of corrections. This enables a realistic comparison with experiment that allows us to highlight the basic features of the pion's measurable valence-quark distribution, $q^\pi(x)$; namely, at a characteristic hadronic scale, $q^\pi(x) \sim (1-x)^2$ for $x\gtrsim 0.85$; and the valence-quarks carry approximately two-thirds of the pion's light-front momentum.
Sketching the pion's valence-quark generalised parton distribution  [PDF]
C. Mezrag,L. Chang,H. Moutarde,C. D. Roberts,J. Rodriguez-Quintero,F. Sabatie,S. M. Schmidt
Physics , 2014,
Abstract: In order to learn effectively from measurements of generalised parton distributions (GPDs), it is desirable to compute them using a framework that can potentially connect empirical information with basic features of the Standard Model. We sketch an approach to such computations, based upon a rainbow-ladder (RL) truncation of QCD's Dyson-Schwinger equations and exemplified via the pion's valence dressed-quark GPD, $H_\pi^{\rm v}(x,\xi,t)$. Our analysis focuses primarily on $\xi=0$, although we also capitalise on the symmetry-preserving nature of the RL truncation by connecting $H_\pi^{\rm v}(x,\xi=\pm 1,t)$ with the pion's valence-quark parton distribution amplitude. We explain that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for $H_\pi^{\rm v}(x,0,t)$, expressed as the Radon transform of a single amplitude. Therewith we obtain results for $H_\pi^{\rm v}(x,0,t)$ and the associated impact-parameter dependent distribution, $q_\pi^{\rm v}(x,|\vec{b}_\perp|)$, which provide a qualitatively sound picture of the pion's dressed-quark structure at an hadronic scale. We evolve the distributions to a scale $\zeta=2\,$GeV, so as to facilitate comparisons in future with results from experiment or other nonperturbative methods.
A lattice determination of the second moment of the polarised valence quark distribution  [PDF]
M. Goeckeler,R. Horsley,L. Mankiewicz,H. Perlt,P. Rakow,G. Schierholz,A. Schiller
Physics , 1997, DOI: 10.1016/S0370-2693(97)01201-X
Abstract: We perform a Monte Carlo calculation of the second moment of the polarised valence quark distributions in the nucleon, using quenched Wilson fermions. The special feature of this moment is that it is directly accessible experimentally. At a scale of $\mu \approx 2$GeV we find $\Delta^{(1)}u = 0.198(8)$, $\Delta^{(1)}d = -0.0477(33)$. We compare these numbers with recent experimental results of the SMC collaboration.
The Polarised Valence Quark Distribution from semi-inclusive DIS  [PDF]
COMPASS Collaboration,M. Alekseev
Statistics , 2007, DOI: 10.1016/j.physletb.2007.12.056
Abstract: The semi-inclusive difference asymmetry A^{h^{+}-h^{-}} for hadrons of opposite charge has been measured by the COMPASS experiment at CERN. The data were collected in the years 2002-2004 using a 160 GeV polarised muon beam scattered off a large polarised ^6LiD target and cover the range 0.006 < x < 0.7 and 1 < Q^2 < 100 (GeV/c)^2. In leading order QCD (LO) the asymmetry A_d^{h^{+}-h^{-}} measures the valence quark polarisation and provides an evaluation of the first moment of Delta u_v + Delta d_v which is found to be equal to 0.40 +- 0.07 (stat.) +- 0.05 (syst.) over the measured range of x at Q^2 = 10 (GeV/c)^2. When combined with the first moment of g_1^d previously measured on the same data, this result favours a non-symmetric polarisation of light quarks Delta u-bar = - Delta d-bar at a confidence level of two standard deviations, in contrast to the often assumed symmetric scenario Delta u-bar = Delta d-bar = Delta s-bar = Delta s.
Direct measurement of the pion valence quark momentum distribution, the pion light-cone wave function squared  [PDF]
E791 Collaboration,E. M. Aitala
Physics , 2000, DOI: 10.1103/PhysRevLett.86.4768
Abstract: We present the first direct measurements of the pion valence quark momentum distribution which is related to the square of the pion light-cone wave function. The measurements were carried out using data on diffractive dissociation of 500 GeV/c $\pi^-$ into di-jets from a platinum target at Fermilab experiment E791. The results show that the $|q\bar {q}>$ light-cone asymptotic wave function, which was developed using perturbative QCD methods, describes the data well for $Q^2 \sim 10 ~{\rm (GeV/c)^2}$ or more. We also measured the transverse momentum distribution of the diffractive di-jets.
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