Spin structure of the pion in a light-cone representation

The spin structure of the pion is discussed by transforming the wave function for the pion in the naive quark model into a light-cone representation. It is shown that there are higher helicity (λ ₁+λ ₂=±1) states in the full light-cone wave function for the pion besides the ordinary helicity (λ ₁+λ ₂=0) component wave functions as a consequence from the Melosh rotation relating spin states in light-front dynamics and those in instantform dynamics. Some low energy properties of the pion, such as the electromagnetic form factor, the charged mean square radius, and the weak decay constant, could be interrelated in this representation with reasonable parameters.     

Exploring light-cone sum rules for pion and kaon form factors

We analyze the higher-twist effects and the SU(3)-flavor symmetry breaking in the correlation functions used to calculate form factors of pseudoscalar mesons in the QCD light-cone sum rule approach. It is shown that the Ward identities for these correlation functions yield relations between twist-4 two- and three-particle distribution amplitudes. In addition to the relations already obtained from the QCD equations of motions, we have found a new one. With the help of these relations, the twist-4 contribution to the light-cone sum rule for the pion electromagnetic form factor is reduced to a very simple form. Simultaneously, we correct a sign error in an earlier calculation. The updated light-cone sum rule prediction for the pion form factor at intermediate momentum transfers is compared with the recent Jefferson Lab data. Furthermore, from the correlation functions with strange-quark currents the kaon electromagnetic form factor and the weak transition form factors are predicted with accuracy. Received: 30 June 2002 / Published online: 7 October 2002 RID="a"     

Direct measurement of the pion valence-quark momentum distribution, the pion light-cone wave function squared

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 dijets from a platinum target at Fermilab experiment E791. The results show that the /q&q> light-cone asymptotic wave function describes the data well for Q2 approximately 10 (GeV/c)(2) or more. We also measured the transverse momentum distribution of the diffractive dijets.     

Possibilities of revealing collective pion degrees of freedomin nuclei by means of quasielastic pion knockout by high-energy electrons

The kinematics of quasielastic pion knockout by longitudinal virtual photons in the electroproduction process is presented. The possibility of directly investigating pion momentum distributions in specific channels owing to pole-amplitude dominance is considered. It is shown that, taking into account the final-state interaction of the knock-on pion and the nucleus involved, one can reveal the existence of a pion condensate in nuclei, since the momentum distribution of collective pions has a pronounced maximum at a momentum in excess of 0.3 GeV/c and since the excitation spectrum of the final recoil nucleus is concentrated in the low-energy region E* ≈ K ²/(2AM _N ) ≤ 1 MeV. The picture of pion knockout from meson clouds of individual nucleons is totally different. The analogous rho-mesonmomentum distributions for the process ρ + γT* → π are also presented.     

The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).     

New Results in Light-Front Phenomenology

The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. In this talk I review the theoretical methods and constraints which can be used to determine these central elements of QCD phenomenology. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and define a kinematical definition of angular momentum. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in four-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The nonperturbative Fock-state wavefunctions contain intrinsic gluons, and sea quarks at any scale Q with asymmetries such as . Intrinsic charm and bottom quarks appear at large x in the light-front wavefunctions since this minimizes the invariant mass and off-shellness of the higher Fock state. In the case of nuclei, the Fock state expansion contains “hidden color” states which cannot be classified in terms of nucleonic degrees of freedom. I also briefly review recent analyses which show that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.Work supported by Department of Energy contract DE-AC02-76SF00515     

Pion and K meson production in the multiperipheral model

A simple multiperipheral model, that utilizes only three parameters, two coupling constants and exponential damping for each momentum transfer is developed and applied to the calculation of inclusive distributions. The pion rapidity and p_⊥² distributions are successfully predicted; as are the energy dependences of strange particle production cross sections. The development of inclusive distributions with increasing energy and possible improvements to the model are discussed.     

The role of the pion cloud in the interpretation of the valence light-cone wavefunction of the nucleon

The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon’s electromagnetic form-factor at high Q² is proportional to the bare nucleon probability Z and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to Z². Our present knowledge of the pion-nucleon system is consistent with Z = 0.7 ± 0.2. If we apply just perturbative QCD to extract a light-cone wavefunction directly from these hard exclusive cross-sections, then the light-cone wavefunction that we extract measures the three valence quarks partially screened by the pion cloud of the nucleon. We discuss how this pion cloud renormalisation effect might be understood at the quark level in terms of the (in-)stability of the perturbative Dirac vacuum in low energy QCD.     

Testing Theories of Chiral Symmetry

We investigate various physical consequences of theories of chiral symmetry. Predictions of the symmetry are given for the meson electroproduction process at an on-shell kinematical point where unknown contributions are minimized. Sum rules are derived for the corrections. Then we present a sum rule for the ∑ term in meson-baryon scattering from the assumptions of Bjorken limit, precocious asymptopia, and finite-mass dispersion relations. We use the commutation relations of the gluon model as input for a numerical evaluation. Next the explicit canonical structure of the light-cone restriction of the commutator of the weak current with its divergence is considered in the interacting quark-gluon model quantized in the infinite–momentum frame. The implications on neutrino scattering are analyzed. W₄ and W₅ are predicted to scale nontrivially as v⁻²F₄(ω) and v⁻²F₅(ω), which provides a simple test of light-cone current algebra feasible in the near future. The ∑ term for weak currents is deduced from a causal representation near the light-cone, and a correction is also made in the W₅ – sum rule obtained by naive infinite momentum techniques. As a by-product we obtain improved derivations of the Adler neutrino sum rules.     

Theoretical Description and Measurement of the Pion–Photon Transition Form Factor

Detailed predictions for the scaled pion–photon transition form factor are given, derived with the method of light-cone sum rules and using pion distribution amplitudes with two and three Gegenbauer coefficients obtained from QCD sum rules with nonlocal condensates. These predictions agree well with all experimental data that are compatible with QCD scaling (and collinear factorization), but disagree with the high-Q ² data of the BaBar Collaboration that grow with the momentum. A good agreement of our predictions with results obtained from AdS/QCD models and Dyson–Schwinger computations is found.     

Pions in nuclear interior — sensitive test by hypernuclear decay

The effect of the pion wave distortion on the pi-mesonic weak decay ofΛ-hyperon in hypernuclei is studied by using two different pion optical potentials, one by Gmitro, Kamalov and Mach, which is given in momentum space, and the other by MSU group, which is in the standard Kisslinger form. The two potentials lead to a striking difference in the pi-mesonic decay, reflecting different behaviors of the pion wavefunctions deep inside the nucleus.     

Three-dimensional kaon and pion emission source extraction from √sNN = 200 GeV Au + Au collisions at RHIC-STAR

Three-dimensional source images for mid-rapidity, low transverse momentum kaon and pion pairs have been extracted from central Au + Au collisions data at √s _NN = 200 GeV by the STAR experiment at RHIC. The pion source function displays significant non-Gaussian features implying a finite pion emission duration. On the other hand, the kaon source function is essentially Gaussian, consistent with instantaneous emission from the fireball.     

Coherent pion-photoproduction by deuterons at intermediate energies

Non-relativistically exact single scattering calculations for coherent pion photoproduction by deuterons at intermediate photon energies (200 MeV to 500 MeV) are presented. For the two-bodyγN→πN process we use the well-known dispersion theoretic model by Chewet al and for the deuteron wave-functions we employ the Yamaguchi and the two term Gaussian wave-function. We find that while both the wavefunctions reproduce the deuteron e.m. form factor reasonably well, the results for the pion photoproduction cross-section show, however, a sensitive dependence on their detailed forms. The angular distributions at various energies are found to have considerable variations from the usual impulse approximation calculations but tend to improve the agreement with the data in a large kinematical region.     

Probing nucleon structure on the lattice

The QCDSF/UKQCD Collaboration has an ongoing program to calculate nucleon matrix elements with two flavours of dynamical O(a) improved Wilson fermions. Here we present recent results on the electromagnetic form factors, the quark momentum fraction 〈x〉 and the first three moments of the nucleon's spin-averaged and spin-dependent generalised parton distributions, including preliminary results with pion masses as low as 320MeV.     

Molecular orbital momentum distributions and binding energies for H2O using an electron impact coincidence spectrometer

The construction and operation of an instrument which uses the techniques of coincidence counting and electron impact spectroscopy is reported for the study of molecular ionization at large momentum transfer in which the two outgoing electrons are detected at 45° to the incident beam. Variation of the incident energy provides binding-energy spectra for Xe, CH₄ and H₂O up to 45 eV. Alternatively variation of the azimuthal angle (symmetric, non-coplanar geometry) gives a measure of the electron momentum distribution for any selected orbital in the binding-energy spectrum. Momentum distributions for the four valence orbitals of H₂O are compared with various wavefunctions from the literature.     

Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons

The predictions of quantum chromodynamics for meson form factors at large momentum transfer are given. Evolution equations are derived which determine the structure of hadronic wavefunctions at short distances from their form at large distances. The eigenvalues of the evolution equations appear as exponents in anomalous logarithm corrections to the nominal power law of form factors determined by dimensional counting. The results lead to detailed tests of the spin and scaling structure of QCD at short distances. The predictions for the charged pion, kaon and rho form factors and the γ → π⁰ transition form factor of the photon are absolutely normalized at asymptotic momentum transfer.     

Three-dimensional two-pion emission source at SPS: Extraction of source breakup time and emission duration

A model-independent, three-dimensional source function for pion pairs has been extracted from Pb + Pb collisions at √s _NN = 17.3 GeV. The extracted source exhibits long-range non-Gaussian tails in the directions of the pion-pair net transverse momentum and of the beam. Comparison with the Therminatormodel allows for an extraction of the pion source proper breakup time and of emission duration in the collisions. (for the NA49 Collaboration) The text was submitted by the authors in English.     

A mechanism for the production of baryons at large transverse momentum

The difference between the proton and the antiproton distributions and the charged pion distribution are compared at largeP _T and agreement is found with a model attributing baryons to final state rearrangement of hard scattered partons. The model contains a dual topological suppression of baryonic clusters at largeP _T which is partially balanced as the cluster decay distribution into baryons is peaked at higher values of the momentum fractionz. The model implies positive correlations between antiproton triggers and opposite side protons.     

A study of single pion production in nucleon-nucleon collisions

A pion exchange model for NN pion production from threshold up to about 6 GeV/c is constructed. In contrast to other models of this type the full information from πN scattering is fed in whereby the πN partial waves on- and off-shell are identified with each other. Detailed comparison with the data for both the channels isospin one and zero, reveals that the shapes of angle and momentum distributions are, in general, well reproduced but the overall magnitude comes out too small for p_L ? 1.5 GeV/c. It is argued that this defect may be due to dibaryon resonances. For reaction cross sections their effects are quantitatively estimated.     

A study of pion absorption by16O using realistic interactions—I. Twonucleon emission following bound-pion absorption

Matrix element of the Galilean invariant non-relativistic reduction of the pseudoscalar-pseudovector interaction has been calculated assuming the reaction to be a direct process with boundπ ⁻ being absorbed by a correlated pair of nucleons. The Hartree-Fock wavefunctions obtained with the unitary-model-operator approach starting with the realistic nucleon-nucleon interaction have been used forπ-capturing nucleon pair in the initial state. The calculations have been done with and without antisymmetrising the initial state wavefunction of the pion absorbing pair. For the final state nucleon-nucleon interaction has been taken into account. The strongπ-nucleus interaction together with the Coulomb interaction with the finite nuclear size on the bound pion wavefunction are taken into account. Angular distributions of the emitted nucleon-pair, the branching ratios and the total absorption rates are calculated for¹⁶O with and without antisymmetrisation effect. The calculated results are compared with the experimental and other theoretical work.