Experimental tests of non-perturbative pion wave functions

We use the transverse-momentum dependence of the cross section for the diffractive dissociation of high energy pions to two jets to study some non-perturbative light-cone wave functions of the pion. We compare the predictions for this distribution by Gaussian and Coulomb wave functions as well as the wave function derived from a solution of the light-cone Hamiltonian in the singlet model. We conclude that this experimentally measured information provides a powerful tool for these studies. Received: 15 January 2003 / Published online: 14 April 2003 RID="a" ID="a" e-mail: ashery@tauphy.tau.ac.il RID="b" ID="b" e-mail: pauli@mpi-hd.mpg.de     

Measurement of the charged pion electromagnetic form factor

Separated longitudinal and transverse structure functions for the reaction 1H(e,e(')pi(+))n were measured in the momentum transfer region Q2 = 0.6--1.6 (GeV/c)(2) at a value of the invariant mass W = 1.95 GeV. New values for the pion charge form factor were extracted from the longitudinal cross section by using a recently developed Regge model. The results indicate that the pion form factor in this region is larger than previously assumed and is consistent with a monopole parametrization fitted to very low Q2 elastic data.     

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.     

Drawing insights from pion parton distributions

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence,glue and sea distributions within the pion;unifying them with,inter alia,electromagnetic pion elastic and transition form factors.The analysis reveals the following momentum fractions at the scale ζ2:=2GeV:〈xvalence〉=0.48(3),〈xglue〉=0.41(2),〈xsea〉=0.11(2);and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking,the valence-quark distribution function,q^π(x),exhibits the x≈1 behaviour predicted by quantum chromodynamics(QCD).After evolution to ζ=5.2 GeV,the prediction for q^π(x)matches that obtained using lattice-regularised QCD.This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.     

Analysis of pion electroproduction data in terms of a pion distribution function of the proton

Experimental data on the longitudinal π⁺ electroproduction on hydrogen have been analyzed in terms of a pion distribution function of the proton. This interpretation is based on the assumption that the pion can be considered as a parton in the nucleon for low momentum transfer Q². For the kinematical conditions photon mass Q² < 1 GeV² and electron energy loss ν > 2.2 GeV the pion electroproduction in the direction of the virtual photon can be viewed upon as quasielastic eπ⁺ → e′π⁺ scattering. Using the impulse approximation the pion distribution function of the proton can be deduced. According to the distribution function evaluated from pion electroproduction in the infinite momentum frame, the physical proton has a 3% admixture of the nπ⁺ state and the π⁺ in the nπ⁺ state carries 0.6% of the proton momentum.     

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"     

Observation of color-transparency in diffractive dissociation of pions

We have studied the diffractive dissociation into dijets of 500 GeV/c pions scattering coherently from carbon and platinum targets. Extrapolating to asymptotically high energies (where t(min)-->0), we find that when the per-nucleus cross section for this process is parametrized as sigma = sigma0Aalpha, alpha has values near 1.6, the exact result depending on jet transverse momentum. These values are in agreement with those predicted by theoretical calculations of color-transparency.     

Dependence of the interferometric sizes of the pion generation volume on the sizes of the pion wave packet

The effect of the sizes of the initial pion wave packet on the results that the interference method yields for the sizes of the elements of the pion-generation volume is studied experimentally for central MgMg interactions at a momentum of 4.3 GeV/c per nucleon.     

Space- and time-like electromagnetic pion form factors in light-cone pQCD

We present a combined analysis of the space- and time-like electromagnetic pion form factors in light-cone perturbative QCD with transverse momentum dependence and Sudakov suppression. Including the genuine non-perturbative “soft” QCD and the power suppressed twist-3 corrections to the standard twist-2 perturbative QCD result, the experimental form factor data available at moderate energies/momentum transfers can be explained reasonably well. To this end, the bulk of the existing discrepancy between the space- and time-like experimental data is ostensibly reconciled.     

Applying Bayesian neural networks to identify pion, kaon and proton in BES Ⅱ

The Monte-Carlo samples of pion, kaon and proton generated from 0.3 GeV/c to 1.2 GeV/c by the 'tester' generator from SIMBES which are used to simulate the detector of BES Ⅱ are identified with the Bayesian neural networks (BNN). The pion identification and misidentification efficiencies are obviously better at high momentum region using BNN than the methods of X2 analysis of dE/dX and TOF information.The kaon identification and misidentification efficiencies are obviously better from 0.3 GeV/c to 1.2 GeV/c using BNN than the methods of X2 analysis. The proton identification and misidentification efficiencies using BNN are basically consistent with the ones of X2 analysis. The anti-proton identification and misidentification efficiencies are better below 0.6 GeV/c using BNN than the methods of X2 analysis.     

Higher moments of the pion multiplicity distribution in proton-proton interactions at 12 and 24 GeV/c

Results on higher moments of the pion multiplicity distribution are presented for pp interactions at 12 and 24 GeV/c incident lab momentum. A simple parametrization for the pion multiplicity distribution is established at 12 and 24 GeV/c and is then used to discuss the energy dependence of higher moments in a range from 4 to about 500 GeV/c incident lab momentum.     

Bose-Einstein correlations of charged pion pairs in Au + Au collisions at square root sNN = 200 GeV

Bose-Einstein correlations of identically charged pion pairs were measured by the PHENIX experiment at midrapidity in Au + Au collisions at square root s(NN)=200 GeV. The Bertsch-Pratt radius parameters were determined as a function of the transverse momentum of the pair and as a function of the centrality of the collision. Using the standard core-halo partial Coulomb fits, and a new parametrization which constrains the Coulomb fraction as determined from the unlike-sign pion correlation, the ratio R(out)/R(side) is within 0.8-1.1 for 0.25< <1.2 GeV/c. The centrality dependence of all radii is well described by a linear scaling in N(1/3)(part), and R(out)/R(side) for approximately 0.45 GeV/c is approximately constant at unity as a function of centrality.     

Experimental determination of the structure function of the pion

It was shown in the preceeding letter that dimuon production by 22 GeV pions proceeds in part through qq? annihilations in agreement with the Drell-Yan model. Using these data we extract the quark distribution function of the pion. Comparison of our structure function with that obtained from data at higher energy reveals differences compatible with the QCD calculations of the Q²-dependence (scale breaking) of the pion structure function.     

Measurement of the 3He(e,e'p)pn reaction at high missing energies and momenta

Results of the Jefferson Lab Hall A quasielastic 3He(e,e'p)pn measurements are presented. These measurements were performed at fixed transferred momentum and energy, q=1502 MeV/c and omega=840 MeV, respectively, for missing momenta p(m) up to 1 GeV/c and missing energies in the continuum region, up to pion threshold; this kinematic coverage is much more extensive than that of any previous experiment. The cross section data are presented along with the effective momentum density distribution and compared to theoretical models.     

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.     

Direct conversion of mixed phase into free hadronic gas and transverse pion momenta in ultra-relativistic nuclear collisions

The deflagration model is developed for a physically substantiated situation when free pions are radiated directly from a time-like hypersurface formed by a rarefaction shock wave. It is shown that the shock front and pion collective flow velocities are enhanced in this approach as compared to the standard deflagration model. Exotic regimes are also possible. The stability conditions are investigated and analytic solutions are found. We calculate the pion transverse momentum spectra in ultra-relativistic nuclear collisions and indicate their behavior in the region 0.2 GeV/c<p _⊥<1 Gev/c. The spectra are essentially different in this region depending on whether or not longitudinal collective flows are in a mixed phase.     

Precision measurements of the timelike electromagnetic form factors of pion, kaon, and proton

Using 20.7 pb(-1) of e(+)e(-) annihilation data taken at sq.rt(r) = 3.671 GeV with the CLEO-c detector, precision measurements of the electromagnetic form factors of the charged pion, charged kaon, and proton have been made for timelike momentum transfer of |Q(2)| = 13.48 GeV(2) by the reaction e(+)e(-) --> h(+)h(-). The measurements are the first ever with identified pions and kaons of |Q(2)| > 4 GeV(2), with the results F(13.48 GeV(2)) = 0.075 +/- 0.008(stat) +/- 0.005(syst) and F(K)(13.48 GeV(2)) = 0.063 +/- 0.004(stat) +/- 0.001(syst). The result for the proton, assuming G(p)(E) = G(p)(M), is G(p)(M)(13.48 GeV(2)) = 0.014 +/- 0.002(stat) +/- 0.001(syst), which is in agreement with earlier results.     

Investigating in-medium lambda production in pion induced reactions

We present the status of the evaluation of in-medium production cross sections for Lambda baryons and K $_{0}^{S}$ mesons in pion induced reactions at 1.15 GeV/c beam momentum. A systematics of five target nuclei, from carbon to lead, has been measured. The inclusive in-medium cross section is studied as well as possible conclusions on in-medium potential by comparing to transport model calculations. The data have been recorded by the FOPI detector at the GSI.     

Next-to-leading-order calculation in kT factorization

We explain the framework for calculating next-to-leading-order (NLO) corrections to exclusive processes in the kT factorization theorem, taking πγ→γ T as an example. Partons off-shell by k2T are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the kT-dependent hard kernel as their difference. The light-cone singularities in the kT-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. Both the large double logarithms In2 kT and ln2x, x being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function, and the latter into a jet function.