The applicability of perturbative QCD to the pion form factor and the pionic wavefunction

We reanalyse the pionic form factor by using perturbative QCD theory and contributions from endpoint regions. We find that the perturbative QCD can be applied to the pionic form factor asQ ²>4 GeV² and they become unreliable asQ ²≦4 GeV². Therefore the applicability of perturbative QCD to the form factor is questionable only asQ ²≦4 GeV².     

The proton form factor measurements at Jefferson Lab, past and future

Use of the double-polarization technique to obtain the elastic nucleon form factors has resulted in a dramatic improvement of the quality of two of the four nucleon electromagnetic form factors, G _Ep and G _En . It has also changed our understanding of the proton structure, having resulted in a distinctly different Q ²-dependence for both G _Ep and G _Mp , contradicting the prevailing wisdom of the 1990’s based on cross section measurements, namely that G _Ep and G _Mp obey a “scaling” relation μG _Ep ～ G _Mp . A related consequence of the faster decrease of G _Ep revealed by the Jefferson Lab (JLab) polarization results was the disappearance of the early scaling F ₂/F ₁ ～ 1/Q ² predicted by perturbative QCD. In three experiments, GEp(1), GEp(2) and GEp(3), in Halls A and C at JLab, the ratio of the proton’s electromagnetic elastic form factors, G _Ep /G _Mp , was measured up to four momentum transfer Q ² of 8.5 GeV² with high precision, using the recoil polarization technique. The initial discovery that the proton form factor ratio measured in these three experiments decreases approximately linearly with four-momentum transfer, Q ², for values above ～ 1 GeV², was modified by the GEp(3) results, which suggests a slowing down of this decrease. There is an approved experiment, GEp(5), to continue these measurements to 15 GeV². A dedicated experimental setup, the super bigbite spectrometer (SBS), will be built for this purpose. It will be equipped with a new focal plane polarimeter to measure the polarization of the recoil protons. In this presentation, I will review the status of the proton elastic electromagnetic form factors, mention succinctly a number of theoretical approaches to describe results and show some features required for the future GEp(5) experiment.     

Regge-eikonal model for high energy elastic diffractive nucleon-nucleon scattering with a minimum number of reggeons

A phenomenological Regge-eikonal model with nonlinear monotonic parameterizations for Regge trajectories in which their asymptotic behavior in the perturbative region is taken into account explicitly is proposed. It is shown with the example of elastic proton-(anti)proton scattering that in the kinematic region \(\sqrt s \) > 23 GeV, 0.005 GeV² < ?t < 3 GeV², the diffraction pattern is mainly determined by only three Regge trajectories.     

Measurement of the proton structure function F 2 at low x and low Q 2 at HERA

We report on a measurement of the proton structure function F ₂ in the range 3.5 × 10^?5 ≤ x ≤ 4 × 10^?3 and 1.5 GeV² ≤ Q ² ≤ 15 GeV² at the ep collider HERA operating at a centre-of-mass energy of ${sqrt s} = 300 {? GeV}$. The rise of F ₂ with decreasing x observed in the previous HERA measurements persists in this lower x and Q ² range. The Q ² evolution of F ₂, even at the lowest Q ² and x measured, is consistent with perturbative QCD.     

Elastic J/ψ production at HERA

Cross sections for elastic production of J/ψ mesons in photoproduction and electroproduction are measured in electron proton collisions at HERA using an integrated luminosity of 55 pb^-1. Results are presented for photon virtualities Q² up to 80 GeV². The dependence on the photon-proton centre of mass energy W_γp is analysed in the range 40≤W_γp≤305 GeV in photoproduction and 40≤W_γp≤160 GeV in electroproduction. The W_γp dependences of the cross sections do not change significantly with Q² and can be described by models based on perturbative QCD. Within such models, the data show a high sensitivity to the gluon density of the proton in the domain of low Bjorken x and low Q². Differential cross sections dσ/dt, where t is the squared four-momentum transfer at the proton vertex, are measured in the range |t|<1.2 GeV² as functions of W_γp and Q². Effective Pomeron trajectories are determined for photoproduction and electroproduction. The J/ψ production and decay angular distributions are consistent with s-channel helicity conservation. The ratio of the cross sections for longitudinally and transversely polarised photons is measured as a function of Q² and is found to be described by perturbative QCD based models.     

Large-pT protons from constituent diquark scattering

Recent data from the CERN ISR on the fractional proton yield in pp collisions are explained within the Stockholm diquark model. Describing the proton as a u(ud)₀ system, the observed high magnitude and fall-off _pT, θ and $\text{s}$ of the proton yield are natural consequences of constituent diquark elastic scattering. The _pT and θ dependence favour a value of around 10 GeV²/c² for the size parameter in the diquark form factor, corresponding to a diquark rms radius of around 0.2 fm. This is consistent with earlier results of the model applied to deep inelastic lepton-nucleon scattering and e⁺e^? annihilation.     

Diffractive photoproduction of dijets in ep collisions at HERA

Diffractive photoproduction of dijets was measured with the ZEUS detector at the ep collider HERA using an integrated luminosity of 77.2 pb^-1. The measurements were made in the kinematic range Q² < 1 GeV², 0.20<y<0.85 and x_IP<0.025, where Q² is the photon virtuality, y is the inelasticity and x_IP is the fraction of the proton momentum taken by the diffractive exchange. The two jets with the highest transverse energy, E_T ^jet, were required to satisfy E_T ^jet>7.5 and 6.5 GeV, respectively, and to lie in the pseudorapidity range -1.5<η^jet<1.5. Differential cross sections were compared to perturbative QCD calculations using available parameterisations of diffractive parton distributions of the proton.     

QCD constraints for the electromagnetic form factor of the pion

Using the modulus representation, we derive constraints for the behaviour of the electromagnetic form factor of the pion in the time like region [1 GeV², +∞], from information given by perturbative QCD in the space like region [?μ ², ?∞]. A phenomenological μ dependent upper bound for the exponent of the first non leading logarithmic correction is deduced. Restrictions and problems of the method are discussed.     

Precision Measurement of {\mu G_{E}^{p}/G_{M}^p} at Low Q 2

Precision measurements are presented of the proton electric to magnetic form-factors ratios at Q ²?=?0.3 ? 0.8 (GeV/c)², obtained by polarization-transfer in Hall A of the Jefferson Laboratory. The measured ratios are significantly lower than published values. New global fits to the individual form factors indicate a lower electric form factor and a slightly higher magnetic form factor. The proton charge radius extracted from the new results is somewhat smaller but consistent with previous values obtained from electron?Cproton scattering, and is in significant disagreement with the recent value obtained from muonic hydrogen. The effects of the new results on other quantities are briefly discussed.     

Determination of the longitudinal and the transverse part in π+ electroproduction

We report on an experiment where the different contributions from the transverse and longitudinal polarization of the virtual photon are measured separately for the reaction e^?p→e^?π⁺n. The data taken above the resonance region at small ∣t∣ values in the q² range of ∣q²∣ < 0.5 GeV² show a clear dominance of the longitudinal part of the cross section and are well described by a generalized Born-term model. Using this model the electromagnetic form factor of the pion is determined. At q² = ?0.35 GeV² one gets F_π = 0.598 ± 0.021.     

Testing the scale dependence of the scale factor σ eff in double dijet production at the LHC

The scale factor σ _eff is the effective cross section used to characterize the measured rate of inclusive double dijet production in high-energy hadron collisions. It is sensitive to the two-parton distributions in the hadronic projectile. In principle, the scale factor depends on the center of mass energy and on the minimal transverse energy E _T,min? of the jets contributing to the double dijet cross section. Here, we point out that proton–proton collisions at the LHC will provide for the first time experimental access to these scale dependences in a logarithmically wide, nominally perturbative kinematic range 10?E _T,min??100 GeV. This constrains the dependence of two-parton distribution functions on parton momentum fractions and parton localization in impact parameter space. Novel information is to be expected about the transverse growth of hadronic distribution functions in the range of semi-hard Bjorken x (0.001?x?0.1) and high resolution Q ². We discuss to what extent one can disentangle different pictures of the x-evolution of two-parton distributions in the transverse plane by measuring double-hard scattering events at the LHC.     

QCD analysis of the Bjorken sum rule revisited

We present extended analysis of the polarized Bjorken sum rule using the four-loop expression for the coefficient function C _Bj(α_s) available now and the recent low Q ²-data from the Jefferson Lab and COMPASS experiments. We demonstrate that the perturbative series for the function C _Bj gives a hint to its asymptotic nature manifesting itself in the region Q ² ? 1 GeV². It is confirmed by the considered integral model for the perturbative QCD correction. We analyze values of higher-twist terms extracted from the mentioned data and discuss the interplay between higher orders perturbative and higher-twist contributions. We extend our consideration to the Gross-Llewellyn Smith sum rule and investigate the relation between higher twist coefficients in these two sum rules.     

Proton elastic form factor: The JLab data

The ratio of the electric and magnetic proton form factors, G_Ep/G_Mp, has been obtained in two Hall A experiments, from measurements of the longitudinal and transverse polarization of the recoil proton, P_L and P_T, respectively, in the elastic scattering of polarized electrons, . Together these experiments cover the Q² range 0.5 to 5.6 GeV². A new experiment is currently being prepared, to extend the Q² range to 9 GeV² in Hall C.Received: 1 November 2002, Published online: 15 July 2003PACS: 13.40.Gp Specific reactions and phenomenology: Electromagnetic form factors - 14.20.Dh Properties of specific particles: Protons and neutrons - 24.70.+s Nuclear reactions: Polarization phenomena in reactions     

Nucleon charge form factors and chiral quark models

Calculations of the proton and neutron charge form factors G_E^p,n(q²) are presented, based on chiral bag as well as confining Dirac potential models with chiral pion-quark coupling. Special emphasis is placed on a detailed treatment of the charged pion cloud contribution to the nucleon current. The role of a finite extension of the pion-quark vertex in truncating the summation over intermediate quark bag states is studied. Quark core radii (including recoil corrections) are constrained by a simultaneous calculation of the nucleon axial form factor. The proton charge form factor is well reproduced for $\text{|q}{}^2\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 0.7}\text{GeV}$ with quark core rms radii between 0.5–0.6 fm. About $\text{1}\text{3}$ of the proton charge is carried by the pion cloud in this model. The neutron charge form factor is obtained with the correct sign and overall q² dependence but needs further refinements, probably at the level of the isoscalar form factor.     

A measurement of the proton structure function F2(x,Q2)

A measurement of the proton structure function F₂(x, Q²) is reported for momentum transfers squared Q² between 4.5 GeV² and 1600 GeV² and for Bjorken x between 1.8 × 10⁻¹⁴ and 0.13 using data collected by the HERA experiment H1 in 1993. It is observed that F₂ increases significantly with decreasing x, confirming our previous measurement made with one tenth of the data available in this analysis. The Q² dependence is approximately logarithmic over the full kinematic range covered. The subsample of deep inelastic events with a large pseudo-rapidity gap in the hadronic energy flow close to the proton remnant is used to measure the “diffractive” contribution to F₂.     

The ZEUS Leading Proton Spectrometer and its use in the measurement of elastic ρ0 photoproduction at HERA

The differential cross section dσ/dt for elastic ρ⁰ photoproduction, γp → ρ⁰p (ρ⁰ → π⁺π^?), has been measured in ep interactions at HERA. The squared four-momentum exchanged at the proton vertex, t, has been determined directly by measuring the momentum of the scattered proton using the ZEUS Leading Proton Spectrometer (LPS), a large scale system of silicon micro-strip detectors operating close to the HERA proton beam. The LPS allows the measurement of the momentum of high energy protons scattered at small angles with accuracies of 0.4% for the longitudinal momentum and 5 MeV for the transverse momentum. Photoproduction of ρ⁰ mesons has been investigated in the interval 0.073 < ¦t¦< 0.40 GeV², for photon virtualities Q² < 1 GeV² and photon-proton centre-of-mass energies W between 50 and 100 GeV. In the measured range, the t distribution exhibits an exponential shape with a slope parameter b = 9.8 ± 0.8 (stat.) ±1.1 (syst.) GeV^?2. The use of the LPS eliminates the contamination from events with diffractive dissociation of the proton into low mass states.     

QCD corrections at the Z0

All QCD corrections in hadron-initiated lepton-pair production are questionable for Q²?100 GeV² since a perturbative expansion is not justified in this kinematical range. Application of the renormalization group (RG) program at Z₀ energies is meaningful. We exhibit the size of the non-log correction terms, introduce experimental tests, and point to the assumptiona inherent in Drell-Yan (DY) type analyses.     

Masses of the right-handed gauge bosons from the renormalization group equations

Lower bounds on the masses of the right-handed gauge bosons are obtained from the renormalization group analysis. The perturbative approach breaks down unless M_WR≳10⁷ GeV.