Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei

A simple exact covariant model in which a scalar particle is modeled as a bound state of two different particles is used to elucidate relativistic aspects of electromagnetic form factors. The model form factor is computed using an exact covariant calculation of the lowest-order triangle diagram and shown to be the same as that obtained using light-front techniques. The meaning of transverse density is explained using coordinate space variables, allowing us to identify a true mean-square transverse size directly related to the form factor. We show that the rest-frame charge distribution is generally not observable because of the failure to uphold current conservation. Neutral systems of two charged constituents are shown to obey the lore that the heavier one is generally closer to the transverse origin than the lighter one. It is argued that the negative central charge density of the neutron arises, in pion-cloud models, from pions of high longitudinal momentum. The non-relativistic limit is defined precisely and the ratio of the binding energy to that of the mass of the lightest constituent is shown to govern the influence of relativistic effects. The exact relativistic formula for the form factor reduces to the familiar one of the three-dimensional Fourier transform of a square of a wave function for a very limited range of parameters. For masses that mimic the quark-di-quark model of the nucleon we find substantial relativistic corrections for any value of $Q^2$. A schematic model of the lowest s-states of nuclei is used to find that relativistic effects decrease the form factor for light nuclei but increase the form factor for heavy nuclei. Furthermore, these states are strongly influenced by relativity.Comment: 18 pages, 11 figure

Hadron Spin Dynamics

Spin effects in exclusive and inclusive reactions provide an essential new dimension for testing QCD and unraveling hadron structure. Remarkable new experiments from SLAC, HERMES (DESY), and the Jefferson Laboratory present many challenges to theory, including measurements at HERMES and SMC of the single spin asymmetries in pion electroproduction, where the proton is polarized normal to the scattering plane. This type of single spin asymmetry may be due to the effects of rescattering of the outgoing quark on the spectators of the target proton, an effect usually neglected in conventional QCD analyses. Many aspects of spin, such as single-spin asymmetries and baryon magnetic moments are sensitive to the dynamics of hadrons at the amplitude level, rather than probability distributions. I illustrate the novel features of spin dynamics for relativistic systems by examining the explicit form of the light-front wavefunctions for the two-particle Fock state of the electron in QED, thus connecting the Schwinger anomalous magnetic moment to the spin and orbital momentum carried by its Fock state constituents and providing a transparent basis for understanding the structure of relativistic composite systems and their matrix elements in hadronic physics. I also present a survey of outstanding spin puzzles in QCD, particularly the double transverse spin asymmetry A_{NN} in elastic proton-proton scattering, the J/psi to rho-pi puzzle, and J/psi polarization at the Tevatron.Comment: Concluding theory talk presented at SPIN2001, the Third Circum-Pan-Pacific Symposium on High Energy Physics, October, 2001, Beijin

Pretzelosity h1T⊥h_{1T}^{\perp} and quark orbital angular momentum

We calculate the pretzelosity distribution ($h_{1T}^{\perp}$), which is one of the eight leading twist transverse momentum dependent parton distributions (TMDs), in the light-cone formalism. We find that this quantity has a simple relation with the quark orbital angular momentum distribution, thus it may provide a new possibility to access the quark orbital angular momentum inside the nucleon. The pretzelosity distribution can manifest itself through the $\sin(3\phi_h-\phi_S)$ asymmetry in semi-inclusive deep inelastic scattering process. We calculate the $\sin(3\phi_h-\phi_S)$ asymmetry at HERMES, COMPASS and JLab kinematics, and present our prediction on different targets including the proton, deuteron and neutron targets. Inclusion of transverse momentum cut in data analysis could significantly enhance the $\sin(3\phi_h-\phi_S)$ asymmetry for future measurements.Comment: 20 latex pages, 7 figures, to appear in PR

Application of the Principle of Maximum Conformality to Top-Pair Production

A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale $\mu_r$. For example, by using the conventional way of setting $\mu_r \in [m_t/2,2m_t]$, one obtains the total $t \bar{t}$ production cross-section $\sigma_{t \bar{t}}$ with the uncertainty \Delta \sigma_{t \bar{t}}/\sigma_{t \bar{t}}\sim ({}^{+3%}_{-4%}) at the Tevatron and LHC even for the present NNLO level. The Principle of Maximum Conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. In this paper we apply PMC scale-setting to predict the $t \bar t$ cross-section $\sigma_{t\bar{t}}$ at the Tevatron and LHC colliders. It is found that $\sigma_{t\bar{t}}$ remains almost unchanged by varying $\mu^{\rm init}_r$ within the region of $[m_t/4,4m_t]$. The convergence of the expansion series is greatly improved. For the $(q\bar{q})$-channel, which is dominant at the Tevatron, its NLO PMC scale is much smaller than the top-quark mass in the small $x$-region, and thus its NLO cross-section is increased by about a factor of two. In the case of the $(gg)$-channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy $\sqrt{s}$, but it is still smaller than $m_t$ for $\sqrt{s}\lesssim 1$ TeV, and the resulting NLO cross-section is increased by $\sim 20$. As a result, a larger $\sigma_{t\bar{t}}$ is obtained in comparison to the conventional scale-setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting $m_t=172.9\pm 1.1$ GeV, we predict $\sigma_{\rm Tevatron,\;1.96\,TeV} = 7.626^{+0.265}_{-0.257}$ pb, $\sigma_{\rm LHC,\;7\,TeV} = 171.8^{+5.8}_{-5.6}$ pb and $\sigma_{\rm LHC,\;14\,TeV} = 941.3^{+28.4}_{-26.5}$ pb. [full abstract can be found in the paper.]Comment: 15 pages, 11 figures, 5 tables. Fig.(9) is correcte

Perturbative QCD and factorization of coherent pion photoproduction on the deuteron

We analyze the predictions of perturbative QCD for pion photoproduction on the deuteron, gamma D -> pi^0 D, at large momentum transfer using the reduced amplitude formalism. The cluster decomposition of the deuteron wave function at small binding only allows the nuclear coherent process to proceed if each nucleon absorbs an equal fraction of the overall momentum transfer. Furthermore, each nucleon must scatter while remaining close to its mass shell. Thus the nuclear photoproduction amplitude, M_{gamma D -> pi^0 D}(u,t), factorizes as a product of three factors: (1) the nucleon photoproduction amplitude, M_{gamma N_1 -> pi^0 N_1}(u/4,t/4), at half of the overall momentum transfer, (2) a nucleon form factor, F_{N_2}(t/4), at half the overall momentum transfer, and (3) the reduced deuteron form factor, f_d(t), which according to perturbative QCD, has the same monopole falloff as a meson form factor. A comparison with the recent JLAB data for gamma D -> pi^0 D of Meekins et al. [Phys. Rev. C 60, 052201 (1999)] and the available gamma p -> pi^0 p data shows good agreement between the perturbative QCD prediction and experiment over a large range of momentum transfers and center of mass angles. The reduced amplitude prediction is consistent with the constituent counting rule, p^11_T M_{gamma D -> pi^0 D} -> F(theta_cm), at large momentum transfer. This is found to be consistent with measurements for photon lab energies E_gamma > 3 GeV at theta_cm=90 degrees and \elab > 10 GeV at 136 degrees.Comment: RevTeX 3.1, 17 pages, 6 figures; v2: incorporates minor changes as version accepted by Phys Rev

Hadron Optics in Three-Dimensional Invariant Coordinate Space from Deeply Virtual Compton Scattering

The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter \zeta= Q^2/ 2 p.q can be used to provide an image of the target hadron in the boost-invariant variable \sigma, the coordinate conjugate to light-front time \tau=t+ z/ c. As an illustration, we construct a consistent covariant model of the DVCS amplitude and its associated generalized parton distributions using the quantum fluctuations of a fermion state at one loop in QED, thus providing a representation of the light-front wavefunctions of a lepton in \sigma space. A consistent model for hadronic amplitudes can then be obtained by differentiating the light-front wavefunctions with respect to the bound-state mass. The resulting DVCS helicity amplitudes are evaluated as a function of \sigma and the impact parameter \vec b_\perp, thus providing a light-front image of the target hadron in a frame-independent three-dimensional light-front coordinate space. Models for the LFWFs of hadrons in (3+1) dimensions displaying confinement at large distances and conformal symmetry at short distances have been obtained using the AdS/CFT method. We also compute the LFWFs in this model in invariant three dimensional coordinate space. We find that in the models studied, the Fourier transform of the DVCS amplitudes exhibit diffraction patterns. The results are analogous to the diffractive scattering of a wave in optics where the distribution in \sigma measures the physical size of the scattering center in a one-dimensional system.Comment: minor modification to text, preprint number update

The running coupling method with next-to-leading order accuracy and pion, kaon elm form factors

The pion and kaon electromagnetic form factors $F_M(Q^2)$ are calculated at the leading order of pQCD using the running coupling constant method. In calculations the leading and next-to-leading order terms in $\alpha_S((1-x)(1-y)Q^2)$ expansion in terms of $\alpha_S(Q^2)$ are taken into account. The resummed expression for $F_M(Q^2)$ is found. Results of numerical calculations for the pion (asymptotic distribution amplitude) are presented.Comment: 9 pages, 1 figur

The QCD Running Coupling

We review the present knowledge for $\alpha_s$, the fundamental coupling underlying the interactions of quarks and gluons in QCD. The dependence of $\alpha_s(Q^2)$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics -from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on $\alpha_s(Q^2)$ at high $Q^2$, as predicted by perturbative QCD, and its analytic behavior at small $Q^2$, based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of $\alpha_s$, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss the behavior of $\alpha_s(Q^2)$ in the high $Q^2$ domain of QCD. We review how $\alpha_s$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as Commensurate Scale Relations which connect the various definitions of $\alpha_s$ without renormalization-scale ambiguity. We also report recent measurements and theoretical analyses which have led to precise QCD predictions at high energy. In the last part of the review, we discuss the challenge of understanding the analytic behavior $\alpha_s(Q^2)$ in the infrared domain. We also review important methods for computing $\alpha_s$, including lattice QCD, the Schwinger-Dyson equations, the Gribov-Zwanziger analysis and light-front holographic QCD. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of $\alpha_s$ in order to bring better unity to the subject.Comment: Invited review article for Progress in Particle and Nuclear Physics. 195 pages, 18 figures. V3: Minor corrections and addenda compared to V1 and V2. V4: typo fixed in Eq. (3.21