We study the electroproduction of rho mesons in nuclei at intermediate energies, deriving a treatment of the energy lost by the rho in each step of multiple-scattering. This enables a close match between calculations and the experimental kinematic conditions. A standard Glauber calculation is presented, and then the effects of color-transparency are included. The influence of poor experimental resolution on the extracted transparency is assessed. The effects of $ρ$ meson decay inside the nucleus are examined, and are typically about 5 percent at most. This effect disappears rapidly as $Q^2$ increases from about 1 to 3 GeV$^2$, causing a rise in the transparency that is not attributable to color transparency. The size of color transparency effects for C and Fe nuclei is studied for values of $Q^2$ up to 10 GeV$^2$. The detailed results depend strongly on the assumed value of the $ρN$ cross section. The overall effects of color transparency are greater than about 10 % for both nuclear targets if $Q^2$ is greater than about 5 GeV$^2$.
We investigate the early onset of pionic color transparency ($π$CT) observed at Jefferson Laboratory (JLAB) in semi--exclusive pion electroproduction reaction $A(e,e'π^+)$ off nuclei. In the present description the primary $γ^*p \to π^+ n$ interaction is described very well both for the longitudinal and the transverse polarizations. For the final state interactions a coupled--channel treatment of the interactions of transmitted hadrons allows to go beyond the Glauber approximation. We show that a proper distinction between the soft hadronic and hard partonic components of the electroproduction…
A Pomeron-exchange model of exclusive electroproduction of $ρ$-mesons is examined using a dressed-quark propagator. It is shown that by representing the photon-$ρ$-meson-Pomeron coupling by a nonperturbative, confined-quark loop, one obtains predictions for $ρ$-meson electroproduction that are in good agreement with experiment.
A relativistic and quantum mechanical framework to compute nuclear transparencies for pion photo- and electroproduction reactions is presented. Final-state interactions for the ejected pions and nucleons are implemented in a relativistic eikonal approach. At sufficiently large ejectile energies, a relativistic Glauber model can be adopted. At lower energies, the framework possesses the flexibility to use relativistic optical potentials. The proposed model can account for the color-transparency (CT) phenomenon and short-range correlations (SRC) in the nucleus. Results are presented for kinemati…
In the present paper we investigate incoherent rho^0 electroproduction off complex nuclei. We derive a novel, simple expression for the incoherent electroproduction cross section in which one can clearly separate the final state interactions of the reaction products from the 'initial state interactions' of the photon that give rise to nuclear shadowing. In the special case of purely absorptive final state interactions we deduce from our expression the known Glauber result. A more realistic treatment of the final state interactions within a transport model is then used to compare our prediction…
We determine the magnetic dipole moment of the rho meson using preliminary data from the BaBar Collaboration for the $e^+ e^- \to π^+ π^- 2 π^0$ process, in the center of mass energy range from 0.9 to 2.2 GeV. We describe the $γ^* \to 4π$ vertex using a vector meson dominance model, including the intermediate resonance contributions relevant at these energies. We find that $μ_ρ= 2.1 \pm 0.5$ in $e/2 m_ρ$ units.
A multichannel evolution equation is developed for the density matrix describing a hadronic wave packet produced by a virtual photon and propagation through a nuclear matter. This approach is dual to the quark-gluon representation, incorporates the effects of coherence and formation times and gives an exact solution for color transparency problem at any photon energy. We propose a procedure of data analysis, which provides an unambiguous way of detection of a color transparency signal even at medium energies.
So far no theoretical tool for the comprehensive description of exclusive electroproduction of vector mesons off nuclei at medium energies has been developed. We suggest a light-cone QCD formalism which is valid at any energy and incorporates formation effects (color transparency), the coherence length and the gluon shadowing. At medium energies color transparency (CT) and the onset of coherence length (CL) effects are not easily separated. Indeed, although nuclear transparency measured by the HERMES experiment rises with Q^2, it agrees with predictions of the vector dominance model (VDM) with…
We review the perturbative QCD formalism of hadronic electromagnetic form factors and the color transparency ratio for quasi-exclusive electroproduction of the proton and pion from nuclear targets. We have completed the first full calculations including all leading order quark subprocesses and integrations over distribution amplitudes, including Sudakov effects. For the case of the proton, the calculated result shows scaling beyond $Q^2=10$ GeV$^2$. The calculation incorporating filtering due to the nuclear medium is cleaner than the corresponding calculation in free space because of attenuati…
By introducing electromagnetic formfactors in the spacelike region we extend an effective, gauge invariant Lagrangian model considering Born terms, baryon resonances up to 1.7 GeV and vector meson contributions (Rho, Omega) to calculate electroproduction of Pi-mesons. This model forms the basis for predictions of pion induced dilepton production on the nucleon. Therefore, the implemented formfactors are constructed in such a way that their analytic continuation into the timelike region is possible. It is shown that the seagull term and the N*(1520) resonance play a dominant role in the dilepto…
Non-universality of color transparency onset in pion and kaon electroproduction
Center for Exotic Nuclear Studies, Institute for Basic Science（基础科学研究所奇异核研究中心）；Research Institute of Basic Science, Korea Aerospace University（韩国航空大学基础科学研究所）；Department of Physics and Engineering Physics, Yonsei University（延世大学物理与工程物理系）
The exclusive and inclusive electroproduction off the polarized deuteron is considered at large $Q^2$ and $x \ge 0.5$. It is shown that the use of a polarized target will allow to emphasize smaller than average internucleon distances in the deuteron. As a result, we expect amplification of all the effects (color transparency, relativistic dynamics, etc.) sensitive to small internucleon distances. Numerical estimates are given for the processes $e+ \vec d \rightarrow e +p+n$ and $e+ \vec d \rightarrow e +X$.
We calculate quasi-exclusive scattering of a virtual photon and a proton or pion in nuclear targets. This is the first complete calculation of ``color transparency" and "nuclear filtering " in perturbative QCD. The calculation includes full integrations over hard interaction kernels and distribution amplitudes in Feynman -x fractions and transverse spatial separation space $b$. Sudakov effects depending on $b$ and the momentum transfer $Q^2$ are included. Attenuation of the hadronic states propagating through the medium is calculated using an eikonal Glauber formalism. Nuclear correlations are…
Electroproduction of two mesons well separated in rapidity allows the first feasible selective access to chiral-odd transversity GPDs provided one of these mesons is a transversely polarized vector meson rho_T.
We present our results for the exclusive electroproduction of pions off nucleons and nuclei at high values of $Q^2$. In electroproduction of nuclei $A(e,e'π)$ we consider the Color Transparency (CT) effect recently observed at JLAB. It is shown that the description of $π$ production off nucleons is mandatory for the proof of the CT signal at JLAB. We further develop the models for exclusive production of $π$ off nucleons at JLAB and HERMES. At first we describe a model based on exclusive-inclusive connection. In the second approach we combine a Regge pole approach with the residual effect of n…
A Dyson-Schwinger-based model of pomeron exchange is employed to calculate diffractive rho-, phi- and J/psi-meson electroproduction cross sections. It is shown that the magnitude of the current-quark mass m_f of the quark and antiquark inside the produced vector meson determines the onset of the asymptotic-q^2 power-law behavior of the cross section, and how correlated quark-exchanges are included to provide a complete picture of the diffractive electroproduction of light vector mesons applicable over all energies and photon momenta q^2.
We investigate coherence length effects and hadron attenuation in lepton scattering off nuclei in the kinematic regime of the HERMES experiment. The elementary electron-nucleon interaction is described within the event generator PYTHIA while a full coupled-channel treatment of the final state interactions is included by means of a BUU transport model. The results of our calculations are in good agreement with the experimentally measured transparency ratio of incoherent rho0 electroproduction off Nitrogen and the multiplicity ratio R_M^h for charged hadrons, pions, kaons, protons and anti-proto…
We study the nuclear transparency $T$ for the exclusive reaction $γ^*+A\toρ+p+(A-1)^*$ at incident virtual photon energies $ν\ge$ 10 GeV %where the final state of the $A-1$-nucleon system is a one-hole state of the initial nucleus, to investigate the separate dependence on the photon virtuality, $Q^2$ and the 4-momentum-transfer-squared to the knocked-out proton, $t$. If the effects of color transparency are included, $T$ shows significant variation with $t$ even for small values of $Q^2$ for fixed values of the coherence length $l_c$, and also shows significant increase as $Q^2$ is increased …
We use a semi-classical approximation to investigate the effects of color transparency on pion electroproduction reactions. The resulting reduced nuclear interactions produce significant, but not dominating, differences with the results of conventional distorted-wave, Glauber-type treatments at kinematics accessible to Jefferson Laboratory. Nuclear effects that could mimic the influence of color transparency are also discussed.
This dissertation explores two main topics: 1) Color Transparency and quasi-elastic knockout reactions involving pions and $ρ$ mesons; and 2) determination of the $J/ψ$-nucleon scattering amplitude and scattering length via $J/ψ$ electroproduction on the deuteron. It is shown that at the energies available at the COMPASS experiment at CERN, Color Transparency should be detectable in the reaction $π+A\to π+p+(A-1)^*$ (proton knockout). It is also shown that Color Transparency should be detectable in the electroproduction reaction $γ^*+A\toρ+p+(A-1)^*$ at small $Q^2$ (where $Q^2$ is the virtuali…
Interference between vector mesons electroproduced at different longitudinal coordinates leads within Glauber approximation to a $Q^2$-dependence of nuclear effects similar to what is expected to be an onset of color transparency (CT). We suggest such a mapping of the photon energies and virtualities, which eliminates the undesirable $Q^2$-variation and allows to measure a net CT effect. We develop a multichannel evolution equation, which for the first time incorporates CT and the effects of the coherence length in the exclusive electroproduction of vector mesons.
[Background] The recent Jefferson Lab data for the nuclear transparency in $ρ^ {0}$ electroproduction have the potential to settle the scale for the onset of color transparency (CT) in vector meson production. [Purpose] To compare the data to calculations in a relativistic and quantum-mechanical Glauber model and to investigate whether they are in accordance with results including color transparency given that the computation of $ρ$-nucleus attenuations is subject to some uncertainties. [Method] We compute the nuclear transparencies in a multiple-scattering Glauber model and account for effect…
Coherent electroproduction of vector mesons off $^2$H and $^4$He is considered in the kinematics of deep inelastic scattering. Special emphasis is given to the $-t\sim 0.8-1$ GeV$^2$ region where the cross section is dominated by the interaction of the $q\bar q$ configuration in the $γ^*$ with two nucleons. These kinematics provide the unique possibilities to study quantitatively in vector meson production the onset of Color Transparency with increasing $Q^2$ as well as its gradual disappearance at very small $x$, i.e., perturbative Color Opacity.
We study selected meson transition processes and associated form factors within a model of QCD based on the Dyson--Schwinger equations truncated to ladder-rainbow level. The infrared structure of the ladder-rainbow kernel is described by two parameters; the ultraviolet behavior is fixed by the one-loop renormalization group behavior of QCD. The work is restricted to the u and d quark sector and allows a Poincare'-covariant study of the radiative decays: rho -> pi + gamma, omega -> pi + gamma, and pi^0 -> gamma + gamma. Particular attention is paid to the form factors for the associated transit…
We extend our recent study of dilepton invariant-mass spectra from the decays of rho mesons produced by photon reactions off nuclei. We specifically focus on experimental spectra as recently measured by the CLAS Collaboration at the Thomas Jefferson National Accelerator Facility using carbon and iron nuclei. Building on our earlier work we broaden our description to a larger set of observables in order to identify sensitivities to the medium effects predicted by microscopic calculations of the rho spectral function. We compute mass spectra for several target nuclei and study the spectral shape…
We investigate meson electroproduction off complex nuclei in the kinematic regime of the HERMES experiment using a semi-classical transport model which is based on the Boltzmann-Uehling-Uhlenbeck (BUU) equation. We discuss coherence length and color transparency effects in exclusive rho^0 production as well as hadron formation and attenuation of charged pions, kaons, protons and anti-protons in deep inelastic lepton scattering off nuclei.
We present a new method to account for coherence length effects in a semi-classical transport model. This allows us to describe photo- and electroproduction at large nuclei (A>12) and high energies using a realistic coupled channel description of the final state interactions that goes beyond simple Glauber theory. We show that the purely absorptive treatment of the final state interactions can lead to wrong estimates of color transparency and formation time effects in particle production. As an example, we discuss exclusive rho^0 photoproduction on Pb at a photon energy of 7 GeV as well as K^+…
The color transparency (CT) of a hadron, propagating with reduced absorption in a nucleus, is a fundamental property of QCD (quantum chromodynamics) reflecting its internal structure and effective size when it is produced at high transverse momentum, $Q$. CT has been confirmed in many experiments, such as semi-exclusive hard electroproduction, $e A \to e' πX$ for mesons produced at $Q^2 > 3 ~ {\rm GeV}^2$. However, a recent JLab (Jefferson Laboratory) measurement for a proton electroproduced in carbon $e\, {\rm C}\to e' p X$, where $X$ stands for the inclusive sum of all produced final states,…
We present a way to account for coherence length effects in a semi-classical transport model. This allows us to describe photo- and electroproduction at large nuclei (A>12) and high energies using a realistic coupled channel description of the final state interactions that goes far beyond simple Glauber theory. We show that the purely absorptive treatment of the final state interactions as usually done in simple Glauber theory might lead to wrong estimates of color transparency and formation time effects in particle production. As an example we discuss exclusive rho^0 photoproduction on Pb at …
These lecture notes illustrate the application of Dyson-Schwinger equations in QCD. The extensive body of work at zero temperature and chemical potential is represented by a selection of contemporary studies that focus on solving the Bethe-Salpeter equation, deriving an exact mass formula in QCD that describes light and heavy pseudoscalar mesons simultaneously, and the calculation of the electromagnetic pion form factor and the vector meson electroproduction cross sections. These applications emphasise the qualitative importance of the momentum-dependent dressing of elementary Schwinger functi…
