Vector Dominance Model Research Articles

Electric conductivity of hot and dense nuclear matter

Transport coefficients play an important role in characterising hot and dense nuclear matter, such as that created in ultra-relativistic heavy-ion collisions (URHIC). In the present work we calculate the electric conductivity of hot and dense hadronic matter by extracting it from the electromagnetic spectral function, through its zero energy limit at vanishing 3-momentum. We utilise the vector dominance model (VDM), in which the photon couples to hadronic currents predominantly through the ρ meson. Therefore, we use hadronic many-body theory to calculate the ρ-meson's self-energy in hot and dense hadronic matter, by dressing its pion cloud with π-ρ, π-σ, π-K, N-hole, and Δ-hole loops. We then introduce vertex corrections to maintain gauge invariance. Finally, we analyze the low-energy transport peak as a function of temperature and baryon chemical potential, and extract the conductivity along a proposed phase transition line.

Revealing the inner structure of the newly observed η 1(1855) via photoproduction

Very recently, a new hadronic exotic state η 1(1855) at the invariant mass spectrum of was observed by the BESIII Collaboration. According to its properties, such as the mass and decay width, the η 1(1855) have been suggested to be a compact multi-quark state, a hadron molecule, or a hybrid meson. In order to distinguish the various interpretations of the η 1(1855), a Reggeized model combined with the vector dominance model for η 1(1855) photoproduction on the proton target is presented. The η 1(1855) photoproduction is dominated by the t-channel vector mesons ρ, ω, and ϕ exchange. If the η 1(1855) is a hybrid meson, the Primakoff effect also should be included. Our calculations show that the total cross section of the η 1(1855) production via γ p reaction can reach up to 0.276 pb for θ = 15° or 0.119 pb for θ = 0°, about 0.0297% or 0.0128% of the total cross section obtained by considering the η 1(1855) as an S-wave molecule. We also find their line shapes are sizably different. If the η 1(1855) is a molecular state, the photoproduction of η 1(1855) near the threshold offers a nice place to test its molecular nature. However, it should be better to take high energy, at least above E γ = 16.97 GeV, to observe the production of η 1(1855) if η 1(1855) is a hybrid meson. These results can be measured in the GlueX experiment or electron-ion collider in China to test the nature of the η 1(1855).

Electric conductivity of hot pion matter

The determination of transport coefficients plays a central role in characterizing hot and dense nuclear matter. Currently, there are significant discrepancies between various calculations of the electric conductivity of hot hadronic matter. In the present work we calculate the electric conductivity of hot pion matter by extracting it from the electromagnetic spectral function, via its zero energy limit at vanishing 3-momentum, within the Vector Dominance Model (VDM). Since within the VDM the photon couples to the hadronic currents primarily through the ρ meson, we use hadronic many-body theory to calculate the ρ-meson's self-energy in hot pion matter, by dressing its pion cloud with thermal π-ρ and π-σ loops including vertex corrections to maintain gauge invariance. In particular, we analyze the low-energy transport peak of the spectral function, extract its behavior with temperature and compare to (the results of) existing approaches in the literature.

Properties of doubly heavy baryons in QCD

The study of the properties of doubly heavy baryons represents a promising area in particle physics. It can provide us with information about Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and the low energy dynamics of QCD. They have a very rich phenomenology. The investigation of weak, electromagnetic, and strong decays has a vital importance for understanding the dynamics of doubly heavy baryons. The main ingredients of such studies are the spectroscopic parameters, the strong coupling constants, and the transition form factors. For calculations of these quantities, non-perturbative methods are needed. One of these methods is the QCD sum rules. In the present work, we review our studies on the properties of the doubly heavy baryons within the sum rules method, focusing mainly on the mass and strong coupling constants of the doubly heavy baryons. In addition, the radiative decays of doubly heavy baryons are estimated using the vector dominance model. We also make few remarks on the semileptonic decays of the doubly heavy baryons

Contribution of the ρ meson and quark substructure to the nuclear spin-orbit potential

The microscopic origin of the spin-orbit (SO) potential in terms of sub-baryonic degrees of freedom is explored and discussed for application to nuclei and hyper-nuclei. We thus develop a chiral relativistic approach where the coupling to the scalar- and vector-meson fields are controlled by the quark substructure. This approach suggests that the isoscalar and isovector density dependence of the SO potential can be used to test the microscopic ingredients which are implemented in the relativistic framework: the quark substructure of the nucleon in its ground-state and its coupling to the rich meson sector where the $\rho$ meson plays a crucial role. This is also in line with the Vector Dominance Model (VDM) phenomenology and the known magnetic properties of the nucleons. We explore predictions based on Hartree and Hartree-Fock mean field, as well as various scenarios for the $\rho$-nucleon coupling, ranked as weak, medium and strong, which impacts the isoscalar and isovector density dependence of the SO potential. We show that a medium to strong $\rho$ coupling is essential to reproduce Skyrme phenomenology in $N=Z$ nuclei as well as its isovector dependence. Assuming an SU(6) valence quark model our approach is extended to hyperons and furnishes a microscopic understanding of the quenching of the $N\Lambda$ spin-orbit potential in hyper-nuclei. It is also applied to other hyperons, such as $\Sigma$, $\Xi$ and $\Omega$.

Studying time-like electromagnetic baryonic transitions with HADES in pion induced reactions

A dedicated programme aiming at studying electromagnetic baryonic transitions in the time-like region has started at GSI using the pion beam and the High Acceptance Di-Electron Spectrometer (HADES) set-up. A pioneering experiment has been carried out in the second resonance region, at a center-of-mass energy of 1.49 GeV, using carbon and polyethylene targets, allowing for an analysis of the inclusivee+e-production and of the exclusive quasi-freeπ-p→ne+e-reaction, in complement to hadronic channels. Predictions for the Dalitz decay of N(1520) and N(1535) based on real photon couplings strongly underestimate thee+e-yield at invariant masses larger than 300 MeV/c2, which signals effects of time-like baryon transition form factors, in qualitative agreement with the Vector Dominance Models (VDM). A quantitative description of the observede+e-yield is achieved by taking into account the contribution from off-shellρs. The latter was provided by the preliminary results of a Bonn-Gatchina Partial Wave Analysis of the two-pion production channels, which were measured simultaneously in our experiment. A good agreement is also obtained using a covariant model for the time-like electromagnetic form factors for the N-N(1520) transition. The angular distributions for thee+e-production contain additional selective information on the spin structure of the different transitions. The measurements with the pion beam will be extended in future in the third resonance region. Hyperon Dalitz decay studies in proton induced reactions are also foreseen.

Hadronic properties of the photon

Currently it is no doubt that high energy photons (real or virtual) have a hadronic component leading to photon shadowing in its interaction with nuclei. We shortly consider the difficulties appeared in the models like vector dominance model (VDM) and stress that these problems can be solved in a color dipole model inspired by Quantum Chromodynamics (QCD). From the other hand, the color dipole model allows one to investigate the impact of vector meson polarization on their interaction with nucleons and nuclei, the challenge which is crucial for studying, for instance, such a fundamental effect as color transparency.

Studying Time-Like Electromagnetic Baryon Transitions with HADES in $$\pi \hbox {N}$$ π N Reactions

A dedicated program to study electromagnetic baryonic transitions in the time-like region has started using the pion beam and the High Acceptance Di-Electron Spectrometer set-up at GSI. Combined measurements of hadronic and dielectron final states have been performed for the first time in \(\pi \)-N reactions, using polyethylene and carbon targets. Differential cross sections of the exclusive channels with two pions in the final state (\(\pi ^-\pi ^+ n\), \(\pi ^0\pi ^- p\)) were obtained in the second resonance region with an unprecedented statistics. These new data were included in the partial wave analysis of the Bonn–Gatchina group together with the world data from pion and photon beam facilities. The obtained solution provides the excitation function of the two-pion production in photo- and pion- induced reactions around the pole of the D\(_{13}\) resonance N(1520) and of its decomposition into the different resonant, non-resonant and \(\rho \) contributions. Moreover, the exclusive \(ne^+e^-\) production gives insight into time-like electromagnetic structure of baryons using both \(e^+e^-\) invariant masses and angular distributions as most sensitive observables for model comparison. In addition, the extraction of the \(\rho \) contribution in the two-pion production channels can be used to investigate the validity of the Vector Dominance Model for electromagnetic baryon transitions. The prospects for future experiments in the third resonance region is also discussed.

Time-Like Baryon Transitions in Hadroproduction

The Dalitz decay of baryonic resonances (B $$\rightarrow $$ N $$e^+e^-$$ ) gives access to the time-like electromagnetic structure of baryonic transitions at small positive values of the squared four momentum transferred. Such processes were investigated by the HADES collaboration in elementary hadronic interactions. The Dalitz decay branching ratio of the $$\varDelta (1232)$$ resonance has been measured for the first time in pp reactions at 1.25 GeV beam energy. At higher energies, the $$e^+e^-$$ emission from baryonic decays is shown to be sensitive to transition form factors of the Vector Dominance Model type. Using a pion beam, Dalitz decays of baryonic resonances can be measured more directly. In addition, the simultaneous measurement of hadronic channels provides a new data base for baryon spectroscopy issues. Preliminary results of a test experiment in the N(1520) region are shown, together with prospects for higher resonance studies. A project of measuring hyperon Dalitz decays at GSI and later on at FAIR is also discussed. The study of Dalitz decays of baryon resonances and, in particular, the role of the $$\rho $$ meson brings useful constraints for the study of medium effects also investigated by the HADES collaboration in reactions with nuclei.

Search for sterile neutrinos decaying into pions at the LHC

We study the possibility to observe sterile neutrinos with masses in the range between 5 GeV and 20 GeV at the LHC, using the exclusive semileptonic modes involving pions, namely W to lepton + N to n pions + lepton+lepton (n = 1, 2, 3). The two pion and three pion modes require extrapolations of form factors to large time-like $q^2$, which we do using vector dominance models as well as light front holographic QCD, with remarkable agreement. This mass region is difficult to explore with inclusive dilepton+dijet modes or trilepton modes and impossible to explore in rare meson decays. While particle identification is a real challenge in these modes, vertex displacement due to the long living neutrino in the above mass range can greatly help reduce backgrounds. Assuming a sample of $10^9$ W bosons at the end of the LHC Run 2, these modes could discover a sterile neutrino in the above mass range or improve the current bounds on the heavy-to-light lepton mixings by an order of magnitude, $U_{l N}^2 \sim 2 \times 10^{-6}$. Moreover, by studying the equal sign and opposite sign dileptons, the Majorana or Dirac character of the sterile neutrino may be revealed.

Differential distributions in rare four-leptonic B-decays.

The branching ratios and differential distributions for the fourleptonic decays B- → μ+μ- νe e-, B- → e+e- νμ μ- and B- → μ+ νμ μ-μ- are calculated within the Standard Model. The contributions of the virtual photon emission from the b- and u- quarks and the bremsstrahlung contribution were taken into account. The resonances contributions were calculated using the vector dominance model. In this paper we present the differential distributions for the B- → μ+μ- νe e- decay obtained by two methods. Testing the lepton universality in rare multileptonic decays of charged and neutral B mesons are discussed.

Analytic pion form factor

The pion electromagnetic form factor and two-pion production in electron-positron collisions are simultaneously fitted by a vector dominance model evolving to perturbative QCD at large momentum transfer. This model was previously successful in simultaneously fitting the nucleon electromagnetic form factors (spacelike region) and the electromagnetic production of nucleon-antinucleon pairs (timelike region). For this pion case dispersion relations are used to produce the analytic connection of the spacelike and timelike regions. The fit to all the data is good, especially for the newer sets of time-like data. The description of high-$q^2$ data, in the time-like region, requires one more meson with $\rho$ quantum numbers than listed in the 2014 Particle Data Group review.

Phi meson spectral moments and QCD condensates in nuclear matter

A detailed analysis of the lowest two moments of the ϕ meson spectral function in vacuum and nuclear matter is performed. The consistency is examined between the constraints derived from finite energy QCD sum rules and the spectra computed within an improved vector dominance model, incorporating the coupling of kaonic degrees of freedom with the bare ϕ meson. In the vacuum, recent accurate measurements of the e+e−→K+K− cross section allow us to determine the spectral function with high precision. In nuclear matter, the modification of the spectral function can be described by the interactions of the kaons from ϕ→KK‾ with the surrounding nuclear medium. This leads primarily to a strong broadening and an asymmetric deformation of the ϕ meson peak structure. We confirm that, both in vacuum and nuclear matter, the zeroth and first moments of the corresponding spectral functions satisfy the requirements of the finite energy sum rules to a remarkable degree of accuracy. Limits on the strangeness sigma term of the nucleon are examined in this context. Applying our results to the second moment of the spectrum, we furthermore discuss constraints on four-quark condensates and the validity of the commonly used ground state saturation approximation.

Pion-induced production of theZc(3900)off a nuclear target

We investigate the possibility to study the charmoniumlike state ${Z}_{c}(3900)$ through the pion-induced production off a nuclear target. By using a high-energy pion beam, the ${Z}_{c}(3900)$ can be produced off a proton or nucleus though the Primakoff effect. The production amplitude is calculated in an effective Lagrangian approach combined with the vector dominance model. The total cross sections of the $p({\ensuremath{\pi}}^{\ensuremath{-}},{Z}_{c}^{\ensuremath{-}}(3900))$ and $p({\ensuremath{\pi}}^{\ensuremath{-}},{Z}_{c}^{\ensuremath{-}}(3900)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{\ensuremath{-}})$ reactions are calculated, and their order of magnitude is about 0.1 and 0.01 nb, respectively, with an assumption of branch ratio 10% for the ${Z}_{c}(3900)$ decay in $J/\ensuremath{\psi}\ensuremath{\pi}$ channel. If the proton target is replaced by a nuclear target, the production of the ${Z}_{c}(3900)$ enhances obviously. The predicted total cross sections for the $A({\ensuremath{\pi}}^{\ensuremath{-}},{Z}_{c}^{\ensuremath{-}}(3900))$ and $A({\ensuremath{\pi}}^{\ensuremath{-}},{Z}_{c}^{\ensuremath{-}}(3900)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{\ensuremath{-}})$ reactions with $A=^{12}\mathrm{C}$ or $^{208}\mathrm{Pb}$ are on the order of magnitude of 100 and 10 nb, respectively, which is about one thousand times larger than the cross sections off a proton target. Based on these results, we suggest the experimental study of the ${Z}_{c}(3900)$ by using high-energy pion beams with a nuclear target at facilities such as COMPASS and J-PARC.

Radiative $$\Omega _{Q}^{*}\rightarrow \Omega _{Q}\gamma $$ Ω Q ∗ → Ω Q γ and $$\Xi _{Q}^{*}\rightarrow \Xi ^{\prime }_{Q}\gamma $$ Ξ Q ∗ → Ξ Q ′ γ transitions in light cone QCD

We calculate the magnetic dipole and electric quadrupole moments associated with the radiative $$\Omega _{Q}^{*}\rightarrow \Omega _{Q}\gamma $$ and $$\Xi _{Q}^{*}\rightarrow \Xi ^{\prime }_{Q}\gamma $$ transitions with $$Q=b$$ or $$c$$ in the framework of light cone QCD sum rules. It is found that the corresponding quadrupole moments are negligibly small, while the magnetic dipole moments are considerably large. A comparison of the results of the considered multipole moments as well as corresponding decay widths with the predictions of the vector dominance model is performed.

Relations between the QCD sum rules for BBV couplings and vector-dominance model

Story of QCD sum rules is briefly reviewed. The dispersion superconvergence sum rule is shown to relate πN coupling constant with the 33-resonance width without unitary symmetry arguments. The QCD sum rules instead reveal the unitary symmetry pattern as all the correlation functions can be reduced to 2 ones repeating the F and D couplings for the octet baryons 1/2+. Strong relations between the correlators are established. Vector dominance hypothesis allows to put new restrictions to the QCD sum rules for VBB couplings.

τ− → π−π0ντ decay in the extended NJL model

The width of the decay $\tau^{-} \to \pi^{-} \pi^{0} \nu_\tau$ was calculated in the extended NJL model. Contact interaction of $W$ boson with pion pair as well as the contribution of the $\rho$ mesons in ground and first radial-exited states are taken into account. The sum of the contact diagram and diagram with intermediate $\rho$ meson in the ground state leads to the result which coincides with the result of the vector-dominance model. Our results are in satisfactory agreement with experimental data.

EXCLUSIVE PRODUCTION OF ρ0ρ0 PAIRS IN ULTRARELATIVISTIC HEAVY ION COLLISIONS

We disuss exclusive electromagnetic production of two neutral ρ0 mesons and show the predictions for the AA → AAρ0ρ0 reactions for gold-gold collisions at the energy of [Formula: see text] and for lead-lead collisions at the energy of [Formula: see text]. The elementary cross section is calculated with the help of the vector-dominance-model (VDM)-Regge approach which usually very well describes the experimental data at large γγ energy. The low-energy γγ → ρ0ρ0 cross section is parametrized. The cross section for nuclear process is calculated by means of the equivalent photon approximation (EPA). We compare the results with realistic charge density with the results for monopole form factor.

Role of mesons in the electromagnetic form factors of the nucleon

The roles played by mesons in the electromagnetic form factors of the nucleon are explored using as a basis a model containing vector mesons with coupling to the continuum together with the asymptotic Q2 behavior of perturbative QCD. Specifically, the vector dominance model (GKex) developed by E. L. Lomon is employed, as it is known to be very successful in representing the existing high-quality data published to date. An analysis is made of the experimental uncertainties present when the differences between the GKex model and the data are expanded in orthonormal basis functions. A main motivation for the present study is to provide insight into how the various ingredients in this model yield the measured behavior, including discussions of when dipole form factors are to be expected or not, of which mesons are the major contributors, for instance, at low Q2 or large distances, and of what effects are predicted from coupling to the continuum. Such insights are first discussed in momentum space, followed by an analysis of how different and potentially useful information emerges when both the experimental and theoretical electric form factors are Fourier transformed to coordinate space. While these Fourier transforms should not be interpreted as “charge distributions,” nevertheless the roles played by the various mesons, especially those which are dominant at large or small distance scales, can be explored via such experiment–theory comparisons.15 MoreReceived 29 January 2010DOI:https://doi.org/10.1103/PhysRevC.82.045211©2010 American Physical Society

Study of the process e+e− → π+π−π0π0 at energies √s < 1 GeV

In an experiment with the Spherical Neutral Detector at VEPP-2M collider the cross section of the process e+e− → π+π−π0π0 was measured. At energies √s < 920 MeV this cross section was measured for the first time. The energy dependence of the cross section is well discribed by the vector dominance model with contributions from ρ, ρ′, ρ′′ mesons. The decay probability ρ → π +π−π0π0 was found to be Bρ = (1.60±0.74±0.18) × 10−5. The upper limit for the decay ω → π+π−π0π0 was improved by two orders of magnitude compared to the previous measurements and is Bω < 2 × 10−4 at 90% confidence level.