We include effects of chiral symmetry and its restoration in the kinetic equations for baryon propagation and explore the consequences for $η$, $π^0$, $ρ$ and dilepton production in heavy-ion collisions at 1-2A GeV. Numerical calculations are performed using the GiBUU microscopic transport model supplemented by the parity-doublet model for the mean fields of the nucleon and the $N^*(1535)$ resonance. In this chiral model, a strong dropping of the Dirac mass of the $N^*(1535)$ in the high-density stage of a collision leads to a considerable enhancement in the production of this resonance as compared to the standard (non-linear) Walecka model. As the system expands, the Dirac masses of these abundant soft $N^*(1535)$ resonances gradually increase and ultimately cross the $N η$ decay threshold. As a result, an enhanced low-energy $η$ production is observed in the calculations with chiral mean fields. Comparing with TAPS data on $η$ and $π^0$ production we find that the chiral model improves the agreement for the $m_t$-spectra of $η$'s at small $m_t$ in heavy colliding systems. A similar enhancement is also observed in the soft $ρ$ production due to chiral symmetry and its partial restoration. The resulting dilepton yields at low and intermediate invariant masses are slightly enhanced due to these chiral effects which further improve the agreement between GiBUU transport simulations and HADES data for C+C at 1A GeV.
We review recent theoretical progress in low-mass dilepton production at CERN-SpS energies. Various hadronic approaches to calculate the vector correlator in hot/dense hadronic matter are discussed and confronted with each other. Possible consequences for the nature of chiral restoration are indicated.
Recent developments in the evaluation of vector-meson spectral functions in hot and dense matter are discussed with emphasis on connections to the chiral phase transition in QCD. Model independent approaches including chiral low-density expansions, lattice QCD, chiral and QCD sum rules are put into context with model predictions for in-medium vector-spectral function utilizing effective Lagrangians. Hadronic many-body calculations predict a strong broadening (and little mass shift) of the $ρ$ spectral function which rapidly increases close to the expected phase boundary of hadronic and quark-g…
In sqrt(sNN) = 200 GeV Au+Au collisions PHENIX reported a significant enhancement in the low-mass region (0.1 < m_ee < 0.7 GeV) of the dielectron spectrum, which is still not fully understood. Several theoretical works and an indirect measurement suggest that, due to the possible restoration of the U_A(1) part of the chiral symmetry in a hot and dense medium, the mass of the eta' meson may substantially decrease. This work reports on a statistically acceptable description of the PHENIX low-mass dilepton enhancement using a radial flow dominated meson spectra, chain decays of long-lived resonan…
Using a rather complete description of the in-medium $ρ$ spectral function - being constrained by various independent experimental information - we calculate pertinent dilepton production rates from hot and dense hadronic matter. The strong broadening of the $ρ$ resonance entails a reminiscence to perturbative $q\bar q$ annihilation rates in the vicinity of the phase boundary. The application to dilepton observables in Pb(158AGeV)+Au collisions - incorporating recent information on the hadro-chemical composition at CERN-SpS energies - essentially supports the broadening scenario. Possible impl…
We evaluate currently available information on low-mass dilepton and direct-photon emission spectra measured in ultrarelativistic heavy-ion collisions. In the first part an attempt is made to develop a consistent picture of the in-medium effects on the electromagnetic spectral function and pinpoint its emission history by utilizing its radial and elliptic flow signatures. In the second part we elaborate on the implications of the empirical information on the nature of chiral symmetry restoration. We indicate how the melting of the $ρ$ resonance in hot and dense matter is related to, and compat…
Medium modifications of the electromagnetic spectral function in hadronic and quark-gluon matter are reviewed. A strong broadening of the $ρ$ meson, which dominates the spectral function in the low-mass regime, is quantitatively consistent with dilepton excess spectra measured in photoproduction off cold nuclei (CLAS/JLab) and in fixed-target ultrarelativistic heavy-ion collisions (NA45,NA60/CERN-SPS). The large excess observed by PHENIX at RHIC remains unexplained to date, but is most likely not due to emission from the Quark-Gluon Plasma. Connections to thermal lattice QCD promise progress i…
We argue that the NICA fixed target experiment will be able to provide very important new experimental data on dilepton and $ϕ$ meson production in the basically undiscovered energy domain between the SIS and SPS energies. Experimental information about elementary cross sections in this energy region is an essential ingredient of models of nuclear collisions in the same energy range.
We summarize the status of electromagnetic probes of strongly interacting matter produced in relativistic heavy-ion collisions at CERN-SPS with respect to indications of chiral symmetry restoration. Explorative results for studying the open charm dynamics at BNL-RHIC are presented.
We study the structural change of the vector spectral function and integrated production rates of dileptons in the presence of the chiral mixing induced exclusively at finite density. The mixing produces multiple bumps and peaks around the vacuum masses of the $ρ, ω$ and $ϕ$ resonances in the spectral function. The arising modification becomes pronounced when the mass difference between parity partners decreases. In particular, the emergent enhancement around the vacuum $ϕ$ meson in the production rates serves as an excellent signature of the partially-restored chiral symmetry in heavy-ion col…
We report on recent work relating the medium effects observed in dilepton spectra in heavy-ion collisions to potential signals of chiral symmetry restoration. The key connection remains the approach to spectral function degeneracy between the vector-isovector channel with its chiral partner, the axialvector-isovector channel. Several approaches are discussed to elaborate this connection, namely QCD and Weinberg sum rules with input for chiral order parameters from lattice QCD, and chiral hadronic theory to directly evaluate the medium effects of the axialvector channel and the pertinent pion d…
The current theoretical status in the analysis and interpretation of low-mass dilepton measurements in (ultra-) relativistic heavy-ion experiments is reviewed. Special emphasis is put on potential signals of (partial) restoration of dynamically broken chiral symmetry in a hot and dense hadronic medium. It follows from chiral symmetry alone that parity partners of hadronic correlation functions must become identical when the symmetry is restored. The assessment of medium effects in the vector channel, which governs the dilepton production, thus necessitates a simultaneous treatment of the vecto…
We use the microscopic GiBUU transport model to calculate dilepton ($e^+e^-$) production in heavy-ion collisions at SIS18 energies focusing on the effect of collisional broadening of the $ρ$-meson. The collisional width of the $ρ$-meson at finite temperature and baryon density in nuclear matter is calculated on the basis of the collision integral of the GiBUU model. A systematic comparison with HADES data on dilepton production in heavy-ion collisions is performed. The collisional broadening of the $ρ$ improves the agreement between theory and experiment for the dilepton invariant-mass distrib…
A simple schematic model anchored on the notion of hadronic freedom inferred from hidden local symmetry in the vector manifestation, the infinite tower of vector mesons in holographic QCD and "stickiness" of $ππ$ interactions inferred from dispersion relations is used to describe the dileptons produced in relativistic heavy ion collisions at PHENIX/RHIC. It is shown that due to the near "blindness" of dileptons to Brown-Rho scaling, those dileptons with invariant mass less than $m_ρ=770$ MeV come mostly from pion-composites that we interpret as "transient $ρ$'s."
The invariant mass spectrum of the $e^{+}e^{-}$ and $μ^{+}μ^{-}$ pairs from decays of light unflavored mesons with masses below the $ϕ(1020)$-meson mass to final states containing along with a dilepton pair one photon, one meson, and two mesons are calculated within the framework of the effective meson theory. The results can be used for simulations of the dilepton spectra in heavy-ion collisions and for experimental searches of dilepton meson decays.
We discuss how dilepton production is related to chiral symmetry and its restoration. We then analyse presently available data by the CERES collaboration in this context. We find that the present data do not support any conclusions concerning the restoration of chiral symmetry. We finally provide a prediction for the dilepton spectrum for the just completed low energy (40 GeV) run at the SPS.
Dilepton production from hot hadronic matter is studied in an effective chiral Lagrangian with pions, $ρ$-mesons, and $a_1$ mesons, We find that the production rates from reactions that involve axial-vector mesons dominate over contributions from all other reactions when the dilepton invariant mass is above 1.5 GeV.
We study the possibility of $ρ-a_0$ mixing via N-N excitations in dense nuclear matter. This mixing is found to induce a peak in the dilepton spectra at an invariant mass equal to that of the $a_0$. We calculate the cross section for dilepton production through mixing and we compare its size with that of $π-π$ annihilation. In-medium masses and mixing angles are also calculated. Some preliminary results of the mixing effect on the dilepton production rates at finite temperature are also presented.
The HADES collaboration has extracted dilepton mass spectra for $π^-$ induced reactions on the proton from a comparison of data taken on C and CH$_2$ targets. The spectra were interpreted in terms of different versions of vector meson dominance. Here we present results obtained from the theory and generator GiBUU. We first check the subtraction procedure used and then discuss the obtained mass spectra for the proton target. We point out that any conclusions on the version of VMD requires the knowledge of the $ρ$ spectral function in the interesting mass region.
In this comment we point out several problems concerning kinematical singularities which are encountered in the calculation of the dilepton rates in {Ruppert:2004yg}. We also comment on the method introduced in {vanHees:2000bp} and further used in refs. {Riek:2004kx,Renk:2006dt,Renk:2006ax,Ruppert:2004yg}
Assuming that rho-mesons exist in a quark-gluon plasma close to the QCD phase transition, we calculate the dilepton production rate from quark-antiquark annihilation via a rho-meson state using Vector Meson Dominance. The result is compared to the rates from direct quark-antiquark annihilation and from pion annihilation. Furthermore we discuss the suppression of low mass dileptons if the quarks assume an effective mass in the quark-gluon plasma.
The effect of scalar and vector meson mixing on the dilepton radiation from hot and dense hadronic matter is estimated in different isospin channels. In particular, we study the effect of $σ$-$ω$ and $ρ-a_0$ mixing and calculate the corresponding rates. Effects are found to be significant compared to standard $π$-$π$ and $K$-${\bar K}$ annihilations. While the mixing in the isoscalar channel mostly gives a contribution in the invariant mass range between the two-pion threshold and the $ω$ peak, the isovector channel mixing induces an additional peak just below that of the $ϕ$. Experimentally, …
We give a brief survey of theoretical evaluations of light vector mesons in hadronic matter, focusing on results from hadronic many-body theory. We emphasize the importance of imposing model constraints in obtaining reliable results for the in-medium spectral densities. The latter are subsequently applied to the calculation of dilepton spectra in high-energy heavy-ion collisions, with comparisons to recent NA60 data at the CERN-SPS. We discuss aspects of space-time evolution models and the decomposition of the excess spectra into different emission sources.
An introduction to physics of in-medium hadrons with special emphasis towards modification of vector meson properties in dense nuclear matter is given. We start from remarkable analogy between the in-medium behavior of atoms in gases and hadrons in nuclear matter. Modifications of vector meson widths and masses can be registered experimentally in heavy-ion collisions by detecting dilepton spectra from decays of nucleon resonances and light unflavored mesons including $ρ$- and $ω$-mesons. Theoretical schemes for description of the in-medium hadrons are reviewed and recent experimental results o…
An overview is given of chiral symmetry restoration at finite temperature and baryochemical potential. Within hadronic models of the vector correlator its implications for low-mass dilepton spectra in ultrarelativistic heavy-ion collisions are discussed.
The properties of electromagnetic radiation from hot fireballs as created in ultra-relativistic heavy-ion collisions are reviewed. We first outline how the medium effects in the electromagnetic spectral function, which governs thermal production rates, relate to the (partial) restoration of chiral symmetry. In particular, we show how chiral and QCD sum rules, together with constraints from lattice QCD, can render these relations quantitative. Turning to dilepton data, we elaborate on updates in the space-time evolution and quark-gluon plasma emission rates from lattice-QCD calculations. With a…
We study the $p$-wave polarization operator of the $ρ$-meson due to $ρN$ interactions via the $N^*$ (1720) and $Δ(1905)$ resonances and compute the corresponding production rate for $e^+e^-$-pairs at finite temperature and baryon density. At high baryon density we find a significant shift of the spectrum to lower invariant masses.
Theoretical approaches to assess modifications of vector mesons in the medium, as well as their experimental identification via electromagnetic probes, are discussed. Implications for the nature of chiral symmetry restoration in hot/dense matter are outlined and put into context with the axialvector channel.
Dilepton production from both pion-pion and kaon-antikaon annihilation in heavy-ion collisions is studied using the relativistic transport model. The formation of a rho meson from pion-pion annihilation and a phi meson from kaon-antikaon annihilation, their propagation in the medium, and their decay into dileptons are explicitly treated. Including the medium modifications of the masses and widths of vector mesons as predicted by the QCD sum-rule calculations, we study their effects on the dilepton invariant mass spectra from heavy-ion collisions at SIS/GSI energies.
Using the transport model, we have studied dilepton production from heavy-ion collisions at Bevalac energies. It is found that the enhanced production of low-mass dileptons observed in the experiment by the DLS collaboration cannot be explained by the dropping of hadron masses, in particular the $ρ$-meson mass, in dense matter.
Dilepton production from resonance scattering in hot hadronic matter is studied. Including the widths of these resonances, which enhance the phase space for dilepton production, we find that the production rate is significantly increased if a resonance appears in the extended phase space. For the reaction $π+ρ\to l^++l^-$, the finite $ρ$ meson width extends the invariant mass below the $ω$-meson mass, so a peak at the $ω$ meson mass is seen in the dilepton spectrum. Similarly, a $ρ$-meson peak appears in the reaction $ρ+ρ\to l^++l^-$. On the other hand, the effect of particle widths in the rea…
Dilepton spectra from the decay of phi mesons produced in heavy-ion collisions at SIS/GSI energies ($\sim 2$ GeV/nucleon) are studied in the relativistic transport model. We include phi mesons produced from baryon-baryon, pion-baryon, and kaon-antikaon collisions. The cross sections for the first two processes are obtained from an one-boson-exchange model, while that for the last process is taken to be the Breit-Wigner form through the phi meson resonance. For dileptons with invariant mass near the phi meson peak, we also include contributions from neutron-proton bremsstrahlung, pion-pion anni…
The production of dielectrons in reactions involving a_1 mesons and pions is studied. We compare results obtained with different phenomenological Lagrangians that have been used in connection with hadronic matter and finite nuclei. We insist on the necessity for those interactions to satisfy known empirical properties of the strong interaction. Large off-shell effects in dielectron production are found and some consequences for the interpretation of heavy ion data are outlined. We also compare with results obtained using experimentally-extracted spectral functions.
We present a unified description of the vector meson and dilepton production in elementary and in heavy ion reactions. The production of vector mesons is described via the excitation of nucleon resonances. Medium effects in heavy ion reactions are discussed.
Utilizing in-medium vector spectral functions which describe dilepton data in ultra-relativistic heavy-ion collisions, we conduct a comprehensive evaluation of QCD and Weinberg sum rules at finite temperature. The starting point is our recent study in vacuum, where the sum rules have been quantitatively satisfied using phenomenological axial-/vector spectral functions which describe hadronic tau-decay data. In the medium, the temperature dependence of condensates and chiral order parameters is taken from thermal lattice QCD where available, and otherwise estimated from a hadron resonance gas. …
In this work we have re-explored our earlier study on the vector meson spectral function and its spectral property in the form of dilepton rate in a two-flavour Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model in presence of a strong entanglement between the chiral and Polyakov loop dynamics. The entanglement considered here is generated through the four-quark scalar type interaction in which the coupling strength depends on the Polyakov loop and runs with temperature and chemical potential. The entanglement effect is also considered for the four-quark vector type interaction in the same…
After the discovery of the Quantum Chromodynamics (QCD), many experimental and theoretical efforts have been made to investigate physics issues involved in ultra relativistic heavy-ion collisions. The fundamental goal of this work is to present a short guide of the underlying theory of strong interactions with emphasis on the light vector mesons based on the exceptional work of R.Rapp and J.Wambach. Today widely believed that deconfinement and chiral symmetry restoration probably takes place in a hot and dense hadronic medium as this produced at these collisions. We focus at the place where th…
We have studied the vector meson spectral function (VMSF) in a hot and dense medium within an effective QCD model namely the Nambu-Jona-Lasinio (NJL) and its Polyakov Loop extended version (PNJL) with and without the effect of isoscalar vector interaction (IVI). The effect of the IVI has been taken into account using the ring approximation. We obtained the dilepton production rate (DPR) using the VMSF and observed that at moderate temperature it is enhanced in the PNJL model as compared to the NJL and Born rate due to the suppression of color degrees of freedom.
The dilepton production from $pC$ and $pCu$ collisions at $T_{lab}=12$ GeV is calculated using the semi-classical BUU transport model, that includes the off-shell propagation of vector mesons nonperturbatively and calculates the width of the vector mesons dynamically. It is found that the collisional broadening of the vector meson width and dropping vector meson masses lead to a small enhancement of the dilepton yield below the $ω$ meson mass pole in $p Cu$ collisions compared to $p C$, which is, however, not sufficient to explain the enhanced production of dileptons as observed in the experim…
We report on a self-consistent calculation of the in-medium spectral functions of the rho and omega mesons at finite baryon density. The corresponding in-medium dilepton spectrum is generated and compared with HADES data. We find that an iterative calculation of the vector meson spectral functions provides a reasonable description of the experimental data.
The QGP that might be created in ultrarelativistic heavy-ion collisions is expected to radiate thermal dilepton radiation. However, this thermal dilepton radiation interferes with dileptons originating from hadron decays. In the invariant mass region between the $ϕ$ and $J/Ψ$ peak ($1\,$GeV$\lesssim M_{\ell^+ \ell^-} \lesssim 3 \,$GeV) the most substantial background of hadron decays originates from correlated D$\bar{\mathrm{D}}$-meson decays. We evaluate this background using a Langevin simulation for charm quarks. As background medium we utilize the well-tested UrQMD-hybrid model. The requir…
The scattering effects of charm mesons by hadrons such as the pion, rho meson and nucleon are studied in an effective Lagrangian, and are found to be important in heavy ion collisions. At the CERN-SPS energies, hadronic rescatterings are shown to harden the charm meson $m_T$ spectra, leading to a significant enhancement of the yield of intermediate-mass dimuons from charm meson decays.
We study self-consistently the finite $T$ broadening of the $ρ$-meson and its implications for dilepton emission in heavy ion-collisions. For this purpose finite width effects at finite temperature due to the $ρ$-$π$ interaction are investigated in a self-consistent $Φ$-functional approach. The temperature dependence of the $ρ$-meson and pion spectral functions and self-energies is discussed. The spectral functions show considerable broadening in comparison with a perturbative calculation on the one-loop level. Using these spectral functions, we make a comparison to dilepton emission data from…
The double differential dilepton spectrum $dN/ (dM_\perp^2 dM^2)$ at fixed transverse mass $M_\perp$ allows a direct access to the vector meson spectral functions. Within a fireball model the sensitivity of $dN/ (dM_\perp^2 dM^2)$ against variations of both the in-medium properties of mesons and the dynamics of the fireball is investigated. In contrast to the integrated invariant-mass spectrum $dN/dM^2$, in the spectrum $dN/dM^2 dM_\perp^2$ with fixed $M_\perp$ the $ω$ signal is clearly seen as bump riding on the $ρ$ background even in case of strong in-medium modifications.
The properties of the vector meson current-current correlation function and its spectral representation are investigated in details with and without isoscalar-vector interaction within the framework of effective QCD approach, namely Nambu-Jona-Lasinio (NJL) model and its Polyakov Loop extended version (PNJL), at finite temperature and finite density. The influence of the isoscalarvector interaction on the vector meson correlator is obtained using the ring resummation known as the Random Phase Approximation (RPA). The spectral as well as the correlation function in PNJL model show that the vect…
We shed light upon the eta' mass in nuclear matter in the context of partial restoration of chiral symmetry, pointing out that the U_{A}(1) anomaly effects causes the eta'-eta mass difference necessarily through the chiral symmetry breaking. As a consequence, it is expected that the eta' mass is reduced by order of 100 MeV in nuclear matter where partial restoration of chiral symmetry takes place. The discussion given here is based on Ref. [1].
The modification of the width of the rho meson due to in-medium decays and collisions is evaluated. In high temperature and/or high density hadronic matter, the collision width is much larger than the one-loop decay width. The large width of the $ρ$ meson in matter seems to be consistent with some current interpretations of the $e^+ e^-$ mass spectra measured at the CERN/SPS.
Dilepton production in proton- and nucleus-induced reactions at SPS energies is studied in the relativistic transport model using initial conditions determined by the string dynamics from RQMD. It is found that both the CERES and HELIOS-3 data for dilepton spectra in proton-nucleus reactions can be well described by the conventional mechanism of Dalitz decay and direct vector meson decay. However, to provide a quantitative explanation of the observed dilepton spectra in central S+Au and S+W collisions requires contributions other than these direct decays. Introducing a decrease of vector meson…
We present a simple model for the dimuon production from the decay of vector mesons which are hadronized from a baryon-free quark-gluon plasma. Continuous decay of vector mesons in the medium is known to enhance the dimuon production and in our model we can estimate the total yield of dimuons decayed from vector mesons through the rate equations for the number of vector mesons of interest. Muon pair production critically depends on the time duration of both the mixed and hadronic phases. Results are discussed in view of possible measurements in experiments.
We estimate the photon and dilepton emission rates from hot hadronic matter with in-medium spectral shift and broadening of vector mesons. It is observed that both the WA98 photon data and CERES/NA45 dilepton data can be well reproduced with similar initial conditions. The freeze-out condition has been constrained by the transverse mass spectra of pions and protons measured by the NA49 collaboration. We argue that simultaneous measurement of the $p_T$ spectra of single photons as well as invariant mass distribution of dileptons is crucial to understand the in-medium spectral function of the ve…
The pi omega rho coupling constant is calculated in a relativistic hadronic framework incorporating nucleons and Delta(1232) isobars. Medium modifications are included. The vertex is analyzed in context of the omega to pi e+e- and rho to pi e+e- Dalitz decays in nuclear matter. A sizeable increase of the widths for these decays is found for invariant mass of dileptons in the range 0.2-0.5 GeV. This increase may help, among other medium effects, to explain the problem of the low-mass dilepton enhancement seen in relativistic heavy-ion collisions.
Through the analysis of HELIOS-3 data on dilepton spectra, we demonstrate the importance of secondary processes for the dilepton production in heavy-ion collisions in the intermediate mass region. We find that, while the dilepton spectra in proton-induced reactions can be nicely explained by the decay of primary vector mesons, charmed hadrons, and initial Drell-Yan processes, the strong enhancement seen in the heavy-ion data comes mainly from the secondary meson-meson interactions which are unique to heavy-ion collisions.
Within an effective Lagrangian model, we present calculations for cross sections of the dilepton production in proton-proton and proton-neutron collisions at laboratory kinetic energies in 1-5 GeV range. Production amplitudes include contributions from the nucleon-nucleon bremsstrahlung as well as from the mechanism of excitation, propagation, and radiative decay of Delta(1232) and N*(1520) intermediate baryonic resonances. It is found that the delta isobar terms dominate the cross sections in the entire considered beam energy range. Our calculations are able to explain the data of the DLS col…
We present dilepton spectra from nucleus-nucleus collisions at SIS energies, which were simulated with the GiBUU transport model in a resonance-model approach. These spectra are compared to the data published by the HADES collaboration. We argue that the interpretation of dilepton spectra at SIS energies critically depends on the couplings between the ρ meson and the baryonic resonances.
The present status of our understanding of low mass dilepton production in relativistic heavy ion collisions is discussed. The focus of the discussion will be the sensitivity of dilepton measurements to in medium changes of hadrons and the restoration of chiral symmetry. We will finally discuss how the presence of strong long wavelength pion modes, i.e. disoriented chiral condensates can be seen in the dilepton spectrum.
Using a relativistic transport model to describe the expansion of the fire-cylinder formed in the initial stage of heavy-ion collisions at SPS/CERN energies, we study the production of dileptons with mass below about 1 GeV from these collisions. The initial hadron abundance and their momentum distributions in the fire-cylinder are determined by following the general features of the results from microscopic models based on the string dynamics and further requiring that the final proton and pion spectra and rapidity distributions are in agreement with available experimental data. For dilepton pr…
We study the spectrum of heavy-light mesons within a model with linear instantaneous confining potential. The single-quark Green function and spontaneous breaking of chiral symmetry are obtained from the Schwinger-Dyson (gap) equation. For the meson spectrum we derive a Bethe-Salpeter equation (BSE). We solve thiss equation numerically in the heavy-light limit and obtain effective restoration of chiral and $U(1)_A$ symmetries at large spins.
We present a unified description of the vector meson and dilepton production in elementary and in heavy ion reactions. The production of vector mesons ($ρ,ω$) is described via the excitation of nuclear resonances ($R$). The theoretical framework is an extended vector meson dominance model (eVMD). The treatment of the resonance decays $R\longmapsto NV$ with arbitrary spin is covariant and kinematically complete. The eVMD includes thereby excited vector meson states in the transition form factors. This ensures correct asymptotics and provides a unified description of photonic and mesonic decays.…
