An updated investigation of QCD sum rules for the first two moments of rho meson spectral functions, both in vacuum and in-medium, is performed with emphasis on the role of the scale related to spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral distributions do permit an accurate sum rule analysis with controlled input including QCD condensates of the lowest dimensions, whereas higher moments are subject to uncertainties from higher dimensional condensates. Possible connections with Brown-Rho scaling are discussed. The factorization approximation for four-quark condensates is shown not to be applicable in any of the cases studied.
We develop a model-independent analysis of hadronic scattering data in the resonance region, where the resonance shape follows from the matrix elements of a Hamiltonian. We investigate the rho meson in the tau decay. We demonstrate that the rho meson resonance in the two-pion decay of the tau lepton is described well through the coupling of a bare rho meson to the two-pion and the four-pion continuum. Furthermore, this four-pion continuum corresponds with the data of the four-pion decay channel of the tau lepton at energies up to 1.1 GeV.
Using the local flavor SU(4) gauge invariance in the limit of vanishing vector meson masses, we extend our previous study of charm meson scattering cross sections by pion and rho meson, which is based only on the pseudoscalar-pseudoscalar-vector meson couplings, to include also contributions from the couplings among three vector mesons and among four particles. We find that diagrams with light meson exchanges usually dominate the cross sections. For the processes considered previously, the additional interactions lead only to diagrams involving charm meson exchanges and contact interactions, a…
We discuss medium modification of the rho meson originating from its coupling to in medium quasi-pions and delta-hole states. This medium effect leads to a marked structure of the rho meson strength function in the $500 MeV$ invariant mass region. We suggest that this effect may provide an explanation of the structure observed by the DLS collaboration in the $Ca+Ca/C+C$ ratio at $1 GeV/u$.
In this work, propagation properties of the rho meson in symmetric nuclear matter are studied. We make use of a coupled channel unitary approach to meson-meson scattering, calculated from the lowest order Chiral Perturbation Theory lagrangian including explicit resonance fields. Low energy chiral constraints are considered by matching our expressions to those of one loop Ch.P.T. To account for the medium corrections, the rho couples to pion-pion and kaon-antikaon pairs which are properly renormalized in the nuclear medium.
Based on QCD sum rules we explore the consequences of a pure chiral restoration scenario for the rho meson, where all chiral symmetry breaking condensates are dropped whereas the chirally symmetric condensates remain at their vacuum values. This pure chiral restoration scenario causes the drop of the rho spectral moment by about 120 MeV. The complementarity of mass shift and broadening is discussed. A simple parametrization of the rho spectral function leads to a width of about 600 MeV if no shift of the peak position is assumed.
We present a potential of which the short-distance part is given by one gluon exchange plus perturbative one- and two-loop corrections and of which the large-distance part exhibits a temperature-dependent constant value. The Schrodinger equation with this temperature-dependent potential yields a temperature dependence of the mesonic quark-antiquark relative-motion wave function and of meson masses. The temperature dependence of the potential, the wave function and the meson masses brings about temperature dependence of cross sections for the nonresonant reactions pi pi -> rho rho for I=2, KK -…
The rho-meson mass shift, width broadening, and spectral density at finite temperature and nucleon density are estimated using a general formula which relates the self-energy to the real and imaginary parts of the forward scattering amplitude on the constituents of the medium. We saturate the scattering amplitude at low energies with resonances, while at high energies a Regge approach is taken in combination with vector meson dominance; experimental data is used wherever possible. The main result is that the rho-meson becomes increasingly broad with increasing nucleon density. The spectral den…
The scale of a phenomenologically successful charge-symmetry-violating nucleon-nucleon interaction, that attributed to meson exchange with a $ΔI =1$ rho-omega transition, is set by the Coleman-Glashow SU(2) breaking tadpole mechanism. A single tadpole scale has been obtained from symmetry arguments, electromagnetic meson and baryon measured mass splittings, and the observed isospin violating ($ΔI=1$) decay $ω\to π^+π^-$. The hadronic realization of this tadpole mechanism lies in the $I = 1$ $a_0$ scalar meson. We show that measured hadronic and two-photon widths of the $a_0$ meson, with the ai…
We obtain the RPA summed one-meson exchange potential between nucleons in symmetric nuclear matter at zero temperature, from a model which includes $ρ$, $σ$, $ω$ and $π$ mesons. The behavior of rho mesons inside the medium is first discussed using different schemes to extract a finite contribution from the vacuum polarization. These schemes give qualitatively different results for the in-medium rho mass. The results are discussed in connection with the non-renormalizability of the model. We next study the modified potential as density increases. In the intermediate distance range, it is qualit…
The running of the $ρ\bar N N$ couplings in presence of nuclear matter is studied, and the relevant $β$-functions are shown to be different for $ρ^0$ and $ρ^+$, when the nuclear medium is asymmetric.
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.
We calculate the modification of a rho meson in nuclear matter through its coupling to resonance-hole states. Starting from a recently proposed model, we include all four star resonances up to 1.9 GeV. In contrast to previous works, we include not only resonances that couple to the rho in a relative p-wave, but also those that couple to an s-wave state. In addition, we solve the equation for the rho spectral function self-consistently. We find that s-wave resonances affect the in medium spectral function of the rho strongly. In the transverse channel the rho meson is, especially at non zero mo…
Vector mesons containing light quarks are thought to have their masses reduced in dense nuclear matter, sacrificing some of their energy to the scalar field which becomes appreciable at finite baryon density. Model calculations find masses which fall by a couple tens of percents in normal nuclear matter, and by several hundred MeV in dense matter. We estimate the collision rate for rho mesons in such a scenario and at finite temperature. Compared to its free-mass value, the collision rate changes by nearly a factor of two both above and below, depending on the density. This collision broadenin…
We investigate the modification of meson spectral densities in dense nuclear matter at zero temperature. These effects are studied in a fully relativistic mean field model which goes beyond the linear density approximation and also includes baryon resonances. In particular, the role of N*(1520) and N*(1720) on the rho meson spectral density is highlighted. Even though the nucleon-nucleon loop and the nucleon-resonance loop contribute with the opposite sign, an overall reduction of rho meson mass is still observed at high density. Importantly, it is shown that the resonances cause substantial b…
The study of the pi^- p -> rho^0 n and pi^- p -> omega n amplitudes close and below the vector meson production threshold (1.2< sqrt(s) <1.8 GeV) reveals a rich dynamics arising from the presence of specific baryon resonances in this energy range. The interference pattern of the e^+e^- decays of the rho^0 and omega mesons produced in pi^- p reactions reflects directly this dynamics. We discuss this interference pattern in the pi^- p -> e^+e^- n reaction as function of the total center of mass energy sqrt(s). We emphasize the importance of an experimental study of this reaction, which could be …
Contributions of two-pseudoscalar and vector-pseudoscalar meson loops to the rho-omega mass splitting are evaluated in a covariant model based on studies of the Schwinger-Dyson equations of QCD. The role and importance of the different time orderings of the meson loops is analyzed and compared with those obtained within time-ordered perturbation theory. It is shown that each meson loop contributes less than 10% of the bare mass, and decreases as the masses of the intermediate mesons increase beyond approximately m_rho/2. A mass splitting of m_omega - m_rho ~= 25 MeV is obtained from the pi pi,…
Elastic electromagnetic form factors for the $ρ^+$ meson are calculated in a Nambu--Jona-Lasinio model which incorporates quark confinement through the use of the proper-time regularization scheme. A comparison is made with recent lattice QCD results and previous quark model calculations for static quantities and the Sachs form factors. The results are qualitatively in good agreement with the lattice QCD calculations, with the exception of the quadrupole moment and corresponding form factor, which may be related to a lack of spherical symmetry on the lattice.
We examine the Brown-Rho scaling for meson masses in the strong coupling limit of lattice QCD with one species of staggered fermion. Analytical expression of meson masses is derived at finite temperature and chemical potential. We find that meson masses are approximately proportional to the equilibrium value of the chiral condensate, which evolves as a function of temperature and chemical potential.
We study the temperature dependence of the pion decay constant and rho-meson mass in the hidden local symmetry model at one loop. Using the standard imaginary time formalism, we include the thermal effect of rho meson as well as that of pion. We show that the pion gives a dominant contribution to the pion decay constant and rho-meson contribution slightly decreases the critical temperature. The rho-meson pole mass increases as T^4/m_ρ^2 at low temperature dominated by the pion-loop effect. At high temperature, although the pion-loop effect decreases the rho-meson mass, the rho-loop contributio…
The possibility of meson condensation in stars and in heavy-ion collisions has been discussed in the past. Here, we study whether rho meson condensation ($ρ^{-}$) can occur in very dense matter and determine the effect of strong magnetic fields on this condensation. We find that rho meson condensates can appear in the core of the neutron star assuming a rho mass which is reduced due to in-medium effects. We find that the magnetic field has a non-negligible effect in triggering condensation.
We present a unified model describing electroweak properties of the pi and rho mesons. Using a general method of relativistic parametrization of matrix elements of local operators, adjusted for the nondiagonal in total angular momentum case, we calculate the rho-meson lepton-decay constant f_rho using the same parameters of free constituent quarks that have ensured exclusively good results for the pi meson previously. The only free parameter, characterizing quark interactions, which include additional spin-spin contribution and hence differ from the $π$-meson case, is fixed by matching the dec…
Cherenkov gluons may be responsible for the asymmetry of dilepton mass spectra near rho-meson observed in experiment. They can be produced only in the low-mass wing of the resonance. Therefore the dilepton mass spectra are flattened there and their peak is slightly shifted to lower masses compared with the in-vacuum rho-meson mass. This feature must be common for all resonances.
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.
We discuss the properties of vector mesons, in particular the rho^0, in the context of the Hidden Local Symmetry (HLS) model. This provides a unified framework to study several aspects of the low energy QCD sector. Firstly, we show that in the HLS model the physical photon is massless, without requiring off field diagonalization. We then demonstrate the equivalence of HLS and the two existing representations of vector meson dominance, VMD1 and VMD2, at both tree level and one loop order. Finally the S matrix pole position is shown to provide a model and process independent means of specifying …
We investigate QCD sum rules for vector currents in the rho meson channel in the nuclear medium. For increased sensitivity, we subtract out the vacuum contributions. With a saturation scheme often considered in the literature, we find these subtracted sum rules to be unstable. It indicates the importance of other contributions neglected in the saturation scheme. These include more Landau singularities at low energy, additional operators in the medium, and possibly the in-medium width of the rho meson.
The rho meson spectral function in hot and dense asymmetric nuclear matter (number densities of proton and neutron different) is evaluated in an effective chiral SU(3) model within the mean field approximation (MFA). The dependence of the vector meson masses on density and temperature, their variation with the asymmetry parameter, the form of the spectral function when the p <-> n symmetry is broken are studied. One can observe clear splitting of the longitudinal and the transverse modes among the rho isospin multiplets. The role of a running tensor coupling on the spectral function is also st…
The quark-meson coupling (QMC) model is applied to a study of the mass of the $ρ$-meson in helium and carbon nuclei. The average mass of a $ρ$-meson formed in $^{3,4}$He and $^{12}$C is expected to be around 730, 690 and 720 MeV, respectively.
It is simply anticipated that in a strong magnetic configuration, the Landau quantization ceases the neutral rho meson to decay to the charged pion pair, so the neutral rho meson will be long-lived. To closely access this naive observation, we explicitly compute the charged pion-loop in the magnetic field at the one-loop level, to evaluate the magnetic dependence of the lifetime for the neutral rho meson as well as its mass.Due to the dimensional reduction induced by the magnetic field (violation of the Lorentz invariance), the polarization (spin $s_z=-1,0,+1$) modes of the rho meson, as well …
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.
Using a simple parametrization of Breit-Wigner type for the hadronic side of the QCD sum rule for $ρ$ mesons in vacuum as well as in a nuclear medium we explore the range of values for the mass and the width of the $ρ$ meson which are compatible with the operator product expansion.
We present our recent results for the rho and sigma mesons considered as resonances in pion-pion scattering in a thermal bath. We use chiral perturbation theory to fourth order in p for the low energy behaviour, then extend the analysis via the unitarization method of the Inverse Amplitude into the resonance region. The width of the rho broadens about twice the amount required by phase space considerations alone, its mass staying practically constant up to temperatures of order 150 MeV. The sigma meson behaves in accordance to chiral symmetry restoration expectations.
We analyse the structure of one-loop self-energy graphs for the rho meson in real time formulation of finite temperature field theory. We find the discontinuities of these graphs across the unitary and the Landau cuts. These contributions are identified with different sources of medium modification discussed in the literature. We also calculate numerically the imaginary and the real parts of the self-energies and construct the spectral function of the rho meson, which are compared with an earlier determination. A significant contribution arises from the unitary cut of the pi-omega loop, that w…
It is shown, in a model independent way, that the large difference in rho and omega widths gives rise to a new source of momentum dependence for the rho-omega mixing matrix element. The q^2 dependence arising due to the meson widths leads to a significant alteration of the result obtained in the zero-width approximation usually discussed in the literature. The origin of this strong momentum dependence lies in the difference between the rho and omega meson widths.
We extend hadronic models for rho-meson propagation in cold nuclear matter via coupling to in-medium pions to include finite three-momentum. Special care is taken to preserve gauge invariance. Consequences for photoabsorption on the proton and on nuclei as well as for the dilepton production in relativistic heavy-ion collisions are discussed.
Using interpolators with different SU(2)_L \times SU(2)_R transformation properties we study the chiral symmetry and spin contents of the rho- and rho'-mesons in lattice simulations with dynamical quarks. A ratio of couplings of the $\qbarγ^iτq$ and $\qbarσ^{0i}τq$ interpolators to a given meson state at different resolution scales tells one about the degree of chiral symmetry breaking in the meson wave function at these scales. Using a Gaussian gauge invariant smearing of the quark fields in the interpolators, we are able to extract the chiral content of mesons up to the infrared resolution o…
There exist model calculations showing the modification of the hadronic parameters of $ρ$ meson in the nuclear environment. From these parameters, we extract the $ρ$ meson nucleus optical potential and show the medium effect due to this potential on the $ρ$ meson mass distribution spectra in the photonuclear reaction. The calculated results reproduced reasonably the measured $e^+e^-$ invariant mass, i.e., $ρ$ meson mass, distribution spectra in the $( γ, ρ^0 \to e^+e^- )$ reaction on nuclei.
We present a model for the polarized cross-sections of the hard diffractive leptoproduction of rho meson in the high energy limit. Our model is based on the light-cone collinear factorization of the virtual photon to rho meson impact factor when using the impact factor representation of the helicity amplitudes of the rho meson leptoproduction. This gauge invariant treatment when expressed in impact parameter space, leads to the factorization on one hand of the color dipole scattering amplitude and on the other hand of the distribution amplitudes of the rho meson up to twist 2 and 3. We show th…
Our recent work on modifications of rho-mesons formed at the last stage of evolution of hadronic matter produced in heavy ion collisions is summarized. It is found that while the mass shift is on the order of a few tens of MeV, the width and spectral density become so broad that rho may lose its identity as a well defined resonance.
We study the influence of the finite damping width of pions on the in-medium properties of the rho-meson in an interacting meson gas model at finite temperature. Using vector dominance also implications on the resulting dilepton spectra from the decay of the rho-meson are presented. A set of coupled Dyson equations with self energies up to the sunset diagram level is solved self consistently. Following a Phi-derivable scheme the self energies are dynamically determined by the self consistent propagators. Some problems concerning the self consistent treatment of vector or gauge bosons on the pr…
Within a field theoretical model where all damping width effects are treated self-consistently we study the changes of the spectral properties of rho-mesons due to the finite damping width of the pions in dense hadronic matter at finite temperature. The corresponding effects in the di-lepton yields are presented. Some problems concerning the self consistent treatment of vector or gauge bosons are discussed.
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.
We compute dilepton invariant mass spectra from the decays of rho mesons produced by photon reactions off nuclei. Our calculations employ a realistic model for the rho photoproduction amplitude on the nucleon which provides fair agreement with measured cross sections. Medium effects are implemented via an earlier constructed rho propagator based on hadronic many-body theory. At incoming photon energies of 1.5 -3 GeV as used by the CLAS experiment at JLAB, the average density probed for iron targets is estimated at about half saturation density. At the pertinent rho-meson 3-momenta the predicte…
We review the current status of rho-omega mixing and discuss its implication for our understanding of charge-symmetry breaking. In order to place this work in context we also review the photon-hadron coupling within the framework of vector meson dominance. This leads naturally to a discussion of the electromagnetic form-factor of the pion and of nuclear shadowing.
We study the temperature evolution of the rho and sigma mass and width, using a unitary chiral approach. The one-loop pion-pion scattering amplitude in Chiral Perturbation Theory at finite temperature is unitarized via the Inverse Amplitude Method. Our results predict a clear increase with T of both the rho and sigma widths. The masses decrease slightly for high T, while the rho-pion-pion coupling increases. The rho behavior seems to be favored by experimental results. In the sigma case, it signals chiral symmetry restoration.
We study the properties of rho mesons in nuclear matter by means of QCD sum rules at finite density. For increased sensitivity, we subtract out the vacuum contributions. With the spectral function as estimated in the literature, these subtracted sum rules are found to be not well satisfied. We suppose that Landau singularities from higher resonance states in the nearby region in this channel are the cause for this failure.
In this contribution to the proceedings, we present our recent analysis on the chiral symmetry restoration in the generalized hidden local symmetry (GHLS) which incorporates the rho meson, $A_1$ meson and the pion consistently with the chiral symmetry of QCD. It is shown that a set of parameter relations, which ensures the first and second Weinberg sum rules, is invariant under the renormalization group evolution. Then, it is found that the Weinberg sum rules together with the matching of the vector and axial-vector current correlators to the OPE inevitably leads to {\it the dropping masses of…
We study unpolarized cross sections for the endothermic nonresonant reactions: pion pion to rho rho for I=2, KK to K*K* for I=1, KK* to K*K* for I=1, pion K to rho K* for I=3/2, pion K* to rho K* for I=3/2, rho K to rho K* for I=3/2, and pion K* to rho K for I=3/2, which take place in hadronic matter. We provide a potential that is given by perturbative QCD with loop corrections at short distances, becomes a distance-independent and temperature-dependent value at long distances, and has a spin-spin interaction with relativistic modifications. The Schrodinger equation with the potential yields …
The rho-meson eletromagnetic form factors are calculated, both in covariant and light-front framework with constituintes quarks. The effect of the breakdown rotational symmetry for the one-body current operador in the null-plane is investigate by comparing calculations within ligth-front and covariant approaches.
The relativistic point-form formalism that we proposed for the study of the electroweak structure of few-body bound states is applied to calculate the elastic form factors of spin-1 mesons, such as the rho meson, within constituent-quark models. We treat electron-meson scattering as a Poincare-invariant coupled-channel problem for a Bakamjian-Thomas mass operator and extract the meson current from the resulting invariant 1-photon-exchange amplitude. Wrong cluster properties inherent in the Bakamjian-Thomas framework are seen to cause spurious contributions in the current. These contributions, …
We study the chiral symmetry restoration using the generalized hidden local symmetry (GHLS) which incorporates the rho and A_1 mesons as the gauge bosons of the GHLS and the pion as the Nambu-Goldstone boson consistently with the chiral symmetry of QCD. We show that a set of parameter relations, which ensures the first and second Weinberg's sum rules, is invariant under the renormalization group evolution. Then, we found that the Weinberg's sum rules together with the matching of the vector and axial-vector current correlators inevitably leads to {\it the dropping masses of both rho and A_1 me…
Qualitative changes in the collective excitation spectra of the $ρ$-meson triplet in neutron matter is studied, with particular emphasis on the breaking of the discrete $p\leftrightarrow n$ symmetry. The appearance of additional branches in the dispersion characteristics, the mass splitting among the charge states, the splitting between longitudinal and transverse modes of the $ρ^{\pm}$ mesons and the appearance of `island' modes (or loops) in the time-like region are some of the features that are exposed.
Based on the analysis of both Borel and Finite-Energy QCD sum rules, the inclusion of finite mesonic widths leads to a dramatic effect on the predictions for the momentum dependence of the rho-omega mixing matrix element. It is shown that the rho-omega mixing matrix element traditionally discussed in the literature, has the same sign and similar magnitude in the space-like region as its on-shell value. This contrasts the zero-width result where the mixing matrix element is typically of opposite sign in the space-like region.
The modification of the width of rho mesons due to in-medium decays and collisions is evaluated. The decay width is calculated from the imaginary part of the one-loop self-energy at finite temperature. The collision width is related to the cross sections of the $ρ$ + pion and the $ρ$ + nucleon reactions. A calculation based on an effective Lagrangian shows the importance of including the direct $ρπ\toρπ$ scattering which is dominated by the $a_1$ exchange. A large broadening of the spectral function is found, accompanied by a strength suppression at the pole.
It is possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark Fock component of a meson in the infrared, where mass is generated. Using the variational method and a set of interpolators that span a complete chiral basis we extract in a lattice QCD Monte Carlo simulation with two dynamical light quarks the orbital angular momentum and spin content of the rho-meson. We obtain in the infrared a simple 3S1 component as a leading component of the rho-meson with a small admixture of the 3D1 partial wave, in agreement with the…
The modification of the rho-meson self-energy due to the coupling to in-medium pions is calculated consistently at finite baryon density and temperature, keeping the full 3-momentum dependence in a gauge invariant way. As a function of nucleon density, the rho-meson spectral function is strongly enhanced in the invariant mass region M < 650 MeV, while the maximum, i.e. the pole mass, is slightly shifted upwards. As a function of temperature, for fixed nucleon density, the imaginary part of the self-energy increases further due to Bose-enhancement. At the same time the mass shift from the real …
We reanalyze the dissociation process of the $J/ψ$ by $π$ and $ρ$ mesons into $D + \bar{D}$, $D^* + \bar{D}$, $D + \bar{D}^*$, and $D^* + \bar{D}^*$ within a meson exchange model. In addition to the dissociation mechanisms considered in the literature, we consider anomalous parity interactions, whose couplings are constrained by heavy quark spin symmetry and phenomenology. This opens new dissociation channels and adds new diagrams in the previously considered processes. Compared to the previous results, we find that these new additions have only a minor effect on the $ρ+ J/ψ$ total inelastic c…
We argue that in generic AdS/QCD models (confining gauge theories dual to string theory on a weakly-curved background), the couplings g_{rho HH} of any rho meson to any hadron H are quasi-universal, lying within a narrow band near m(rho)^2/f(rho). The argument relies upon the fact that the rho is the lowest-lying state created by a conserved current, and the detailed form of the integrals which determine the couplings in AdS/QCD. Quasi-universality holds even when rho-dominance is violated. The argument fails for all other hadrons, except the lowest-lying spin-two hadron created by the energy-…
