Vector Meson Propagator Research Articles

Elastic proton–neutron and antiproton–neutron scattering in holographic QCD

The total and differential cross sections of the elastic proton–neutron and antiproton–neutron scattering are studied in a holographic QCD model, focusing on the Regge regime. Taking into account the Pomeron and Reggeon exchange, which are described by the Reggeized spin-2 glueball and vector meson propagator respectively, those cross sections are obtained. It is presented that the currently available experimental data of the total cross sections can be well described within the model. Once a single adjustable parameter is determined with the total cross section data, the differential cross sections can be calculated without any additional parameters. Although the available differential cross section data are limited, it is found that our predictions are consistent with those.

The form factors of τ → K π (η) ν and the predictions for CP violation beyond the standard model

We study the hadronic form factors of $\tau$ lepton decays $\tau \to K \pi(\eta) \nu$. We compute one loop corrections to the form factors using the chiral Lagrangian including vector mesons. The counterterms which subtract the divergence of the one-loop amplitudes are determined by using background field method. In the vector form factor, $K^\ast$ resonance behavior is reproduced because the diagram with a vector meson propagator is included. We fit the data of the hadronic invariant mass spectrum measured by Belle by determining some of the counterterms of the Lagrangian. Besides the hadronic invariant mass spectrum, the forward-backward asymmetry is predicted. We also study the effect of CP violation of a two Higgs doublet model. In the model, CP violation of the neutral Higgs sector generates the mixing of CP even Higgs and CP odd Higgs. We show how the mixing leads to the direct CP violation of the $\tau$ decays and predict the CP violation of the forward-backward asymmetry.

The form factors of -> K ( ) and the predictions for CP violation beyond the standard model

We study the hadronic form factors of the τ lepton decays |$\tau \rightarrow K \pi (\eta) \nu $|⁠. We compute one-loop corrections to the form factors using the chiral Lagrangian including vector mesons. The counterterms that subtract the divergence of the one-loop amplitudes are determined by using the background field method. In the vector form factor, K* resonance behavior is reproduced because a diagram with a vector meson propagator is included. We fit the data of the hadronic invariant mass spectrum measured by Belle by determining some of the counterterms of the Lagrangian. Besides the hadronic invariant mass spectrum, forward–backward asymmetry is predicted. We also study the effect of CP violation of a two Higgs doublet model. In the model, CP violation of the neutral Higgs sector generates the mixing of CP-even Higgs and CP-odd Higgs. We show how the mixing leads to direct CP violation of the τ decays and predict the CP violation of the forward–backward asymmetry.

Propagation of photons and massive vector mesons between a parity breaking medium and vacuum

The problem of propagation of photons and massive vector mesons in the presence of Lorenz and CPT invariance violating medium is studied when the parity-odd medium is bounded by a hyperplane separating it from the vacuum. The solutions in both half-spaces are carefully discussed and in the case of space-like boundary stitched on the boundary with help of the Bogolubov transformations provided by the space-like Chern-Simons vector. The presence of two different Fock vacua is shown and the probability amplitude for transmission of particles from vacuum to parity breaking medium is calculated. We have also found classical solutions and showed that the results are consistent with ones obtained by canonical quantization formalism. In the cases, both of entrance to and of escaping from parity-odd medium, the probabilities for reflecting and passing through were found for each polarization using the classical solutions. Finally, the propagator for each polarization is obtained in the momentum space. Boundary effects under consideration are of certain importance for registration of local parity violation in the finite volume of heavy ion fireball and/or of a star with cold axion condensate.

The vector meson mass in the large N limit of QCD

The vector meson mass is computed as a function of quark mass in the large N limit of QCD. We use continuum reduction and directly compute the vector meson propagator in momentum space. Quark momentum is inserted using the quenched momentum prescription.

Renormalization of the antisymmetric tensor field propagator and dynamical generation of the 1 + − mesons in Resonance Chiral Theory

We discuss the renormalization of the 1 −− vector meson propagator within Resonance chiral theory at one loop. Using the particular form of the interaction Lagrangian we show that additional poles of the renormalized propagator corresponding to 1 + − degrees of freedom can be generated. We give a concrete example of such an effect.

Dilepton production at SIS energies

In this short review the results of detailed studies for dilepton production from p+A andA+A reactions at SIS energies are presented. The calculations are based on a semi-classical BUU transport model that includes the off-shell propagation of vector mesons and evaluates the width of the vector mesons dynamically. Different scenarios of in-medium modifications of vector mesons, such as collisional broadening and dropping vector meson masses, are investigated and the possibilities for an experimental observation of in-medium effects in p+A reactions at 1–4 GeV are discussed for a variety of nuclear targets.

Effects on the Hadron Propagators due to kμkν Terms in the Vector Meson Propagator**The project supported in part by National Natural Science Foundation of China and the Foundation of the Ministry Education of China

In an approximation where the baryon current conservation is violated, the contribution of the kμkν terms in the vector meson propagator may not vanish. Their effects on the baryon and meson spectral functions and on the consequences of self-consistency are studied in the relativistic self-consistent Hartree-Fock approximation by means of the σ-ω model. Two cases where the kμkν terms are and are not neglected are compared. It is found that there is a marked change in the baryon spectral function which becomes more peaked in the latter case. Such a change remains even by a proper readjustment of parameters. The effects of self-consistency in the σ-ω model are qualitatively the same in both cases, though quantitatively there is some significant difference.

ρ/ω properties from dilepton spectra in pA reactions at 12 GeV

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 $\omega$ 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 experiment by the KEK-PS E325 collaboration. It is argued that such in-medium effects are expected to be small due to kinematical reasons -- the dominant part of vector mesons radiate dileptons and decay outside the nucleus due to the finite formation time for $\rho$ and $\omega$ mesons, which is large by Lorentz covariance since the produced vector mesons move with high velocity relative to the target nucleus.

E +e − production in p A reactions at SIS energies

Detailed predictions for dilepton production from p A reactions at SIS energies are presented within a semiclassical BUU transport model that includes the off-shell propagation of vector mesons nonperturbatively and calculates the width of the vector mesons dynamically. Different scenarios of in-medium modifications of vector mesons, such as collisional broadening and dropping vector-meson masses, are investigated and the possibilities for an experimental observation of in-medium effects in p A reactions at 1–4 GeV are discussed for a variety of nuclear targets.

Vector mesons in asymmetric nuclear matter

The propagation of a vector meson (ϱ and ω) in dense asymmetric nuclear matter (with the number density of protons and neutrons different) is studied. Of particular interest is the density dependence of the vector meson masses, as also their variation with the asymmetry parameter, mass splitting among the ϱ isospin multiplets and the change of the form of the ϱ meson self-energy or the polarization tensor ( II μν ) when the p ↔ n symmetry is broken. Contributions of both the Fermi sea and Dirac vacuum have been considered. It is shown that while the density dependent dressing of the vector meson propagator lifts the dispersion characteristics into the region of instability, the Dirac vacuum on the other hand contributes with opposite sign, thereby enhancing the possibility of stable collective modes even for higher values of vector meson momenta. The role of tensor coupling on the dispersion characteristics is also presented.

QCD sum rule analysis of the mixed-isospin vector current correlator reexamined.

The mixed-isospin vector current correlator, $\langle 0\vert T(V^\rho_\mu V^\omega_\nu )\vert 0\rangle$ is evaluated using both QCD sum rules and Chiral Perturbation Theory (ChPT) to one-loop order. The sum rule treatment is a modification of previous analyses necessitated by the observation that those analyses produce forms of the correlator that fail to be dominated, near $q^2=0$, by the most nearby singularities. Inclusion of contributions associated with the $\phi$ meson rectify this problem. The resulting sum rule fit provides evidence for a significant direct $\omega\rightarrow\pi\pi$ coupling contribution in $e^+e^-\rightarrow\pi^+\pi^-$. It is also pointed out that results for the $q^2$-dependence of the correlator cannot be used to provide information about the (off-shell) $q^2$-dependence of the off-diagonal element of the vector meson propagator unless a very specific choice of interpolating fields for the vector mesons is made. The results for the value of the correlator near $q^2=0$ in ChPT are shown to be more than an order of magnitude smaller than those extracted from the sum rule analysis and the reasons why this suggests slow convergence of the chiral series for the correlator given.

Electro-magnetic nucleon form factors and their spectral functions in soliton models

It is demonstrated that in simple soliton models essential features of the electro-magnetic nucleon form factors observed over three orders of magnitude in momentum transfer $t$ are naturally reproduced. The analysis shows that three basic ingredients are required: an extended object, partial coupling to vector mesons, and relativistic recoil corrections. We use for the extended object the standard skyrmion, one vector meson propagator for both isospin channels, and the relativistic boost to the Breit frame. Continuation to timelike $t$ leads to quite stable results for the spectral functions in the regime from the 2- or 3-pion threshold to about two rho masses. Especially the onset of the continuous part of the spectral functions at threshold can be reliably determined and there are strong analogies to the results imposed on dispersion theoretic approaches by the unitarity constraint.

Two model-independent results for the momentum dependence of ϱ-ω mixing

Two model-independent results on the momentum-dependence of ϱ-ω mixing are described. First, an explicit choice of interpolating fields for the vector mesons is displayed for which both the mixing in the propagator and the isospin-breaking at the nucleon-vector meson vertices (and hence also the one-vector-meson-exchange contribution to NN charge symmetry breaking) vanish identically at q 2 = 0. Second, it is shown, using the constraints of unitarity and analyticity on the spectral function of the vector meson propagator, that there is no possible choice of interpolating fields for the ϱ 0, ω 0 mesons such that, with the ϱω element of the propagator defined by Δ μν ϱω(q 2) = (g μν − q μq ν q 2 )θ(q 2) (q 2 − m ϱ 2)(q 2 − m ω 2) , θ(q 2) is independent of momentum. It follows that the standard treatment of charge symmetry breaking in few-body systems cannot be interpreted as arising from any realizable effective meson-baryon Lagrangian and must, therefore, be considered purely phenomenological in content.

Scaled effective chiral lagrangians for the propagation of scalar and vector mesons in dense matter

We explore various chiral lagrangians in which the QCD scale anomaly is implemented by introducing a dilaton field representing the gluon condensate. The lagrangians are used to study the chiral phase transition and the propagators of both scalar and vector mesons in dense baryonic matter. A hybrid model is proposed which allows an unambiguous definition of meson masses and coupling constants in dense matter. Meson masses are calculated as a function of density.

Vertex corrections to vacuum polarization in hadronic field theories.

Vacuum polarization is studied in a model with neutral vector mesons and Dirac baryons. The lowest-order polarization is known to produce a ghost pole when it is summed to all orders in the vector meson propagator. It is also known that the infrared structure of the meson-baryon (NN\ensuremath{\omega}) vertex in this model produces a proper vertex function that is strongly damped at large spacelike momentum transfer; this is analogous to the result first derived by Sudakov in quantum electrodynamics. When the model vertex function is approximated by its on-shell form and combined with the lowest-order polarization, the vacuum contributions are significantly reduced. The resulting random-phase approximation meson propagator has no ghost pole and is finite at large spacelike momenta. Implications and perspectives of this result and necessary extensions of this calculation are also discussed.

A theory of highly condensed matter

To discuss properties of cold, condensed stellar objects such as neutron stars, it is necessary to know the stress tensor T μν , the source in Einstein's field equations, from nuclear matter densities upwards. To overcome some of the difficulties with the conventional many-body approach to this problem, a model relativistic, many-body, quantum field theory composed of a baryon field, a neutral scalar meson field coupled to the scalar density ψψ , and a neutral vector meson field coupled to the conserved baryon current i Ψγλψ is developed. For a uniform system of given baryon density ϱ B , the linearized theory obtained by replacing the scalar and vector fields by their expectation pectation values, φ → φ 0, V λ → iδ λ4 V 0 can be solved exactly. The resulting equation of state for nuclear matter exhibits nuclear saturation, and if the two dimensionless coupling constants in this theory are matched to the binding energy and density of nuclear matter, predictions are obtained for all other systems at all densities. In particular, neutron matter is unbound and the equation of state for neutron matter at all densities is presented; it extrapolates smoothly into the relativistic form P = ϵ. Comparison is made with some conventional many-body calculations. The full field theory is developed by expanding the fields about the condensed values φ 0, V 0, and the unperturbed hamiltonian is shown to correspond to the linearized theory. The energy shift due to these quantum fluctuations in the fields is related to the baryon Green's function. V 0 is related directly to ϱ B ; φ 0, however, must be determined through a self-consistency relation involving the baryon Green's function. The Feynman rules for this theory are developed. Expressions for the lowest-order contributions of the quantum fluctuations to the energy shift and φ 0 are derived. It is shown that the terms q μ q ν in the vector-meson propagator do not contribute to these expressions, and a prescription involving assumptions on the limiting form of the theory as ϱ B → 0 is presented which ensures that these lowest-order quantum fluctuations will yield finite results.

Neutron-proton form factors. II

In a recent letter we suggested that the momentum dependence of the exact meson propagator may be responsible for the dipole-like behavior of the nucleon electromagnetic form factors over the limited range of data available. In this paper we extend the analysis to include more than one vector-meson propagator, and, by assuming a simplified form for the imaginary part of the level shift, we calculate the form factors explicitly. The nucleon electromagnetic form-factor data are fitted for momentum transfer to $2\frac{\mathrm{GeV}}{c}$ assuming just one isovector-vector meson and two isoscalar-vector mesons. The resulting fit is much better than that obtained using the dipole formula, and min ${\ensuremath{\chi}}^{2}$ occurs for values of the masses and widths of the vector mesons close to the experimental values of the $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\phi}$ resonances. The six independent meson-nucleon coupling constants are determined. Their values are consistent with the assumption that the nucleon charge and the magnetic moment distributions are extended, that is, that there are no hard-core contributions to the form factors. This assumption completely determines the isovector coupling constants and reduces the number of independent coupling constants to two. The pion and kaon charge form factors, as deduced from the nucleon charge form factors assuming universality, are compared with the available data. The pion form factors fit the data in both the spacelike and the timelike regions, including the resonance shape for the $\ensuremath{\rho}$ contribution to the pion form factor. The kaon form-factor data disagree with the assumption of universality in both the spacelike and timelike regions.