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Register a new userP-Wave Polarization of the $rho$-Meson and the Dilepton Spectrum in Dense Matter
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Authors
Bengt Friman
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We study the $p$-wave polarization operator of the $rho$-meson due to $rho N$ interactions via the $N^*$ (1720) and $Delta (1905)$ 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.
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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 $rho$-meson. The collisional width of the $rho$-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 $rho$ improves the agreement between theory and experiment for the dilepton invariant-mass distributions near the $rho$ pole mass and for the excess radiation in Au+Au at $1.23 A$ GeV. We furthermore show that some remaining underprediction of the experimental dilepton spectra in C+C at $1 A$ GeV and Au+Au at $1.23 A$ GeV at intermediate invariant masses $0.2-0.4$ GeV can be accounted for by adjusting the $pn$ bremsstrahlung cross section in a way to agree with the inclusive dilepton spectrum from $dp$ collisions at $1.25 A$ GeV.
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 predicted medium effects on the rho propagator are rather moderate. The resulting dilepton spectra approximately agree with recent CLAS data.
Dilepton production rate (DPR) from hot and dense quark matter is studied in the presence of an arbitrary external magnetic field using the 2-flavour Nambu--Jona-Lasinio (NJL) model. The anomalous magnetic moment (AMM) of the quarks is taken into consideration while calculating the constituent quark mass as well as the DPR from the thermo-magnetic medium. An infinite number of quark Landau levels is incorporated so that no approximations are made on the strength of the background magnetic field. The analytic structure of the two point vector current correlation function in the complex energy plane reveals that, in addition to the usual Unitary cut, a non-trival Landau cut appears in the physical kinematic domains solely due to the external magnetic field. Moreover, these kinematic domains of the Unitary and Landau cuts are found to be significantly modified due to the AMM of the quarks. With finite AMM of the quarks, for certain values of the external magnetic field, the kinematically forbidden gap between the Unitary and Landau cuts are shown to vanish leading to the generation of a continuous spectrum of dilepton emission over the whole invariant mass region not observed earlier.
We calculate the rho meson mass in a weak magnetic field using effective $rhopipi$ interaction. It is seen that both $rho^0$ and $rho^pm$ masses decrease with the magnetic field in vacuum. $rho$ meson dispersion relation has been calculated and shown to be different for $rho^0$ and $rho^pm$. We also calculate the $rhopipi$ decay width and spectral functions of $rho^0$ and $rho^pm$. The width is seen to decrease with $eB$ and the spectral functions become narrower.
A symmetry-preserving treatment of mesons, within a Dyson-Schwinger and Bethe-Salpeter equations approach, demands an interconnection between the kernels of the quark gap equation and meson Bethe-Salpeter equation. Appealing to those symmetries expressed by the vector and axial-vector Ward-Green-Takahashi identitiges (WGTI), we construct a two-body Bethe-Salpeter kernel and study its implications in the vector channel; particularly, we analyze the structure of the quark-photon vertex, which explicitly develops a vector meson pole in the timelike axis and the quark anomlaous magnetic moment term, as well as a variety of $rho$ meson properties: mass and decay constants, electromagnetic form factors, and valence-quark distribution amplitudes.
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