Meson Self-energies Research Articles

ϕ meson mass and decay width in strange hadronic matter

The in-medium mass and decay width of the $\phi$ meson in the hot asymmetric strange hadronic matter are calculated using an effective Lagrangian approach for $\phi$ $K\bar K$ interaction. The in-medium contributions of $K \bar K$ loop to the $\phi$ meson self-energy are computed by the medium modified kaon and antikaon mass which is evaluated using the chiral SU(3) model. To deal with the ultraviolet divergence, we regularize the loop integral of self-energy with a dipole form factor, and present the results for cut-off mass, $\Lambda_c$=3 GeV. In chiral model calculations, for strange matter, we find that the mass of kaons and antikaons decreases with the increase in baryonic density whereas the finite temperature causes an increase in the mass. We observed that the in-medium $\phi$ meson mass decreases slowly with baryonic density whereas the decay width increases rapidly. The results in the present investigation support result in the literature which indicate a small downward shift in mass and a large broadening in the decay width. In the asymmetric strange hadronic matter, the study of the $\phi$ mesons can be relevant for the compressed strange baryonic matter and experimental observables such as dilepton spectra which can result from the experiments in the future FAIR facility at GSI.

Φ -meson–nucleus bound states

$\phi$-meson--nucleus bound state energies and absorption widths are calculated for seven selected nuclei by solving the Klein-Gordon equation with complex optical potentials. Essential input for the calculations, namely the medium-modified $K$ and $\overline{K}$ meson masses, as well as the density distributions in nuclei, are obtained from the quark-meson coupling model. The attractive potential for the $\phi$-meson in the nuclear medium originates from the in-medium enhanced $K\overline{K}$ loop in the $\phi$-meson self-energy. The results suggest that the $\phi$-meson should form bound states with all the nuclei considered. However, the identification of the signal for these predicted bound states will need careful investigation because of their sizable absorption widths.

The electric conductivity of a pion gas

The determination of transport coefficients plays a central role in characterizing hot and dense nuclear matter. In the present work we calculate the electric conductivity of hot hadronic matter by extracting it from the ρ meson spectral function, as its zero-energy limit at vanishing momentum. Using hadronic many-body theory, we calculate the ρ meson self-energy in a pion gas. This requires the dressing of the pion propagators in the ρ self-energy with π-ρ loops, and the inclusion of vertex corrections to maintain gauge invariance. The resulting spectral function is used to calculate the electric conductivity of hot hadronic matter. In particular, we analyze the transport peak of the spectral function and extract its behavior with temperature and coupling strength. Our results suggest that, while obeying lower bounds proposed by conformal field theories in the strong-coupling limit, hot pion matter is a strongly-coupled medium.

QED effects in the pseudoscalar meson sector

We present results on the pseudoscalar meson masses from a fully dynamical simulation of QCD+QED. We concentrate particularly on violations of isospin symmetry. We calculate the $\pi^+$-$\pi^0$ splitting and also look at other isospin violating mass differences. We have presented results for these isospin splittings in arXiv:1508.06401 [hep-lat]. In this paper we give more details of the techniques employed, discussing in particular the question of how much of the symmetry violation is due to QCD, arising from the different masses of the $u$ and $d$ quarks, and how much is due to QED, arising from the different charges of the quarks. This decomposition is not unique, it depends on the renormalisation scheme and scale. We suggest a renormalisation scheme in which Dashen's theorem for neutral mesons holds, so that the electromagnetic self-energies of the neutral mesons are zero, and discuss how the self-energies change when we transform to a scheme such as $\bar{MS}$, in which Dashen's theorem for neutral mesons is violated.

Properties of strange vector mesons in dense and hot matter

We investigate the in-medium properties of strange vector mesons ($K^*$ and $\bar K^*$) in dense and hot nuclear matter based on chirally motivated models of the meson selfenergies. We parameterise medium effects as density or temperature dependent effective masses and widths, obtain the vector meson spectral functions within a Breit-Wigner prescription (as often used in transport simulations) and study whether such an approach can retain the essential features of full microscopic calculations. For $\mu_B\ne 0$ the medium corrections arise from $\bar K^* (K^*) N$ scattering and the $\bar K^* (K^*) \to \bar K (K) \pi$ decay mode (accounting for in-medium $\bar K (K)$ dynamics). We calculate the scattering contribution to the $K^*$ selfenergy based on the hidden local symmetry formalism for vector meson nucleon interactions, whereas for the $\bar K^*$ selfenergy we implement recent results from a selfconsistent coupled-channel determination within the same approach. For $\mu_B\simeq 0$ and finite temperature we rely on a phenomenological approach for the kaon selfenergy in a hot pionic medium consistent with chiral symmetry, and evaluate the $\bar K^* (K^*) \to \bar K (K) \pi$ decay width. The emergence of a mass shift at finite temperature is studied with a dispersion relation over the imaginary part of the vector meson selfenergy.

Chiral behavior of vector meson self-energies

We employ a chiral Lagrangian framework with three dynamical flavors to calculate the masses of the lowest-lying vector mesons to one-loop accuracy, and use the resulting formulas to extrapolate recent lattice data from the QCDSF Collaboration on vector meson masses and mass ratios to the physical point. Our representation for the vector meson self-energies also enables us to discuss loop corrections to the $\ensuremath{\omega}\ensuremath{\phi}$ mixing amplitude.

CHARMING MESONS WITH BARYONS AND NUCLEI

The properties of charmed mesons in nuclear matter and nuclei are reviewed. Different frameworks are discussed paying a special attention to unitarized coupled-channel approaches which incorporate heavy-quark spin symmetry. Several charmed baryon states with negative parity are generated dynamically by the s-wave interaction between pseudoscalar and vector meson multiplets with 1/2+ and 3/2+ baryons. These states are compared to experimental data. Moreover, the properties of open-charm mesons in matter are analyzed. The in-medium solution accounts for Pauli blocking effects, and for the meson self-energies in a self-consistent manner. The behavior in the nuclear medium of the rich spectrum of dynamically-generated baryon states is studied as well as their influence in the self-energy and, hence, the spectral function of open charm. The possible experimental signatures of the in-medium properties of open charm are finally addressed, such as the formation of charmed nuclei, in connection with the future FAIR facility.

Charmed Mesons in Nuclei with Heavy-Quark Spin Symmetry

We study the properties of charmed pseudoscalar and vector mesons in dense matter within a unitary meson–baryon coupled-channel model which incorporates heavy-quark spin symmetry. This is accomplished by extending the SU(3) Weinberg–Tomozawa Lagrangian to incorporate spin-flavor symmetry and implement a suitable flavor symmetry breaking. Several resonances with negative parity are generated dynamically by the s-wave interaction between pseudoscalar and vector meson multiplets with 1/2+ and 3/2+ baryons. Those states are then compared to experimental data as well as theoretical models. Next, Pauli-blocking effects and meson self-energies are introduced in a self-consistent manner to obtain the open-charm meson spectral functions in a dense nuclear environment. We finally discuss the formation of D-mesic nuclei.

Strangeness and charm in nuclear matter

The properties of strange ($K$, $\bar K$ and $\bar K^*$) and open-charm ($D$, $\bar D$ and $D^*$) mesons in dense matter are studied using a unitary approach in coupled channels for meson-baryon scattering. In the strangeness sector, the interaction with nucleons always comes through vector-meson exchange, which is evaluated by chiral and hidden gauge Lagrangians. For the interaction of charmed mesons with nucleons we extend the SU(3) Weinberg-Tomozawa Lagrangian to incorporate spin-flavor symmetry and implement a suitable flavor symmetry breaking. The in-medium solution for the scattering amplitude accounts for Pauli blocking effects and meson self-energies. On one hand, we obtain the $K$, $\bar K$ and $\bar K^*$ spectral functions in the nuclear medium and study their behaviour at finite density, temperature and momentum. We also make an estimate of the transparency ratio of the $\gamma A \to K^+ K^{*-} A^\prime$ reaction, which we propose as a tool to detect in-medium modifications of the $\bar K^*$ meson. On the other hand, in the charm sector, several resonances with negative parity are generated dynamically by the s-wave interaction between pseudoscalar and vector meson multiplets with $1/2^+$ and $3/2^+$ baryons. The properties of these states in matter are analyzed and their influence on the open-charm meson spectral functions is studied. We finally discuss the possible formation of $D$-mesic nuclei at FAIR energies.

In-medium vector mesons and low mass lepton pairs from heavy ion collisions

The ρ and ω meson self-energy at finite temperature and baryon density have been analysed for an exhaustive set of mesonic and baryonic loops in the real time formulation of thermal field theory. The large enhancement of spectral strength below the nominal ρ mass is seen to cause a substantial enhancement in dilepton pair yield in this mass region. The integrated yield after space-time evolution using relativistic hydrodynamics with quark gluon plasma in the initial state leads to a very good agreement with the experimental data from In-In collisions obtained by the NA60 collaboration.

D−mesic atoms

The anti-D meson self-energy is evaluated self-consistently, using unitarized coupled-channel theory, by computing the in-medium meson-baryon T-matrix in the C=-1,S=0 sector. The heavy pseudo-scalar and heavy vector mesons, anti-D and anti-D^*, are treated on equal footing as required by heavy quark spin symmetry. Results for energy levels and widths of D^- mesic atoms in 12C, 40Ca, 118Sn and 208Pb are presented. The spectrum contains states of atomic and of nuclear types for all nuclei. anti-D^0--nucleus bound states are also obtained. We find that, after electromagnetic and nuclear cascade, these systems end up with the anti-D bound in the nucleus, either as a meson or as part of a exotic anti-D N (pentaquark) loosely bound state.

ρ self-energy at finite temperature and density in the real-time formalism

The ρ meson self-energy in nuclear matter from baryonic loops is analysed in the real-time formulation of field theory at finite temperature and density. The discontinuities across the branch cuts of the self-energy function are evaluated for an exhaustive set of resonances in the loops considering the fully relativistic thermal baryon propagator including anti-baryons. Numerical calculations show a significant broadening of the ρ spectral function coming from the Landau cut. Adding the contribution from mesonic loops, the full spectral function of the ρ in a thermal gas of mesons, baryons and anti-baryons in equilibrium is evaluated at various values of temperature and baryonic chemical potential.

Open-charm mesons in nuclear matter at finite temperature beyond the zero-range approximation

The properties of open charm mesons, $D$, $\bar D$, $D_s$ and $\bar D_s$ in nuclear matter at finite temperature are studied within a self-consistent coupled-channel approach. The interaction of the low lying pseudoscalar mesons with the ground state baryons in the charm sector is derived from a $t$-channel vector-exchange model. The in-medium scattering amplitudes are obtained by solving the Lippmann-Schwinger equation at finite temperature including Pauli blocking effects, as well as $D$, $\bar D$, $D_s$ and $\bar D_s$ self-energies taking their mutual influence into account. We find that the in-medium properties of the $D$ meson are affected by the $D_s$-meson self-energy through the intermediate $D_s Y$ loops coupled to $DN$ states. Similarly, dressing the $\bar{D}$ meson in the $\bar{D}Y$ loops has an influence over the properties of the $\bar{D}_s$ meson.

Baryonic loop in theρ-meson self-energy

A relativistic formula is derived for the self-energy of $\ensuremath{\rho}$ meson in nuclear matter from a baryonic loop graph containing nucleon and $\ensuremath{\Delta}(1232)$. After identifying the Lindhard function, we find another term in it that contributes appreciably to the real part of the self-energy. We also note small errors that may appear in the numerical calculation owing to the use of incorrect $\ensuremath{\Delta}$ coupling with other fields and presence of quadratic distribution functions in the self-energy formula.

Strange Meson Production at High Density and Temperature

The properties of strange mesons ($K$, $\bar K$ and $\bar K^*$) in dense matter are studied using a unitary approach in coupled channels for meson-baryon scattering. The kaon-nucleon interaction incorporates $s$- and $p$-wave contributions within a chiral model whereas the interaction of $\bar K^*$ with nucleons is obtained in the framework of the local hidden gauge formalism. The in-medium solution for the scattering amplitude accounts for Pauli blocking effects, mean-field binding on baryons, and meson self-energies. We obtain the $K$, $\bar K$ and $\bar K^*$ (off-shell) spectral functions in the nuclear medium and study their behaviour at finite density, temperature and momentum. We also analyze the energy weighted sum rules of the kaon propagator as a quality test of model calculations. We finally estimate the transparency ratio of the $\gamma A \to K^+ K^{*-} A^\prime$ reaction, which we propose as a feasible scenario at present facilities to detect in-medium modifications of the $\bar K^*$ meson.

Charmed hadrons in nuclear medium

We study the properties of charmed hadrons in dense matter within a coupled-channel approach which accounts for Pauli blocking effects and meson self-energies in a self-consistent manner. We analyze the behaviour in this dense environment of dynamically-generated baryonic resonances as well as the open-charm meson spectral functions. We discuss the implications of the in-medium properties of open-charm mesons on the Ds0(2317) and the predicted X(3700) scalar resonances.

CHARM MESONS AT FAIR

The in-medium properties of charm mesons (D and [Formula: see text]) in a hot and dense matter are studied. A self-consistent coupled-channel approach is driven by a broken SU(4) s-wave Tomozawa-Weinberg interaction supplemented by an attractive isoscalar-scalar term. As medium effects, we include Pauli blocking, baryon mean-field bindings, and π and open-charm meson self-energies. The dynamically generated [Formula: see text] and [Formula: see text] resonances in the DN sector remain close to their free space position but acquire large widths. The resultant D meson spectral function, which shows a single pronounced quasiparticle peak close to the free mass that broadens with increasing density, also has a long low energy tail associated with smeared [Formula: see text], [Formula: see text] configurations. The low-density approximation for the [Formula: see text] is questionable already at subsaturation densities. We touch upon the implication of our study for J/Ψ suppression at FAIR.

Open charm in nuclear matter at finite temperature

We study the properties of open-charm mesons ($D$ and $\overline{D}$) in nuclear matter at finite temperature within a self-consistent coupled-channel approach. The meson-baryon interactions are adopted from a type of broken SU(4) $s$-wave Tomozawa-Weinberg term supplemented by an attractive scalar-isoscalar interaction. The in-medium solution at finite temperature incorporates Pauli blocking effects, mean-field binding on all the baryons involved, and \ensuremath{\pi} and open-charm meson self-energies in a self-consistent manner. In the $\mathit{DN}$ sector, the ${\ensuremath{\Lambda}}_{c}$ and ${\ensuremath{\Sigma}}_{c}$ resonances, generated dynamically at 2593 and 2770 MeV in free space, remain close to their free-space position while acquiring a remarkable width due to the thermal smearing of Pauli blocking as well as from the nuclear matter density effects. As a result, the $D$ meson spectral density shows a single pronounced peak for energies close to the $D$ meson free-space mass that broadens with increasing matter density with an extended tail particularly toward lower energies. The $\overline{D}$ potential shows a moderate repulsive behavior coming from the dominant $I=1$ contribution of the $\overline{D}N$ interaction. The low-density theorem is, however, not a good approximation for the $\overline{D}$ self-energy in spite of the absence of resonance-hole contributions close to threshold in this case. We speculate the possibility of $D$-mesic nuclei as well as discuss some consequences for the $J/\ensuremath{\Psi}$ suppression in heavy-ion collisions, in particular for the future CBM experiment at FAIR.

In-medium modification and decay asymmetry of ω mesons in cold nuclear matter

We discuss an asymmetry of the decay {omega}{yields}e{sup +}e{sup -} in nuclear matter with respect to the electron and positron energies. This asymmetry is sensitive to the properties of the {omega} meson self-energy and, in particular, it has a nontrivial dependence on the {omega} energy and momentum. Therefore, this asymmetry may serve as a powerful tool in studying the properties of the {omega} meson in the nuclear medium.

The In-Medium \barK NInteraction within a Chiral Unitary Approach

The s- and p-wave contributions to the \barK N interaction in dense nuclear matter are obtained using a chiral unitary approach. We perform a self-consistent calculation of the \barK self-energy including Pauli blocking effects, meson self-energies modified by short-range correlations and baryon binding potentials. We find that the on-shell factorization cannot be applied to evaluate the in-medium corrections to p-wave amplitudes. Furthermore, the Λ and Σ develop a mass shift of -30 MeV at saturation density while the Σ* width increases to 80 MeV. We conclude that no deep and narrow \barK bound states could be observed.