In-medium Mass Shift Research Articles

Antikaon-induced K1(1270)+ meson production on nuclei near threshold

We study the inclusive strange axial-vector meson K1(1270)+ production in K−A reactions at near-threshold laboratory incident antikaon momenta within a nuclear spectral function approach, which describes incoherent direct K1(1270)+ meson production in K− meson–proton K−p→K1(1270)+Ξ− production processes and accounts for three different options for its in-medium mass shift (or for its effective scalar potential) at central density ρ0. We calculate the absolute differential and total cross sections for the production of K1(1270)+ mesons on 12C and 184W target nuclei at laboratory angles of 0∘–45∘ by K− mesons with momenta of 2.5, 2.8 and 3.5 GeV/c, which are close to the threshold momentum (≈ 2.95 GeV/c) for K1(1270)+ meson production off the free target proton at rest. The intrinsic properties of carbon and tungsten target nuclei have been described in terms of their spectral functions, which take into account the momenta of target protons and the energies of their separation from the considered nuclei. We show that the differential and total (absolute and relative) K1(1270)+ antikaon-induced production cross sections at initial momenta not far from threshold – at momenta ∼ 2.8–3.5 GeV/c, at which there is yet no strong drop in their strength, reveal a distinct sensitivity to changes in the in-medium shift of the K1(1270)+ mass, studied in the paper, both in the K1(1270)+ meson low-momentum (0.1–1.0 GeV/c) and in its full-momentum ranges. This would permit evaluating this shift. Experimental data necessary for this aim can be obtained in a dedicated experiment at the J-PARC Hadron Experimental Facility.

Near-threshold K*(892)+ meson production in the interaction of π− mesons with nuclei

We study the inclusive production of strange vector mesons in reactions at near-threshold laboratory incident pion momenta of 1.4–2.0 GeV/c via a nuclear spectral function approach. The approach accounts for incoherent primary meson–proton production processes as well as the influence of the scalar –nucleus potential (or the in-medium mass shift) on these processes. We calculate the absolute differential and total cross sections for the production of mesons from carbon and tungsten nuclei at laboratory angles of 0 –45 and at the aforementioned momenta in five scenarios for the aforenoted shift. We show that the momentum distributions and their excitation functions (absolute and relative) possess a high sensitivity to changes in the in-medium mass shift in the low-momentum region of 0.1–0.6 GeV/c. Therefore, the measurement of such observables in a dedicated experiment at the GSI pion beam facility in the near-threshold momentum domain will allow us to get valuable information on the in-medium properties.

Effect of in-medium mass-shift on transverse-momentum spectrum and elliptic anisotropy of ϕ meson

We study the effect of in-medium mass-shift on transverse-momentum spectrum and elliptic anisotropy of [Formula: see text] meson. It is found that the mass-shift enhances the [Formula: see text] yields and suppresses the elliptic flow [Formula: see text] in large momentum region, and the effects increase with the increasing mass-shift. The effects are various for different sources and decrease with the increasing collision energy. We further study the effects for parts of all [Formula: see text] meson with mass-shift, and the effects decrease with the decreasing probability of [Formula: see text] meson with mass-shift. A possible method to detect the mass-shift of [Formula: see text] meson via transverse-momentum spectrum and [Formula: see text] is proposed.

Charmonia and bottomonia in asymmetric magnetized hot nuclear matter

We investigate the mass-shift of P-wave charmonium ( , ), and S and P-wave bottomonium ( , , , and ) states in magnetized hot asymmetric nuclear matter using the unification of QCD sum rules (QCDSR) and the chiral model. Within QCDSR, we use two approaches, i.e., the moment sum rule and the Borel sum rule. The magnetic field induced scalar gluon condensate and the twist-2 gluon operator calculated in the chiral ) model are utilised in QCD sum rules to calculate the in-medium mass-shift of the above mesons. The attractive mass-shift of these mesons is observed, which is more sensitive to magnetic field in the high density regime for charmonium, however less so for bottomonium. These results may be helpful to understand the decay of higher quarkonium states to the lower quarkonium states in asymmetric heavy ion collision experiments.

Momentum dependence of pion-induced ϕ meson production on nuclei near threshold

We study the near-threshold pion-induced production of ϕ mesons off nuclei in the kinematical conditions of the HADES experiment, recently performed at GSI. The calculations have been performed within a collision model based on the nuclear spectral function. The model accounts for both the primary π− meson–proton π−p → ϕn and the secondary pion–nucleon πN → ϕN ϕ production processes as well as the effects of the nuclear ϕ and nucleon mean-field potentials. We find that the primary reaction channel π−p → ϕn dominates in the ϕ production off 12C and 184W target nuclei in the HADES acceptance window at incident pion momentum of 1.7 GeV/c. We calculate the momentum dependence of the absolute and relative (transparency ratio) ϕ meson yields from the above direct channel. The calculations have been performed for this initial pion momentum allowing for different options for the ϕN absorption cross section σϕN and different scenarios for the in-medium mass shifts of the ϕ meson and secondary neutron, produced together with ϕ in this channel. We demonstrate that the transparency ratio for the ϕ mesons has, contrary to the absolute cross sections, an insignificant sensitivity to the ϕ meson and secondary neutron in-medium mass shifts at ϕ momenta studied in the HADES experiment. On the other hand, we show that there are measurable changes in the transparency ratio due to the ϕN absorption cross section, which means that such a relative observable can be useful to help determine this cross section from the data taken in the HADES experiment.

Mass shift of charmonium states in [formula omitted] collision

The masses of the low lying charmonium states, namely, the J/Ψ, Ψ(3686), and Ψ(3770) are shifted downwards due to the second order Stark effect. In p¯+Au collisions at 6–10 GeV we study their in-medium propagation. The time evolution of the spectral functions of these charmonium states is studied with a Boltzmann–Uehling–Uhlenbeck (BUU) type transport model. We show that their in-medium mass shift can be observed in the dilepton spectrum. Therefore, by observing the dileptonic decay channel of these low lying charmonium states, especially for Ψ(3686), we can gain information about the magnitude of the gluon condensate in nuclear matter. This measurement could be performed at the upcoming PANDA experiment at FAIR.

Momentum dependence of J/ψ production in proton–nucleus reactions at near-threshold beam energies

We study the inclusive J/ψ production in proton–nucleus collisions in the near-threshold energy region within the spectral function approach for incoherent primary proton–nucleon charmonium production. Our approach takes into account the effect of the nuclear J/ψ mean-field potential on these processes, as well as the elementary final state interaction (FSI) between the outgoing nucleons participating in them. We calculate the momentum dependence of the various J/ψ observables (transparency ratio, absolute and relative charmonium yields) as well as the total cross section for J/ψ production in pC, pW and pAu interactions at incident proton kinetic energies of 8, 11 and 23 GeV within the different scenarios for the J/ψ in-medium modification. We show that the transparency ratio for J/ψ mesons has an insignificant sensitivity to the J/ψ in-medium mass shift at these energies. On the other hand, our studies demonstrate that the momentum distributions (absolute and relative) for low momentum J/ψ near-threshold production in pA reactions have distinct sensitivity to the J/ψ in-medium modification. Therefore, the measurement of such observables in the CBM experiment at FAIR in the near-threshold energy domain will allow to study the modification of the charmonium properties in the nuclear medium.

In-medium properties of mesons

In the project B.4 , the modification of meson properties (mass, width) in a nuclear medium has been studied in photoproduction of mesons off nuclear targets. This work has been motivated by theoretical expectations of in-medium modifications of hadrons based on the conjecture of a partial restoration of chiral symmetry in a strongly interacting medium. It has been shown that these in-medium changes can be discussed in a compact form in terms of an optical potential describing the meson-nucleus interaction. Experimental approaches to determine the real and imaginary part of the meson-nucleus potential have been developed. The experiments have been performed with the Crystal Barrel/TAPS detector at the electron accelerator ELSA (Bonn) and the Crystal Ball/TAPS detector at MAMI (Mainz). Measuring the excitation function and momentum distribution for photo production of ω and η′ mesons, the real parts of the ω and η′ -nucleus potential, given by the in-medium mass shift, have been determined. For the η′ meson a lowering of the mass at normal nuclear matter density by -(39±7(stat)±15(syst)) MeV is observed, while for the ω meson a slightly smaller mass shift is found, however, with much larger uncertainties, not excluding a zero mass shift. The imaginary part of the potentials has been extracted from the measurement of the transparency ratio which compares the meson production cross section per nucleon within a nucleus to the production cross section off the free proton. For the η′ meson the imaginary part of the potential is found to be smaller than the real part. In case of the ω meson the opposite is observed. This makes the η′ meson a good candidate for the search for meson-nucleus bound states while no resolved ω mesic states can be expected. The results are compared with theoretical predictions. An outlook on future experiments is given.

Study of in-medium properties in the (γ, ) reaction on nuclei

We study the near-threshold photoproduction of mesons from nuclei in coincidence with forward going protons in the kinematical conditions of the Crystal Barrel/TAPS experiment, recently performed at ELSA. The calculations have been performed within a collision model based on the nuclear spectral function. The model accounts for both the primary process and the two-step intermediate nucleon rescattering processes as well as the effect of the nuclear mean-field potential. We calculate the exclusive kinetic energy distributions for the 12C(γ, ) reaction for different scenarios of in-medium modification. We find that the considered two-step rescattering mechanism plays an insignificant role in photoproduction off the carbon target. We also demonstrate that the calculated kinetic energy distributions in primary photon–proton production reveal strong sensitivity to the depth of the real potential at normal nuclear matter density (or to the in-medium mass shift) in the studied incident photon energy regime. Therefore, such observables may be useful to help determine the above in-medium renormalization from the comparison of the results of our calculations with the data from the CBELSA/TAPS experiment. In addition, we show that these distributions are also strongly influenced by the momentum-dependent optical potential, which the outgoing participant proton feels inside the carbon nucleus. This potential should be taken into account in the analysis of these data with the aim to obtain information on the modification in cold nuclear matter.

In-medium Properties of Hadrons

An overview is given over recent results on in-medium properties of hadrons, obtained in experiments with photon, proton and deuteron beams at ANKE, CBELSA/TAPS, Crystal Ball, HADES, and BigRIPS. These experiments focus on identifying spectral inmedium modifications of hadrons, frequently discussed in the context of a partial restoration of chiral symmetry at finite nuclear densities. Three experimental approaches are presented: the measurement of the transparency ratio, the meson line shape analysis, and the search for meson-nucleus bound states. Results for ω, ϕ, and η' mesons indicate a broadening in the nuclear medium. Corresponding inelastic in-medium meson-nucleon cross sections have been extracted. Evidence for an in-medium mass shift has not been reported. Further information on the meson-nucleus interaction is derived from a spectroscopy of meson-nucleus bound states. A critical comparison of the results with theoretical predictions is presented.

In-mediumωmass from theγ+Nb→π0γ+Xreaction

Data on the photoproduction of $\omega$ mesons on nuclei have been re-analyzed in a search for in-medium modifications. The data were taken with the Crystal Barrel(CB)/TAPS detector system at the ELSA accelerator facility in Bonn. First results from the analysis of the data set were published by D. Trnka et al. in Phys. Rev. Lett 94 (2005) 192303 \cite{david}, claiming a lowering of the $\omega$ mass in the nuclear medium by 14$%$ at normal nuclear matter density. The extracted $\omega$ line shape was found to be sensitive to the background subtraction. For this reason a re-analysis of the same data set has been initiated and a new method has been developed to reduce the background and to determine the shape and absolute magnitude of the background directly from the data. Details of the re-analysis and of the background determination are described. The $\omega$ signal on the $Nb$ target, extracted in the re-analysis, does not show a deviation from the corresponding line shape on a $LH_2$ target, measured as reference. The earlier claim of an in-medium mass shift is thus not confirmed. The sensitivity of the $\omega$ line shape to different in-medium modification scenarios is discussed.

Squeezed correlations of strange particles–antiparticles

Squeezed correlations of hadron–antihadron pairs are predicted to appear if their masses are modified in the hot and dense medium formed in high-energy heavy ion collisions. If discovered experimentally, they would be an unequivocal evidence of in-medium mass shift found by means of hadronic probes. We discuss a method proposed to search for this novel type of correlation, illustrating it by means of Ds-mesons with in-medium shifted masses. These particles are expected to be more easily detected and identified in future upgrades at RHIC.

Finite-temperature spectral function of the vector mesons in a holographic QCD model

We use the soft-wall anti--de Sitter/QCD model to investigate the finite-temperature effects on the spectral function in the vector channel. The dissociation of the vector meson tower onto the anti--de Sitter black hole leads to the in-medium mass shift and the width broadening in a way similar to the lattice QCD results for the heavy quarkonium at finite temperature. We also show the momentum dependence of the spectral function and find it consistent with screening in a hot wind.

Quarkonium transport in thermal AdS/CFT

We consider a heavy meson moving slowly through high temperature non-Abelian plasmas. Using a simple dipole effective Lagrangian, we calculate the in-medium mass shift and the drag coefficient of the meson in = 4 Super Yang Mills theory at weak and strong coupling. As anticipated, in the large N limit the mass shift is finite while the drag is suppressed by 1/N2 . After comparing results to perturbative QCD estimates (which are also calculated), we reach the conclusion that relative to weak coupling expectations the effect of strong coupling is to reduce the momentum diffusion rate and to increase the relaxation time by up to a factor of four.

Medium modifications of mesons in elementary reactions and heavy-ion collisions

Experimental searches for modifications of vector mesons in the nuclear medium are reviewed. Data on ρ , ω and Φ mesons are presented. The results have been obtained in elementary reactions with proton and photon beams as well as in heavy-ion collisions. Compared to the free particle properties, the ω and Φ mesons are found to have a drop in mass at normal nuclear matter density by 9%–14% and 3.5% whereas their widths are reported to increase by factors of about 16 and 3.6, respectively. For the ρ meson, conflicting results on in-medium mass shifts and broadening have been published. The experimental data are compared to recent model calculations.

Medium modifications of vector mesons in elementary reactions and heavy-ion collisions

The current status of experimental searches for modifications of vector mesons in the nuclear medium is reviewed. Results on ρ, ω and Φ mesons are presented, obtained in elementary reactions with proton and photon beams as well as in heavy-ion collisions. At normal nuclear matter density, ω and Φ mesons are found to be lowered in mass by 9–14% and 3.5% and broadened by about factors 10 and 3.6, respectively, compared to the free particle properties. For the ρ meson, conflicting results on in-medium mass shifts and broadening have been reported by different experiments.

What does the ρ-meson do? In-medium mass shift scenarios versus hadronic model calculations

The NA60 experiment has studied low-mass muon pair production in In–In collisions at 158 A GeV with unprecedented precision. With these results there is hope that the in-medium modifications of the vector meson spectral function can be constrained more thoroughly than before. We investigate in particular what can be learned about collisional broadening by a hot and dense medium and what constraints the experimental results put on in-medium mass shift scenarios. The data show a clear indication of considerable in-medium broadening effects but disfavor mass shift scenarios where the ρ-meson mass scales with the square root of the chiral condensate. Scaling scenarios which predict at finite density a dropping of the ρ-meson mass that is stronger than that of the quark condensate are clearly ruled out since they are also accompanied by a sharpening of the spectral function.

Evaluation of QCD sum rules for light vector mesons at finite density and temperature

QCD sum rules are evaluated at finite nucleon densities and temperatures to determine the change of mass parameters for the lightest vector mesons ρ, ω and φ in a strongly interacting medium. For conditions relevant for the starting experiments at HADES we find that the in-medium mass shifts of the ρ- and ω-mesons are governed, within the Borel QCD sum rule approach, by the density and temperature dependence of the four-quark condensate. In particular, the variation of the strength of the density dependence of the four-quark condensate reflects directly the decreasing mass of the ρ-meson and can lead to a change of the sign of the ω-meson mass shift as a function of the density. In contrast, the in-medium mass of the φ-meson is directly related to the chiral strange quark condensate which seems correspondingly accessible.

Coulomb distortion and experimental mass resolution in dielectron spectroscopy at relativistic energy

We present a classical estimate of the Coulomb effect on dielectron invariant mass measurements at intermediate energy (about 1 GeV). Simplified simulations of the reactions π −(1.3 GeV/c)+ Au→ ω+ X and Au(1−1.6 GeV/ A)+ Au→ ω+ X are used for both the Coulomb distortion estimate and the investigation of the capability for ω in-medium mass shift observation. The Coulomb distortion is found at the 1% level, similar to typical experimental resolutions. Direct mass shift observation is significantly obscured, and the hadronic medium effect mostly translates into a weakening of the ω outside decay peak.

Model independent constraints from vacuum and in-medium QCD Sum Rules

We discuss QCD sum rule constraints based on moments of vector meson spectral distributions in the vacuum and in a nuclear medium. Sum rules for the two lowest moments of these spectral distributions do not suffer from uncertainties related to QCD condensates of dimension higher than four. We exemplify these relations for the case of the omega meson and discuss the issue of in-medium mass shifts from this viewpoint.