A. Ohnishi, N. Kawamoto, K. Miura
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.
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The scalar and vector self-energies obtained through QCD sum rules are introduced in Quantum Hadrodynamics (QHD) equations. The results indicate that the ratios of coupling constants to respective meson mass have a very small dependence on density. Then, an extended Brown-Rho scaling law is conjectured.
We present a description of symmetric nuclear matter within the framework of Landau Fermi liquid theory. The low momentum nucleon-nucleon interaction V(low-k) is used to calculate the effective interaction between quasiparticles on the Fermi surface, from which we extract the quasiparticle effective mass, the nuclear compression modulus, the symmetry energy, and the anomalous orbital gyromagnetic ratio. The exchange of density, spin, and isospin collective excitations is included through the Babu-Brown induced interaction, and it is found that in the absence of three-body forces the self-consi…
Core-polarization (CP) and Brown-Rho (BR) scaling were among Gerry's most favorite topics. In this contribution, we will discuss some of the early history as well as more recent work associated with these two fascinating phenomena. I (TTSK) will begin with some recollections of Princeton, where I met Gerry for the first time in 1964 and worked as his postdoc. Core polarization was in fact the first topic he assigned to me. JWH started working with Gerry at Stony Brook from 2003 and was Gerry's last student in nuclear physics. We three had teamed up well, working closely on both CP and BR scali…
We present a combined analysis of the in-medium behavior of rho and omega mesons within the Borel QCD sum rule taking into account finite widths.
Relationships between mass intervals for free hadrons and in nuclei are studied in two theoretical approaches inspired by QCD: naive quark model and skyrmion model, taking one example each from mesons and baryons, that of pi-rho splitting in mesons, and nucleon-Delta splitting in baryons. Possible deconfinement effects in nuclei are examined.
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 factoriza…
We present shell model calculations for the beta-decay of the 14C ground state to the 14N ground state, treating the states of the A=14 multiplet as two 0p holes in an 16O core. We employ low-momentum nucleon-nucleon (NN) interactions derived from the realistic Bonn-B potential and find that the Gamow-Teller matrix element is too large to describe the known lifetime. By using a modified version of this potential that incorporates the effects of Brown-Rho scaling medium modifications, we find that the GT matrix element vanishes for a nuclear density around 85% that of nuclear matter. We find th…
We study the role of density-dependent low-momentum nucleon-nucleon interactions in describing the anomalously long beta decay lifetime of 14C. We approach this problem both from the perspective of chiral effective field theory, in which genuine three-body forces generate an effective density-dependent two-body interaction, as well as from the perspective of Brown-Rho scaling, in which the masses and form factor cutoffs in one-boson-exchange interactions are modified in a dense nuclear medium due to the partial restoration of chiral symmetry. The beta decay transition of 14C to the ground stat…
Recent work reported at the Quark Matter Conference 2005 has led to the suggestion that Brown-Rho scaling is ruled out by the NA60 data. (Brown-Rho scaling describes the reduction of hadronic masses in matter and at finite temperature.) In the present work we argue that the interpretation of the experimental data presented at the Quark Matter Conference is not correct and that Brown-Rho scaling is valid. To make this argument we discuss the evolution in time of the excited hadronic system and suggest that the system is deconfined at the earliest times and becomes confined when the density and …
Model-space effective interactions $V_{eff}$ derived from free-space nucleon-nucleon interactions $V_{NN}$ are reviewed. We employ a double decimation approach: first we extract a low-momentum interaction $V_{low-k}$ from $V_{NN}$ using a $T$-matrix equivalence decimation method. Then $V_{eff}$ is obtained from $V_{low-k}$ by way of a folded-diagram effective interaction method. For decimation momentum $Λ\simeq 2 fm^{-1}$, the $V_{low-k}$ interactions derived from different realistic $V_{NN}$ models are nearly model independent, and so are the resulting shell-model effective interactions. For …
Neutron star properties, such as its mass, radius, and moment of inertia, are calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations using the ring-diagram equation of state (EOS) obtained from realistic low-momentum NN interactions $V_{low-k}$. Several NN potentials (CDBonn, Nijmegen, Argonne V18 and BonnA) have been employed to calculate the ring-diagram EOS where the particle-particle hole-hole ring diagrams are summed to all orders. The proton fractions for different radial regions of a $β$-stable neutron star are determined from the chemical potential conditions $μ_n-μ_p = μ_…
We have calculated the nuclear symmetry energy $E_{sym}(ρ)$ up to densities of $4 \sim 5 ρ_0$ with the effects from the Brown-Rho (BR) and Ericson scalings for the in-medium mesons included. Using the $V_{low-k}$ low-momentum interaction with and without such scalings, the equations of state (EOS) of symmetric and asymmetric nuclear matter have been calculated using a ring-diagarm formalism where the particle-particle-hole-hole ring diagrams are included to all orders. The EOS for symmetric nuclear matter and neutron matter obtained with linear BR scaling are both overly stiff compared with th…
In connection with the claim made at the Quark Matter 2005 Conference that the Brown-Rho scaling is ruled out by NA60 data we consider dimuon production from semi-central In+In collisions in a full dynamical model. It is shown that if only a modification of the density-dependent $ρ$-mass is allowed, the maximum of dimuon invariant mass spectra is only slightly below experimental one. The additional inclusion of the temperature-dependent modification factor shifts the spectrum maximum toward lower invariant masses making calculation results incompatible with data. A further study is needed to d…
QCD sum rules are studied for the vector-isovector current at finite baryon density in the limit of large number of colors N_c. For the condensate side it is shown that in this limit the four-quark condensate factorizes also for the finite density case. At the hadronic side the medium dependence is expressed in terms of the current-nucleon forward scattering amplitude. Generalizing vector meson dominance we allow for a direct coupling of the current to the nucleon as well as a coupling via the rho meson. We discuss the N_c dependence of (a) modifications of the pion cloud of the rho meson, (b)…
The medium modified hadron properties are studied by using the scale-chiral perturbation theory $χ$PT$_σ$ in which the lightest scalar meson $f_0(500)$ is included as an explicit degree of freedom by regarding it as the Nambu-Goldstone boson of scale symmetry both spontaneously broken and explicitly broken by the QCD trace anomaly. We derive Brown-Rho scaling at the leading order of scale symmetry from $χ$PT$_σ$ and formulate how to make higher-order scale-chiral corrections going beyond the leading order of scale symmetry. By taking into account the intrinsic density dependence given by the d…
We use classical/large Nc (number of colors) QCD to study nucleon--antinucleon annihilation at rest. We include pion, rho and omega fields in the classical dynamics, starting from the nonlinear sigma model. We begin with a spherical blob of pionic matter with zero baryon number and energy of twice the nucleon mass. This evolves according to the classical dynamics to pion and vector meson fields into the radiation zone. The radiation fields are quantized using the method of coherent states modified to include isospin and four momentum conservation. Empirical information is extracted from that c…
Recent developments in our description of RHIC and related heavy-ion phenomena in terms of hidden local symmetry theories are reviewed with a focus on the novel nearly massless states in the vicinity of -- both below and above -- the chiral restoration temperature T_c. We present complementary and intuitive ways to understand both Harada-Yamawaki's vector manifestation structure and Brown-Rho scaling -- which are closely related -- in terms of "melting" of soft glues observed in lattice calculations and join the massless modes that arise in the vector manifestation (in the chiral limit) just b…
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.
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 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.
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-…
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.
Analytical solutions of dispersion relations in the nuclear optical model have been found for both imaginary volume and surface potentials. A standard Brown-Rho shape has been assumed for the volume imaginary term and a Brown-Rho shape multiplied by a decreasing exponential for the surface contribution. The analytical solutions are valid for any even value of the exponent appearing in these functional forms.
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.
Thermal Finite Energy QCD sum rules for the vector current correlator are used to study quark-gluon deconfinement. Assuming $ρ$-meson saturation of the correlator in the hadronic sector, and the Operator Product Expansion in QCD, we obtain the temperature behavior of the resonance parameters (coupling, mass, and width), and of the leading vacuum condensates, as well as the perturbative QCD threshold in the complex squared energy plane. The results are consistent with quark-gluon deconfinement at a critical temperature $T_c \simeq 197 MeV$. The temperature dependence of the $ρ$-meson width is o…
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 discuss the similarities and differences for the theories of Rapp, Wambach and collaborators (called R/W in short) and those based on Brown-Rho scaling (called B/R), as applied to reproduce the dileptons measured by the CERES collaboration in the CERN experiments. In both theories the large number of dileptons at invariant masses $\sim$~$m_ρ/2$ are shown to be chiefly produced by a density-dependent $ρ$-meson mass. In R/W the medium dependence is dynamically calculated using hadronic variables defined in the matter-free vacuum. In B/R scaling it follows from movement towards chiral symmetry…
We compute the dimuon-excess invariant mass distribution at the rho-meson peak in the context of relativistic heavy-ion collisions at SPS energies. The temperature, T, and chemical potential, mu, dependent parameters describing the rho-meson --its width, mass and leptonic decay constant-- are determined from finite energy QCD sum rules. Results show that the rho-meson width increases whereas its mass and leptonic decay constant decrease near the (chemical potential-dependent) critical temperature T_c(mu) for chiral symmetry restoration/quark-gluon deconfinement. As a consequence, starting from…
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 perform a high-precision calculation of the phase shifts for $π$-$π$ scattering in the I = 1, J = 1 channel in the elastic region using elongated lattices with two mass-degenerate quark favors ($N_f = 2$). We extract the $ρ$ resonance parameters using a Breit-Wigner fit at two different quark masses, corresponding to $m_π = 226$MeV and $m_π = 315$MeV, and perform an extrapolation to the physical point. The extrapolation is based on a unitarized chiral perturbation theory model that describes well the phase-shifts around the resonance for both quark masses. We find that the extrapolated valu…
The QCD sum rule method is applied to derive a formula for the rho, omega, phi meson-nucleon spin-isospin-averaged scattering lengths $a_{ρ,ω,ϕ}$. We found that the crucial matrix elements are $\langle\bar{q}γ_μD_νq\rangle_N$ ($q=u,d$) (twist-2 nucleon matrix element) for $a_{ρ,ω}$ and $m_s\langle\bar{s}s\rangle_N$ for $a_ϕ$, and obtained $a_ρ=0.14\pm 0.07$ fm, $a_ω=0.11\pm 0.06$ fm and $a_ϕ=0.035\pm 0.020$ fm. These small numbers originate from a common factor $1/(m_N+m_{ρ,ω,ϕ})$. Our result suggests a slight increase ($< 60$ MeV for $ρ$, $ω$, and $<15$ MeV for $ϕ$) of the effective mass of t…
The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the non-perturbatively determined physical state. It is then possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark component of a meson in the infrared, where mass is generated. Using a unitary transformation from the chiral basis to the LSJ basis one may extract a partial wave content of a meson. We present results for the ground state of the rho-meson using quenched simulations as well as simulat…
In simulations with dynamical quarks it has been established that the ground state rho in the infrared is a strong mixture of the two chiral representations (0,1)+(1,0) and (1/2,1/2)_b. Its angular momentum content is approximately the 3S1 partial wave which is consistent with the quark model. Effective chiral restoration in an excited rho-meson would require that in the infrared this meson couples predominantly to one of the two representations. The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the non-perturbatively dete…
QCD phase transition at finite isospin density and magnetic field
本文基于扩展的两味Nambu-Jona-Lasinio模型，在有限异ospin密度和磁场下研究QCD相变，通过Ginzburg-Landau近似分析从正常 chiral 对称破缺相到π超流或ρ超导相的转变，发现磁场大小影响超流和超导相的倾向。
Tomography of the Rho meson in the QCD Instanton Vacuum: Transverse Momentum Dependent Parton Distribution Functions
本研究在瞬子液体模型中分析ρ介子的横动量依赖部分子分布函数，推导其近似形式与分布特征，并通过演化得到高快度、高分辨率下的偏斜特性。
Phases of cold holographic QCD: baryons, pions and rho mesons
本研究在Witten-Sakai-Sugimoto模型中改进冷全息QCD的重子物质全息描述，纳入实际π介子质量、动态π凝聚与各向异性规范场引入的ρ凝聚，得到零温相图，揭示重子密度对π凝聚的抑制、ρ凝聚的出现条件及非单调相边界等特性。
Finite energy sum rules for vector and axial-vector currents are derived in a thermal medium to provide constraints for the spectral behavior of rho and a1 mesons at nonvanishing temperature and hence to study the tendency toward chiral symmetry restoration. The parity-mixing ansatz for the rho and a1 spectra, including finite widths, is investigated as a function of temperature. Characteristic differences between vector and axial-vector channels are discussed with regard to the implementation of the chiral-symmetry-breaking scale, 4pi times the pion decay constant, in the sum rule approach.
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.
Based on an effective Lagrangian which combines chiral SU(3) dynamics with vector meson dominance, we have developed a model for the forward vector meson-nucleon scattering amplitudes. We use this as an input to calculate the low energy part of the current-current correlation function in nuclear matter. Its spectrum enters directly in the ``left hand side'' of QCD sum rules. For the isovector channel we find a significant enhancement of the in-medium spectral density below the rho resonance while the rho meson mass itself changes only slightly. The situation is different in the isoscalar chann…
Rotational Brownian motion and heavy quark polarization in QCD medium
研究QCD介质中重夸克的旋转布朗运动，分析其极化特性，并提出横动量依赖性作为强磁场的标志。
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,…
We study selected meson transition processes and associated form factors within a model of QCD based on the Dyson--Schwinger equations truncated to ladder-rainbow level. The infrared structure of the ladder-rainbow kernel is described by two parameters; the ultraviolet behavior is fixed by the one-loop renormalization group behavior of QCD. The work is restricted to the u and d quark sector and allows a Poincare'-covariant study of the radiative decays: rho -> pi + gamma, omega -> pi + gamma, and pi^0 -> gamma + gamma. Particular attention is paid to the form factors for the associated transit…
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 …
The photonuclear production of vector mesons in ultraperipheral heavy ion collisions is investigated within the QCD color dipole picture, with particular emphasis on the saturation model. The integrated cross section and the rapidity distribution for the A + A --> V + A + A (V = rho, omega, phi, J/Psi) process are computed and theoretical estimates for scattering on both light and heavy nuclei are given for energies of RHIC and LHC. A comparison with the recent STAR data on coherent production of rho mesons is also presented. Furthermore, we calculate the photoproduction of vector mesons in pr…
By extending the Bielefeld LGS (Lattice Gauge Simulation) color singlet interaction, we find that the masses of pi, sigma, rho and a_1 excitations, 32 degrees of freedom in all, go to zero (in the chiral limit) as T -> T_c. This result indicates a smooth phase transition at T_c, at which from above the masses and couplings of mesons vanish `a la Brown-Rho scaling. We discuss that our scenario successfully explains the STAR (STAR Collaboration) rho^0/pi^- ratio in Au-Au peripheral collisions at RHIC.
Within the framework of a holographic dual model of QCD, we develop a formalism for calculating form factors of vector mesons. We show that the holographic bound states can be described not only in terms of eigenfunctions of the equation of motion, but also in terms of conjugate wave functions that are close analogues of quantum-mechanical bound state wave functions. We derive a generalized VMD representation for form factors, and find a very specific VMD pattern, in which form factors are essentially given by contributions due to the first two bound states in the Q^2-channel. We calculate ele…
Utilizing in-medium vector spectral functions which describe dilepton data in ultra-relativistic heavy-ion collisions, we conduct a comprehensive evaluation of QCD and Weinberg sum rules at finite temperature. The starting point is our recent study in vacuum, where the sum rules have been quantitatively satisfied using phenomenological axial-/vector spectral functions which describe hadronic tau-decay data. In the medium, the temperature dependence of condensates and chiral order parameters is taken from thermal lattice QCD where available, and otherwise estimated from a hadron resonance gas. …
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…
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