Meson Propagators Research Articles

Thermal dielectron measurements in Au+Au collisions at √SNN = 7.7, 14.6, and 19.6 GeV with the STAR experiment

Dielectrons emitted during the evolution of the hot and dense QCD medium created in relativistic heavy-ion collisions offer an effective way to probe the medium properties, as they do not interact via the strong force. The rate of the dielectron emission is proportional to the medium’s electromagnetic spectral function. In the dielectron invariant mass range from 400 MeV/c2 to 800 MeV/c2, the spectral function probes the in-medium ρ meson propagator which is sensitive to the medium’s properties including the total baryon density and the temperature. Meanwhile, the low energy range of the spectral function provides information about the medium’s electrical conductivity. Therefore, by measuring thermal dielectron production, we can study the microscopic interactions between the electromagnetic current and the medium. The STAR experiment has recorded large datasets of Au+Au collisions during the Beam Energy Scan Phase-II (BES-II) program, spanning center-of-mass energies between √SNN = 3.0 and 19.6 GeV with detector upgrades that benefit the dielectron measurement via extended transverse momentum and rapidity coverages as well as enhanced particle identification capability. In these proceedings, we will report on the measurements of thermal dielectrons produced in Au+Au collisions at √SNN = 7.7, 14.6, and 19.6 GeV using the STAR experiment.

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.

Pomeron and Reggeon contributions to elastic proton-proton and proton-antiproton scattering in holographic QCD

The total and differential cross sections of elastic proton-proton and proton-antiproton scattering are studied in a holographic QCD model, considering the Pomeron and Reggeon exchanges in the Regge regime. In our model setup, the Pomeron and Reggeon exchanges are described by the Reggeized spin-2 glueball and vector meson propagators, respectively. How those contributions change with the energy is explicitly shown, focusing on the contribution ratios. The adjustable parameters included in the model are determined with the experimental data, and it is presented that the resulting total and differential cross sections are consistent with the data in a wide kinematic region.

Lack of thermalization in (1+1)-d quantum chromodynamics at large Nc

Motivated by recent works aimed at understanding the status of equilibration and the eigenstate thermalization hypothesis in theories with confinement, we return to the ’t Hooft model, the large-Nc limit of (1 + 1)-d quantum chromodynamics. This limit has been studied extensively since its inception in the mid-1970s, with various exact results being known, such as the quark and meson propagators, the quark-antiquark interaction vertex, and the meson decay amplitude. We then argue this model is an ideal laboratory to study non-equilibrium phenomena, since it is manifestly non-integrable, yet one retains a high level of analytic control through large-Nc diagrammatics. We first elucidate what are the non-equilibrium manifestations of the phenomenon of large-Nc volume independence. We then find that within the confined phase, there is a class of initial states that lead to a violation of the eigenstate thermalization hypothesis, i.e. the system never thermalizes. This is due to the existence of heavy mesons with an extensive amount of energy, a phenomenon that has been numerically observed recently in the quantum Ising chain.

In-medium thermal conductivity and diffusion coefficients of a hot hadronic gas mixture

The relativistic kinetic theory approach has been employed to estimate for a hot mixture constituting of nucleons and pions, four transport coefficients that characterize heat flow and diffusion. Medium effects on the cross-section for binary collisions ([Formula: see text]) have been taken into consideration by incorporating self-energy corrections to modify the [Formula: see text] and [Formula: see text] meson propagators for [Formula: see text] interaction and the [Formula: see text] propagator for [Formula: see text] interaction. The temperature dependence of the various coefficients has been studied for several values of the baryon chemical potential.

Pions in magnetic field at finite temperature

Pions in external magnetic field are investigated in the frame of a Pauli-Villars regularized Nambu--Jona-Lasinio model. The meson propagators in terms of quark bubbles in Ritus and Schwinger schemes are analytically derived, and pion masses are numerically calculated in the Ritus scheme. For neutral and charged pions at finite temperature, there exist respectively one and three mass jumps at the corresponding Mott transition points, due to the discrete energy levels of the two constituent quarks in magnetic field.

Low-lying eigenmodes and meson propagator symmetries

In situations where the low-lying eigenmodes of the Dirac operator are suppressed one observed degeneracies of some meson masses. Based on these results a hidden symmetry was conjectured, which is not a symmetry of the Lagrangian but emerges in the quantization process. We show here how the difference between classes of meson propagators is governed by the low modes and shrinks when they disappear.

Nonperturbative quark, gluon, and meson correlators of unquenched QCD

We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark and scalar-pseudoscalar meson propagators, as well as gluon, ghost-gluon, quark-gluon, quark, quark-meson, and meson interactions. Our results stress the crucial importance of the quantitatively correct running of different vertices in the semi-perturbative regime for describing the phenomena and scales of confinement and spontaneous chiral symmetry breaking without phenomenological input.

The reactions $\pi\pi \rightarrow \pi\pi$ π π → π π and $\gamma\gamma \rightarrow \pi\pi$ γ γ → π π in $\chi$ χ PT with an isosinglet scalar resonance

The lowest-lying resonance in the QCD spectrum is the $0^{++}$ isoscalar $\sigma$ meson, also known as the $f_0(500)$. We augment SU(2) chiral perturbation theory ($\chi$PT) by including the $\sigma$ meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarr\'us and others. In this effective field theory, denoted $\chi$PT$_S$, the $\sigma$ meson's well-established mass and decay width are not sufficient to properly renormalize its self energy. At $\mathcal{O}(p^4)$ another low-energy constant appears in the dressed $\sigma$-meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the $\pi\pi\rightarrow\pi\pi$ and $\gamma\gamma\rightarrow\pi\pi$ reactions to data from threshold through the energies at which the $\sigma$-meson resonance affects observables. The leading-order (LO) $\pi \pi$ amplitude reproduces the $\sigma$-meson pole position, the isoscalar $\pi \pi$ scattering lengths and $\pi \pi$ scattering and $\gamma \gamma \rightarrow \pi \pi$ data up to $\sqrt{s} \approx 0.5$ GeV. It also yields a $\gamma\gamma\rightarrow\pi\pi$ amplitude that obeys the Ward identity. The value obtained for the $\pi^0$ polarizability is, however, only slightly larger than that obtained in standard $\chi$PT.

Fluctuation-induced modifications of the phase structure in ( 2+1 )-flavor QCD

The low-energy sector of QCD with $N_f = 2\!+\!1$ dynamical quark flavors at non-vanishing chemical potential and temperature is studied with a non-perturbative functional renormalization group method. The analysis is performed in different truncations in order to explore fluctuation-induced modifications of the quark-meson correlations as well as quark and meson propagators on the chiral phase transition of QCD. Depending on the chosen truncation significant quantitative implications on the phase transition are found. In the chirally symmetric phase, the quark flavor composition of the pseudoscalar $(\eta,\eta^{\prime})$-meson complex turns out to be drastically sensitive to fluctuation-induced modifications in the presence of the axial $U(1)_A$ anomaly. This has important phenomenological consequences for the assignment of chiral partners to these mesons.

Generalized Beth--Uhlenbeck Approach to the Equation of State for Quark--Hadron Matter

A unified equation of state for quark-hadron matter is presented in the generalized Beth-Uhlenbeck form. It follows from a $\Phi-$derivable approach to the thermodynamic potential where the ansatz for the $\Phi$ functional contains all 2PI diagrams at two-loop order formed with quark cluster Green's functions for quark, diquark, meson and baryon propagators. We present numerical results using an effective model for the generic behaviour of hadron masses and phase shifts at finite temperature which shares basic features with recent developments within the PNJL model for correlations in quark matter. We obtain the transition between a hadron resonance gas phase and the quark gluon plasma where the Mott dissociation of hadrons is encoded in the hadronic phase shifts. The resulting thermodynamics is in very good agreement with recent lattice QCD simulations.

Next to leading order calculation with dimensional regularization in Nambu–Jona-Lasinio model

The Nambu–Jona-Lasinio model is investigated in the 1/Nc expansion with the dimensional regularization. At the four-dimensional limit, the meson propagators have simple forms in the leading order of the 1/Nc expansion. Thus, the next to leading order calculation reduces to an ordinary one loop calculation. Here we obtain an explicit form of the 1/Nc correction and numerically evaluate the Nc dependence for the gap equation.

An asymptotic solution of large-N QCD

We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic $S$-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic $S$-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the $LSZ$ reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-$N$ $QCD$, and in particular on any string solution.

Broadening of ρ(→ e+e−) meson produced coherently in the photonuclear reaction

The $e^+e^-$ invariant mass distribution spectra are calculated to estimate the hadron parameters of the $\rho$ meson produced coherently in the photonuclear reaction. The elementary reaction occurring in the nucleus is considered to proceed as $ \gamma N \to \rho^0 N ; ~ \rho^0 \to e^+e^- $. We describe the elementary $\rho$ meson photoproduction by the experimentally determined reaction amplitude $ f_{ \gamma N \to \rho^0 N } $. The $\rho$ meson propagator is presented by the eikonal form, and the $\rho$ meson nucleus optical potential $V_{O\rho}$ appearing in it is estimated using the "$t\varrho$" approximation. The $\rho$ meson nucleon scattering amplitude $ f_{ \rho N } $ extracted from the measurements is used to generate this potential. The calculated $e^+e^-$ invariant mass distribution spectra are compared with those measured at Jefferson Laboratory. The calculated results for the transparency ratio are also presented.

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.

Glueball and meson propagators of any spin in large-N QCD

We prove an asymptotic structure theorem for glueball and meson propagators of any spin in large-N QCD and in N=1SUSY QCD with massless quarks, that determines asymptotically the residues of the poles of the propagators in terms of their anomalous dimensions and of the spectral density of the masses. The asymptotic theorem follows by the severe constraints on the propagators in large-N QCD with massless quarks, or in any large-N confining asymptotically-free gauge theory massless in perturbation theory, that arise by perturbation theory in conjunction with the renormalization group and by the OPE on the ultraviolet side. The asymptotic theorem is inspired by a recently proposed Topological Field Theory (TFT) underlying large-N pure YM, that computes sums of the scalar and of the pseudoscalar correlators satisfying the asymptotic theorem and that implies for the large-N joint scalar and pseudoscalar glueball spectrum exact linearity in the masses squared. On the infrared side we test the prediction of the exact linearity in the TFT by Meyer–Teper lattice numerical computation of the masses of the low-lying glueballs in SU(8)YM, finding accurate agreement. Besides, we employ the aforementioned ultraviolet and infrared constraints in order to compare critically the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/large-N Gauge Theory correspondence with those of the TFT underlying large-N YM. We find that only the TFT satisfies the ultraviolet and infrared constraints.

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.

ππinteraction in theρchannel in finite volume

The aim of this paper is to investigate an efficient strategy that allows to obtain pi-pi phase shifts and rho meson properties from QCD lattice data with high precision. For this purpose we evaluate the levels of the pi-pi system in the rho channel in finite volume using chiral unitary theory. We investigate the dependence on the pi mass and compare with other approaches which use QCD lattice calculations and effective theories. We also illustrate the errors induced by using the conventional Luscher approach instead of a more accurate one recently developed that takes into account exactly the relativistic two meson propagators. Finally we make use of this latter approach to solve the inverse problem, getting pi-pi phase shifts from "synthetic" lattice data, providing an optimal strategy and showing which accuracy is needed in these data to obtain the $\rho$ properties with a desired accuracy.

A Mean-Field Treatment in Studying Nuclear Matter Through a Thermodynamic Consistent Resummation Scheme

We used the Cornwall, Jackiw and Tomboulis (CJT) resummation scheme to study nuclear matter. In the CJT formalism the meson propagators are treated as the bare propagators and the the higher order loop corrections of the thermodynamic potential are evaluated at the Hartree approximation, while the vacuum fluctuations are ignored. Under these treatments in the CJT formalism we derived exact mean-field theory (MFT) results for the nuclear matter. The results are thermodynamically consistent, and our study indicates that the MFT result is the lowest order resummation result in the CJT resummation scheme. The relation between CJT formalism and MFT is clearly presented through the calculations.

Unbreaking chiral symmetry

In quantum chromodynamics (QCD) the eigenmodes of the Dirac operator with small absolute eigenvalues have a close relationship to the dynamical breaking of the chiral symmetry. In a simulation with two dynamical quarks, we study the behavior of meson propagators when removing increasingly more of those modes in the valence sector, thus partially removing effects of chiral symmetry breaking. We find that some of the symmetry aspects are restored (e.g., the masses of $\ensuremath{\rho}$ and ${a}_{1}$ approach each other) while confining properties persist.