Meson Pole Research Articles

Evolution and fluctuations of chiral chemical potential in heavy ion collisions

The possible appearance of the effects of local parity breaking in the QCD medium formed in heavy ion collisions due to violation of chiral symmetry can be quantified by corresponding chiral chemical potential [Formula: see text]. The experimental observables sensitive to the effects of local parity violation in strong interaction include search for polarization splitting of the [Formula: see text] and [Formula: see text] mesons via angular dependence of spectral functions in their decay to leptons. In this paper, we study the space-time evolution and fluctuations of [Formula: see text] using relativistic hydrodynamics and estimate their effect on the light vector meson polarization splitting in Pb–Pb collisions at LHC energy.

Impact of vector meson polarization on its interaction with matter

The production of unstable particles on different nuclei provides the possibility to determine the total cross section of the interaction of vector mesons V=rho ,omega ,varphi , K^{*0}(892),J/psi etc. with nucleons. This interaction is defined by a set of amplitudes that correspond to the transverse (helicity lambda =pm 1) or longitudinal (lambda =0) polarization of the vector meson. The total cross section for the interaction of transversely polarized vector mesons with nucleon sigma _T=sigma (V_T N) has been extracted from the coherent photoproduction of vector mesons off nuclei, while the vector meson production in charge exchange reactions as pi ^pm (K^pm )+Arightarrow V^0(K^{*0})+A' provides the unique opportunity to obtain the not yet measured total cross section for longitudinally polarized vector meson interacting with nucleon sigma _L=sigma (V_L N). We shortly discuss the importance of the knowledge of sigma _L and possibility to extract its value from experiments on nuclear target.

Effect of mesonic off-shell correlations in the PNJL equation of state

We study the meson contribution to the equation of state of the 2-flavor PNJL model, including the full momentum dependence of the meson polarization loops. Within the Beth-Uhlenbeck approach, we demonstrate that the contribution from the quark-antiquark continuum excitations in the spacelike region $\omega^2 - q^2 < 0$, i.e. the Landau damping, leads to an increase of the pressure for temperatures $\gtrsim 0.8\,T_c^\chi$ and a significant meson momentum cut-off dependence in the mesonic pressure and the QCD trace anomaly. We investigate the dependence of the results on the choice of the Polyakov-loop potential parameter $T_0$. From the dependence of the mesonic pressure on the current quark mass, by means of the Feynman-Hellmann theorem, we evaluate the contribution of the pion quasiparticle gas and Landau damping to the chiral condensate.

Dispersion-theoretical analysis of the electromagnetic form factors of the Lambda hyperon

The electromagnetic form factors of the Lambda hyperon in the time-like region are determined precisely through a dispersion-theoretical analysis of the world data for the cross section of the annihilation process e^+e^-rightarrow {bar{Lambda }}{Lambda }. The spectral function is represented by a superposition of narrow and broad vector meson poles. We test different scenarios for the spectral function and obtain a good description of the world data in the time-like region. The uncertainties in the extracted form factors are estimated by means of the bootstrap sampling method. The analytical continuation of the form factors to the space-like region introduces large errors due to the lack of data. When the electric Lambda radius from chiral perturbation theory is taken as a constraint, the magnetic radius is predicted as r_M = 0.681 pm 0.002 fm. We also extract various vector meson to baryon coupling constants.

Charged pseudoscalar and vector meson masses in strong magnetic fields in an extended NJL model

The mass spectrum of ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\rho}}^{+}$ mesons in the presence of a static uniform magnetic field $\stackrel{\ensuremath{\rightarrow}}{B}$ is studied within a two-flavor Nambu-Jona-Lasinio-like model. We improve previous calculations, taking into account the effect of Schwinger phases carried by quark propagators and using an expansion of meson fields in terms of the solutions of the corresponding equations of motion for nonzero $B$. It is shown that the meson polarization functions are diagonal in this basis. Our numerical results for the ${\ensuremath{\rho}}^{+}$ meson spectrum are found to disfavor the existence of a meson condensate induced by the magnetic field. In the case of the ${\ensuremath{\pi}}^{+}$ meson, $\ensuremath{\pi}$---$\ensuremath{\rho}$ mixing effects are analyzed for the meson lowest-energy state. The predictions of the model are compared with available lattice QCD results.

Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field

Unusual constituent quark axial current couplings to light vector mesons, $\rho$ and $\omega$, are derived in the vacuum and under weak magnetic field by considering a quark-antiquark interaction mediated by a non perturbative gluon exchange. Similarly, light axial mesons are found to couple anomalously with the constituent quark vector current. These interactions are of the type of the Wess-Zumino-Witten terms, being strongly anisotropic and dependent on the vector (or axial) meson polarization. They also provide axial (vector) form factors for the vector (axial) mesons and are quite small, suppressed nearly by $1/{M^*}^2$ with respect to the vector mesons minimal coupling to the quark vector current. Some three leg meson vertices are also presented: $\pi-\rho-A_1$ and $V_1V_2 A$ (where $V_1,V_2$ are vector mesons and $A$ an axial meson). A vector and axial-vector mesons mixing is identified at non zero magnetic field which however can contribute only in the presence of a third particle or in a medium. Numerical results are presented for different effective gluon propagators.

Bottomonium production and polarization in the NRQCD with k_T-factorization. III: Upsilon (1S) and chi _b(1P) mesons

The Upsilon (1S) meson production and polarization at high energies is studied in the framework of the k_T-factorization approach. Our consideration is based on the non-relativistic QCD formalism for a bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative chi _b(mP) decays and contributions from Upsilon (3S) and Upsilon (2S) decays are taken into account. The transverse momentum dependent (TMD) gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation and the Kimber-Martin–Ryskin prescription. Treating the non-perturbative color octet transitions in terms of multipole radiation theory, we extract the corresponding non-perturbative matrix elements for Upsilon (1S) and chi _b(1P) mesons from a combined fit to transverse momenta distributions measured at various LHC experiments. Then we apply the extracted values to investigate the polarization parameters lambda _theta , lambda _phi and lambda _{theta phi }, which determine the Upsilon (1S) spin density matrix. Our predictions have a reasonably good agreement with the currently available Tevatron and LHC data within the theoretical and experimental uncertainties.

The $$D_sDK^*$$ Vertex in QCD Sum Rules: Form Factors and Coupling Constant

In this work we study the meson vertex $D_sDK^*$ using the QCD sum rules. We compute the three point correlation functions for the three cases of different off-shell mesons. The form factors for each case are fitted to the numerical calculation of the correlation functions and the coupling constant of the vertex is obtained by comparing the form factors at their respective off-shell meson pole. The result obtained for the coupling constant is $g_{D_sDK^*} = 2.29^{+0.65}_{-0.41}$.

Quark anomalous magnetic moment and its effects on the ρ meson properties

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.

Chiral phase transition and kaon-to-pion ratios in the entanglement SU(3) PNJL model

Within the three-flavor PNJL and EPNJL chiral quark models we have obtained pseudoscalar meson properties in quark matter at finite temperature T and baryochemical potential μB. We compare the meson pole (Breit-Wigner) approximation with the Beth-Uhlenbeck (BU) approach that takes into account the continuum of quark-antiquark scattering states when determining the partial densities of pions and kaons. We evaluate the kaon-to-pion ratios along the (pseudo-)critical line in the T − μB plane as a proxy for the chemical freezeout line, whereby the variable x = T∕μB is introduced that corresponds to the conserved entropy per baryon as initial condition for the heavy-ion collision experiments. We present a comparison with the experimental pattern of kaon-to-pion ratios within the BU approach and using x-dependent pion and strange quark potentials. A sharp “horn” effect in the energy dependence K+∕π+ ratio is explained by the enhanced pion production at energies above √sNN=8 GeV, when the system enters the regime of meson dominance. This effect is in line with the enhancement of low-momentum pion spectra that is discussed as a precursor of the pion Bose condensation and entails the occurrence of a nonequilibrium pion chemical potential of the order of the pion mass. We elucidate that the horn effect is not related to the existence of a critical endpoint in the QCD phase diagram.

Thermo-magnetic spectral properties of neutral mesons in vector and axial-vector channels using NJL model

In this work the neutral meson properties have been investigated in the presence of thermo-magnetic background using two-flavor Nambu--Jona-Lasinio model. Mass, spectral function and dispersion relations are obtained in the scalar ($\sigma$) and pseudo-scalar ($\pi^0$) channels as well as in the vector ($\rho^0$) and axial vector ($a^0_1$) channels. The general Lorentz structures for the vector and axial-vector meson polarization functions have been considered in detail. The ultra-violet divergences appearing in this work have been regularized using a mixed regularization technique where the gamma functions arising in dimensional regularization are replaced with incomplete gamma functions as usually done in the proper time regularization procedure. The meson spectral functions obtained in the presence of a magnetic field possess nontrivial oscillatory structure. Similar to the scalar and pseudo-scalar channel, the spectral functions for each of the modes of $\rho^0$ are observed to overlap with the corresponding modes of its chiral partner $a_1^0$ mesons in the chiral symmetry restored phase. We observe discontinuities in the masses of all the mesonic excitations for a non-zero external magnetic field.

Single pseudoscalar meson pole and pion box contributions to the anomalous magnetic moment of the muon

We present results for single pseudoscalar meson pole contributions and pion box contributions to the hadronic light-by-light (LBL) correction of the muon's anomalous magnetic moment. We follow the recently developed dispersive approach to LBL, where these contributions are evaluated with intermediate mesons on-shell. However, the space-like electromagnetic and transition form factors are not determined from analytic continuation of time-like data, but directly calculated within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations. This strategy allows for a systematic comparison with a strictly dispersive treatment and also with recent results from lattice QCD. Within error bars, we obtain excellent agreement for the pion electromagnetic and transition form factor and the resulting contributions to LBL. In addition, we present results for the η and η′ pole contributions and discuss the dynamical effects in the η−η′ mixing due to the strange quarks. Our result for the total pseudoscalar pole contributions is aμPS-pole=91.6(1.9)×10−11 and for the pion-box contribution we obtain aμπ−box=−16.3(2)(4)×10−11.

Neutral meson properties in hot and magnetized quark matter: A new magnetic field independent regularization scheme applied to an NJL-type model

A magnetic field independent regularization scheme (zMFIR) based on the Hurwitz-Riemann zeta function is introduced. The new technique is applied to the regularization of the mean-field thermodynamic potential and mass gap equation within the SU(2) Nambu-Jona-Lasinio model in a hot and magnetized medium. The equivalence of the new and the standard MFIR scheme is demonstrated. The neutral meson pole mass is calculated in a hot and magnetized medium and the advantages of using the new regularization scheme are shown.

Hadronic properties of the photon

Currently it is no doubt that high energy photons (real or virtual) have a hadronic component leading to photon shadowing in its interaction with nuclei. We shortly consider the difficulties appeared in the models like vector dominance model (VDM) and stress that these problems can be solved in a color dipole model inspired by Quantum Chromodynamics (QCD). From the other hand, the color dipole model allows one to investigate the impact of vector meson polarization on their interaction with nucleons and nuclei, the challenge which is crucial for studying, for instance, such a fundamental effect as color transparency.

Modification of the masses of the lightest neutral mesons in a hadronic medium under an external magnetic field

The effective masses of the neutral mesons in a hadronic medium and under an external magnetic field are evaluated as functions of the baryonic density and the field intensity. For this purpose the meson polarization is evaluated in the one loop approximation using a Quantum Hadrodynamics model which includes pions, sigma, omega, and rho mesons. The propagators of the baryons include the full effect of the coupling to the magnetic field through their charges and their anomalous magnetic moments. Within the range of magnetic intensities considered here $10^{17}$ G $< B < 10^{19}$ G, the dependence on B is moderate for the pion and the longitudinal component of the omega meson, and negligible for the remaining mesons.

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.

Model prediction for temperature dependence of meson pole masses from lattice QCD results on meson screening masses

We propose a practical effective model by introducing temperature ($T$) dependence to the coupling strengths of four-quark and six-quark Kobayashi-Maskawa-'t Hooft interactions in the 2+1 flavor Polyakov-loop extended Nambu-Jona-Lasinio model. The $T$ dependence is determined from LQCD data on the renormalized chiral condensate around the pseudocritical temperature $T_c^{\chi}$ of chiral crossover and the screening-mass difference between $\pi$ and $a_0$ mesons in $T > 1.1T_c^\chi$ where only the $U(1)_{\rm A}$-symmetry breaking survives. The model well reproduces LQCD data on screening masses $M_{\xi}^{\rm scr}(T)$ for both scalar and pseudoscalar mesons, particularly in $T \ge T_c^{\chi}$. Using this effective model, we predict meson pole masses $M_{\xi}^{\rm pole}(T)$ for scalar and pseudoscalar mesons. For $\eta'$ meson, the prediction is consistent with the experimental value at finite $T$ measured in heavy-ion collisions. We point out that the relation $M_{\xi}^{\rm scr}(T)-M_{\xi}^{\rm pole}(T) \approx M_{\xi'}^{\rm scr}(T)-M_{\xi'}^{\rm pole}(T)$ is pretty good when $\xi$ and $\xi'$ are scalar mesons, and show that the relation $M_{\xi}^{\rm scr}(T)/M_{\xi'}^{\rm scr}(T) \approx M_{\xi}^{\rm pole}(T)/M_{\xi'}^{\rm pole}(T)$ is well satisfied within 20% error when $\xi$ and $\xi'$ are pseudoscalar mesons and also when $\xi$ and $\xi'$ are scalar mesons.

Variational path-integral approach to back-reactions of composite mesons in the Nambu–Jona-Lasinio model

For the investigation of back-reactions of composite mesons in the NJL model, a variational path-integral treatment is formulated which yields an effective action Aeff[Dσ,Dπ;S], depending on the propagators Dσ, Dπ of σ− and π−mesons and on the full quark propagator S. The stationarity conditions δAeff/δS=0, δAeff/δDσ=0, δAeff/δDπ=0, then lead to coupled Schwinger–Dyson (SD) equations for the quark self-energy and the meson polarization functions. These results reproduce and extend results of the so-called “Φ−derivable” approach and provide a functional formulation for diagrammatic resummations of 1/Nc−corrections in the NJL model. Finally, we perform a low-momentum estimate of the quark and meson loop contributions to the polarization function of the pion and on this basis discuss the Goldstone theorem.

Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis

The baryon electromagnetic form factors are expressed in terms of two-dimensional densities describing the distribution of charge and magnetization in transverse space at fixed light-front time. We calculate the transverse densities of the spin-1/2 flavor-octet baryons at peripheral distances b=O(Mπ−1) using methods of relativistic chiral effective field theory (χEFT) and dispersion analysis. The densities are represented as dispersive integrals over the imaginary parts of the form factors in the timelike region (spectral functions). The isovector spectral functions on the two-pion cut t>4Mπ2 are calculated using relativistic χEFT including octet and decuplet baryons. The χEFT calculations are extended into the ρ meson mass region using an N/D method that incorporates the pion electromagnetic form factor data. The isoscalar spectral functions are modeled by vector meson poles. We compute the peripheral charge and magnetization densities in the octet baryon states, estimate the uncertainties, and determine the quark flavor decomposition. The approach can be extended to baryon form factors of other operators and the moments of generalized parton distributions.

π0 pole mass calculation in a strong magnetic field and lattice constraints

The $\pi_0$ neutral meson pole mass is calculated in a strongly magnetized medium using the SU(2) Nambu-Jona-Lasinio model within the random phase approximation (RPA) at zero temperature and zero baryonic density. We employ a magnetic field dependent coupling, $G(eB)$, fitted to reproduce lattice QCD results for the quark condensates. Divergent quantities are handled with a magnetic field independent regularization scheme in order to avoid unphysical oscillations. A comparison between the running and the fixed couplings reveals that the former produces results much closer to the predictions from recent lattice calculations. In particular, we find that the $\pi_0$ meson mass systematically decreases when the magnetic field increases while the scalar mass remains almost constant. We also investigate how the magnetic background influences other mesonic properties such as $f_{{\pi}_0}$ and $g_{\pi_0 q q}$.