Meson Loops Research Articles

Chiral restoration at finite temperature with meson loop corrections

We investigate chiral-restoration patterns of QCD for N_{c}=3 and N_{f}=2 at finite temperature (T) and zero quark-chemical potential beyond the chiral limit, indicating the explicit chiral-symmetry breaking. To this end, we employ the instanton-vacuum configuration for the flavor SU(2) sector and the Harrington-Shepard caloron for modifying relevant instanton parameters as functions of T. The meson-loop corrections (MLC), which correspond to 1/N_{c} corrections, are also taken into account to reproduce appropriate m_{q} dependences of chiral order parameters. We compute chiral condensate as a function of T and/or m_{q}. From the numerical calculations, we observe that MLC play an important role to have a correct universality-class behavior of chiral-restoration patterns in this framework, depending on m_{q}: Second-order phase transition in the chiral limit, m_{q}=0 and crossover for m_{q}>0. Without MLC, all the restoration patterns are crossover, due to simple saddle-point approximations. It turns out that T^{\chi}_{c}=159 MeV in the chiral limit and T^{\chi}_{c}=(177,186,196) MeV for m_{q}=(5,10,15) MeV, using the phenomenological choices for the instanton parameters at T=0.

Point-Form Hamiltonian Dynamics and Applications

This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincare invariant multichannel formalism which describes particle production and annihilation via vertex interactions that are derived from field theoretical interaction densities. We sketch how this rather general formalism can be used to derive electromagnetic form factors of confined quark-antiquark systems. As a further application it is explained how the chiral constituent quark model leads to hadronic states that can be considered as bare hadrons dressed by meson loops. Within this approach hadron resonances acquire a finite (non-perturbative) decay width. We will also discuss the point-form dynamics of quantum fields. After recalling basic facts of the free-field case we will address some quantum field theoretical problems for which canonical quantization on a space-time hyperboloid could be advantageous.

Manifestation of intermediate meson loop effects in charmonium decays

We report the progress on understanding some of those existing puzzles in charmonium decays. We show that the intermediate meson loops (IML) as a long-distance transition mechanism will provide novel insights into these issues. In particular, we show that the IML mechanism would be essentially important for understanding the Ψ(3770) non-DD̄ decays. We also comment that such a mechanism is correlated with the Okubo–Zweig–Iizuka (OZI) rule evasions in charmonium hadronic decays.

Radiative decays of scalar mesons σ(600), f 0(980) and a 0(980) in the local Nambu-Jona-Lasinio model

Abstract The two-photon decay widths of scalar mesons σ(600), f 0(980) and a 0(980) as well a 0 → ju(ω)γ and f 0 → ju(ω)γ are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N c-approximation where N c is the number of colors) are taken into account. The values of these contributions, as we show, are of the same order of magnitude. For the f 0 decay the K-loop contribution plays the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a 0 → ju(ω)γ and f 0 → ju(ω)γ widths are given.

2γ decays of scalar mesons (σ(600), f 0(980), and a 0(980)) in the Nambu-Jona-Lasinio model

The two-photon decay widths of scalar mesons \sigma(600), f_0(980) and a_0(980) are calculated in framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N_c-approximation where N_c is the number of colors) are taken into account. These contributions, as we show, are the values of the same order of magnitude. For the f_0 decay the K-loop contribution turns out to play the dominant role. The results are in satisfactory agreement with modern experimental data.

Further insights into the “ρπ puzzle"

Based on a systematic investigation of J/Ψ(Ψ′) → VP, where V and P stand for light vector and pseudoscalar mesons, we identify the role played by the electromagnetic (EM) transitions and intermediate meson loop transitions, which are essential ingredients for understanding the J/Ψ and Ψ′ couplings to VP. We show that on the one hand, the EM transitions have relatively larger interferences in Ψ′ → ρπ and K*K̄ + c.c. as explicitly shown by vector meson dominance (VMD). On the other hand, the strong decay of Ψ′ receives relatively larger destructive interferences from the intermediate meson loop transitions. By identifying these mechanisms in an overall study of J/Ψ(Ψ′) → VP, we provide a coherent understanding of the so-called “ρπ puzzle".

Evasion of helicity selection rule inχc1→VVandχc2→VPvia intermediate charmed meson loops

The hadronic decays of $\chi_{c1}\to VV$ and $\chi_{c2}\to VP$ are supposed to be suppressed by the helicity selection rule in the pQCD framework. With an effective Lagrangian method, we show that the intermediate charmed meson loops can provide a mechanism for the evasion of the helicity selection rule, and result in sizeable decay branching ratios in some of those channels. The theoretical predictions can be examined by the forthcoming BES-III data in the near future.

Two-photon mechanism of scalar meson production by colliding beams

Cross sections of scalar mesons f 0(980), a 0(980), and σ(600) production by colliding electron-positron beams are calculated. Two-photon decay widths of scalar mesons obtained in the Nambu-Jona-Lasinio model are used with quark and meson loops taken into account.

Pion polarizability in the Nambu–Jona-Lasinio model and possibilities of its experimental studies in Coulomb nuclear scattering

The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model, where the quark loops (in the mean field approximation) and the meson loops (in the $1/{N}_{c}$ approximation) are taken into account. We show that quark loop contribution dominates because the meson loops strongly conceal each other. The sigma-pole contribution $({m}_{\ensuremath{\sigma}}^{2}\ensuremath{-}t{)}^{\ensuremath{-}1}$ plays the main role and contains strong $t$-dependence of the effective pion polarizability at the region $|t|\ensuremath{\ge}4{M}_{\ensuremath{\pi}}^{2}$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb nuclear scattering are estimated for the COMPASS experiment.

Radiative scalar-meson decays f 0(980) → ρ(ω)γ and a 0(980) → ρ(ω)γ within the local Nambu-Jona-Lasinio model

The widths with respect to the radiative decays f0(980) → ργ and a0(980) → ωγ were calculated within the local Nambu-Jona-Lasinio model. The contributions of both quark and meson loops were taken into account. The latter and the former play a dominant role for the radiative decays of, respectively, the f0(980) and the a0(980) meson.

Extraction of the Light Quark Mass Ratio from the Decaysψ′→J/ψπ0(η)

Light quark masses are important fundamental parameters of the Standard Model. The decays psi'-->J/psi pi^0 (eta) were widely used in determining the light quark mass ratio m_u/m_d. However, there is a large discrepancy between the resulting value of m_u/m_d and the one determined from the light pseudoscalar meson masses. Using the technique of non-relativistic effective field theory, we show that intermediate charmed meson loops lead to a sizeable contribution to the decays and hence make the psi'-->J/psi pi^0 (eta) decays not suitable for a precise extraction of the light quark mass ratio.

Study of isospin violating ϕ excitation in e+e− → ωπ0

We study the reaction e+e− → ωπ0 in the vicinity of the ϕ mass region. The isospin-violating ϕ excitation is accounted for by two major mechanisms. One is electromagnetic transition and the other is strong isospin violations. For the latter, we consider contributions from the intermediate hadronic meson loops and ϕ–ρ0 mixing as the major mechanisms via the t- and s-channel transitions, respectively. By fitting the recent KLOE data, we succeed in constraining the model parameters and extracting the ϕ → ωπ0 branching ratio. It shows that the branching ratio is sensitive to the ϕ excitation line shape and background contributions. Some crucial insights into the correlation between isospin violation and Okubo–Zweig–Iizuka rule evading transitions are also learned.

Comment on “Two-photon decay width of the sigma meson”

We comment on a recent paper by Giacosa, Gutsche, and Lyobovitskij [Phys. Rev. D 77, 034007 (2008)], in which it is argued that a quarkonium interpretation of the $\ensuremath{\sigma}$ meson should give rise to a much smaller two-photon decay width than commonly assumed. The reason for this claimed discrepancy is a term in the transition amplitude, necessary for gauge invariance, which allegedly is often omitted in the literature, including the work of the present authors. Here we show their claims to be incorrect by demonstrating, in the context of the quark-level linear $\ensuremath{\sigma}$ model, that the recently extracted experimental values are compatible with a $q\overline{q}$ assignment for the $\ensuremath{\sigma}$, provided that meson loops are taken into account as well.

Towards a Dynamical Understanding of the Non-DD¯Decay ofψ(3770)

We investigate the psi(3770) non-DD decays into VP, where V and P denote vector and pseudoscalar mesons, respectively, via Okubo-Zweig-Iizuka-rule-evading intermediate meson rescatterings in an effective Lagrangian theory. By identifying the leading meson loop transitions and constraining the model parameters with the available experimental data for psi(3770)-->J/psieta, phieta, and rhopi, we succeed in making a quantitative prediction for all psi(3770)-->VP with BRVP from 0.41% to 0.64%. It indicates that the Okubo-Zweig-Iizuka-rule-evading long-range interactions play a role in psi(3770) strong decays, and could be a key towards a full understanding of the mysterious psi(3770) non-DD decay mechanism.

Connected parts of decuplet electromagnetic properties

We determine the electromagnetic properties of decuplet resonances using chiral perturbation theory at next-to-leading order. Utilizing a partially quenched charge matrix, we isolate and remove the quark disconnected contractions. This allows us to compare the physical meson loop contributions to the connected contributions, of which the latter are currently calculated using lattice QCD. Finally we determine linear combinations of decuplet resonance and hyperon electromagnetic properties that are exactly independent of disconnected contractions in the isospin limit.

Vector meson-vector meson interaction in a hidden gauge unitary approach

The formalism developed recently to study vector meson-vector meson interaction, and applied to the case of $\ensuremath{\rho}\ensuremath{\rho}$, is extended to study the interaction of the nonet of vector mesons among themselves. The interaction leads to poles of the scattering matrix corresponding to bound states or resonances. We show that 11 states (either bound or resonant) get dynamically generated in nine strangeness-isospin-spin channels. Five of them can be identified with those reported in the PDG, i.e., the ${f}_{0}(1370)$, ${f}_{0}(1710)$, ${f}_{2}(1270)$, ${f}_{2}^{\ensuremath{'}}(1525)$, and ${K}_{2}^{*}(1430)$. The masses of the latter three tensor states have been used to fine-tune the free parameters of the unitary approach, i.e., the subtraction constants in evaluating the vector meson-vector meson loop functions in the dimensional regularization scheme. The branching ratios of these five dynamically generated states are found to be consistent with data. The existence of the other six states should be taken as predictions to be tested by future experiments.

Hadron loops and hybrid mixing

We investigate how coupling of valence qq to meson pairs can modify the properties of conventional qq and hybrid mesons. In a symmetry limit the mixing between hybrids and conventional qq with the same J{sup PC} is shown to vanish. Flavor mixing between heavy and light qq due to meson loops is shown to be dual to the results of gluon mediated pQCD and qualitatively different from mixing involving light flavors alone. The validity of the OZI rule for conventional qq and hybrid mesons is discussed.

Scalar susceptibility from the instanton vacuum with meson-loop corrections

The scalar susceptibility (${\ensuremath{\chi}}_{s}$) of QCD, which represents the response of the chiral condensate to a small perturbation of explicit chiral-symmetry breaking ($m\ensuremath{\ne}0$), is investigated within the nonlocal chiral quark model ($\mathrm{NL}\ensuremath{\chi}\mathrm{QM}$) based on the instanton vacuum configuration for ${N}_{f}=2$. We also take into account $1/{N}_{c}$ meson-loop (ML) corrections including scalar and pseudoscalar mesons. It turns out that the chiral condensate is modified to a large extend by the ML corrections in the vicinity of $m=0$, whereas its effect becomes weak beyond $m\ensuremath{\approx}100\text{ }\text{ }\mathrm{MeV}$. As numerical results, we find that ${\ensuremath{\chi}}_{s}=\ensuremath{-}0.34\text{ }{\mathrm{GeV}}^{2}$ with the ML corrections and $0.18\text{ }\text{ }{\mathrm{GeV}}^{2}$ without it. From these observations, we conclude that the ML corrections play an important role in the presence of finite current-quark mass.

Hadronic loop contributions to [formula omitted] and [formula omitted] radiative decays into [formula omitted] or [formula omitted

Intermediate hadronic meson loop contributions to J/ψ, ψ′→γηc (γηc′) are studied apart from the dominant M1 transitions in an effective Lagrangian approach. Due to the property of the unique antisymmetric tensor coupling in V→VP, the hadronic loop transitions provide explicit corrections to the M1 transition amplitudes derived from the naive “quenched”cc¯ transitions via the coupling form factors. This mechanism interfering with the M1 transition amplitudes naturally accounts for the deviations from the Godfrey–Isgur model predictions in J/ψ and ψ′→γηc. It also predicts a small branching ratio of ψ′→γηc′, which can be examined by experimental measurements at BES and CLEO-c.

Possible contributions toe+e−→J/ψ+ηcdue to intermediate meson rescatterings

Inspired by the obvious discrepancies between experiment and nonrelativistic QCD (NRQCD) studies of e(+)e(-) -> J/psi + eta(c) at root s similar or equal to 10.6 GeV , we investigate contributions from intermediate meson loops as long-range interaction transitions to this process. The intermediate meson loops include D (D) over bar((D) over bar*), D (D) over bar* (D or (D) over bar*, D*(D) over bar*(D) and corresponding D-s intermediate mesons. With the constraints from experimental data on the vertex couplings, we find that the intermediate meson loops account for 2.7 similar to 6.7 fb of the cross sections within a reasonable range of cutoff energies of the factor parameter. We also investigate contributions from the absorptive part and find that it accounts for approximately 0.58 similar to 1.38 fb. These results imply that contributions from long-range interaction transitions may still play a role in such an energy region.